INSTRUCTOR’S TESTING MANUAL for USING AND UNDERSTANDING MATHEMATICS A QUANTITATIVE REASONING APPROAC by StudyGuide

Table of Contents 1

Thinking Critically 1A Living in the Media Age....................................................................... 1 1B Propositions and Truth Values ............................................................. 9 1C Sets and Venn Diagrams .................................................................... 17 1D Analyzing Arguments ......................................................................... 29 1E Critical Thinking in Everyday Life .................................................... 37

Approaches to Problem Solving 2A Understand, Solve, and Explain ......................................................... 46 2B Extending Unit Analysis..................................................................... 52 2C Problem-Solving Hints ....................................................................... 58

Numbers in the Real World 3A Uses and Abuses of Percentages ........................................................ 66 3B Putting Numbers in Perspective ......................................................... 74 3C Dealing with Uncertainty ................................................................... 80 3D Index Numbers: The CPI and Beyond................................................ 88 3E Numerical Surprises: Polygraphs, Mammograms, and More ................................................................... 96

Managing Money 4A Taking Control of Your Finances ..................................................... 108 4B The Power of Compounding ............................................................ 114 4C Savings Plans and Investments ......................................................... 120 4D Loan Payments, Credit Cards, and Mortgages ................................. 126 4E Personal Income Taxes ..................................................................... 132 4F Understanding the Federal Budget ................................................... 140

Statistical Reasoning 5A Fundamentals of Statistics ................................................................ 146 5B Should You Believe a Statistical Study? .......................................... 154 5C Statistical Tables and Graphs ........................................................... 162 5D Graphics in the Media ...................................................................... 172 5E Correlation and Causality ................................................................. 180

Putting Statistics to Work 6A Characterizing Data .......................................................................... 190 6B Measures of Variation ...................................................................... 198 6C The Normal Distribution .................................................................. 206 6D Statistical Inference .......................................................................... 214 Copyright © 2023 Pearson Education, Inc. iii

Probability: Living with the Odds 7A Fundamentals of Probability............................................................. 222 7B Combining Probabilities ................................................................... 230 7C The Law of Large Numbers ............................................................. 238 7D Assessing Risk .................................................................................. 246 7E Counting and Probability .................................................................. 254

Exponential Astonishment 8A Growth: Linear versus Exponential .................................................. 260 8B Doubling Time and Half-Life ........................................................... 268 8C Real Population Growth ................................................................... 274 8D Logarithmic Scales: Earthquakes, Sounds, and Acids ..................... 282

Modeling Our World 9A Functions: The Building Blocks of Mathematical Models............... 288 9B Linear Modeling ............................................................................... 294 9C Exponential Modeling ...................................................................... 303

Modeling with Geometry 10A Fundamentals of Geometry .............................................................. 313 10B Problem Solving with Geometry ...................................................... 323 10C Fractal Geometry .............................................................................. 330

Mathematics and the Arts 11A Mathematics and Music .................................................................... 334 11B Perspective and Symmetry ............................................................... 338 11C Proportion and the Golden Ratio ...................................................... 344

Mathematics and Politics 12A Voting: Does the Majority Always Rule? ........................................ 350 12B Theory of Voting .............................................................................. 358 12C Apportionment: The House of Representatives and Beyond ........... 368 12D Dividing the Political Pie.................................................................. 379 Answers to Unit Exams ................................................................................ 387

Name:

Unit 1A Test 1

Date:

1. List the two components of a logical argument.

2. Summarize the fallacy of personal attack.

3. Summarize the fallacy of false cause.

4. Give an example of an argument that involves a straw man.

5. List the premise and the conclusion of the following argument: The dogs are barking. Someone must be outside.

6. List the premise and the conclusion of the following argument: People love puppies, so don’t count on there being any puppies at the animal shelter.

Unit 1A Test 1 (continued)

Name:

7. For the following argument, briefly explain how the fallacy of hasty generalization occurs in the argument. Obviously it is best not to testify on your own behalf. Casey Anthony and George Zimmerman each declined to testify, and they were both found “not guilty.”

8. For the following argument, briefly explain how the fallacy of appeal to popularity occurs in the argument. Most people find out what’s happening on social media or other internet sites so it is the most reliable source for news.

9. For the following argument, identify one or more of the 10 fallacies described in this unit. Explain how the fallacy is involved. “Finding Bigfoot” has yet to provide evidence that bigfoots exist, so all those sightings are obviously bogus.

10. When evaluating information from media, explain the importance to consider the source.

Name:

Unit 1A Test 2 1.

Date:

Define fallacy.

2. Summarize the fallacy of circular reasoning.

3. Summarize the fallacy of appeal to ignorance.

4. Give an example of an argument that involves a hasty generalization.

5. List the premise and the conclusion of the following argument: Not many people were in the theatre when I went to see the movie version of “IT.” Horror stories are not popular around here.

6. List the premise and the conclusion of the following argument: No one who would wear a hat like that has the judgement to be mayor!

Unit 1A Test 2 (continued)

Name:

7. For the following argument, briefly explain how the fallacy of appeal to emotion occurs in the argument. A poster which reads “Support the Humane Society,” shown with pictures of small dogs and cats in cages.

8. For the following argument, briefly explain how the fallacy of appeal to ignorance occurs in the argument. None of those haunted places shown ever show proof positive that ghosts exist, so obviously they do not.

9. For the following argument, identify one or more of the 10 fallacies described in this unit. Explain how the fallacy is involved. The president of that university is campaigning for funds to build a new stadium. He doesn’t care about academics.

10. When evaluating information from media, explain the importance to Check the date.

Name:

Unit 1A Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following is the study of the methods and principles of reasoning? (a) Fallacy

(b) Premise

(d) Argument

2. Which of the following describes an argument based on the idea that if you have a few cases, you can draw a conclusion? (a) Hasty generalization

(b) Limited choice

(d) Appeal to ignorance

3. Which of the following describes an argument based on the idea that since something is desired or chosen by a majority of the people, it must be true or desirable? (a) Circular reasoning (c) Appeal to popularity

(b) Appeal to ignorance (d) Appeal to emotion

4. Which of the following describes an argument based on the idea that since something has not been proved to be false, it must therefore be true? (a) Hasty generalization (c) Diversion (red herring)

(b) Appeal to ignorance (d) Straw man

5. Which argument involves the fallacy of limited choice? (a) Buy this television—it’s the most popular brand! (b) Three dentists on Main Street recommend SuperWhite Toothpaste. Therefore, all dentists prefer SuperWhite. (c) If you didn’t have Wheatie O’s for breakfast, then you must have had granola. (d) A television commercial for a board game features healthy, happy people enjoying the game. 6. Identify the conclusion of the following argument: Steve bought a new car, and then he got into a traffic accident. Buying the new car must have caused the accident. (a) Steve bought a new car. (b) Steve got into a traffic accident. (c) Buying the new car must have caused the accident. (d) None of the above 7. Which argument involves the fallacy of appeal to popularity? (a) You’d better get there on time, since otherwise you’ll be late. (b) Since America’s Founding Fathers were in favor of free speech, they would certainly have opposed any ban of pornography. (c) Since most people are in favor of the bill, it must certainly be a good law. (d) There is no evidence that this product causes heart attacks. Therefore, it is perfectly safe.

Unit 1A Test 3 (continued)

Name:

8. When confronted with questions from the press about alleged political scandals, a congress woman replies that the allegations against her should be ignored since her accuser is part of a vast right-wing conspiracy. This argument is an example of which of the following fallacies? (a) Appeal to popularity (c) Personal attack

(b) Circular reasoning (d) Limited choice

9. A senatorial candidate favors eliminating affirmative action programs. His opponent writes that “The other candidate doesn’t think there’s anything wrong with discriminatory hiring practices.” This argument is an example of which of the following fallacies? (a) Hasty generalization (c) False cause

(b) Limited choice (d) Straw man

10. Going onto the internet to check information delivered in the media is an example of which step in Evaluating Media Information? (a) Watch for hidden agenda (c) Don’t miss the big picture

(b) Consider the source (d) Validate accuracy

Name:

Unit 1A Test 4

Date:

Choose the correct answer to each problem. 1. The use of a set of facts to support a conclusion is called: (a) Logic (c) Circular reasoning

(b) Argument (d) Fallacy

2. Which of the following describes an argument based on the idea that since many people believe something is true, it must be true? (a) Appeal to ignorance (c) Straw man

(b) False cause (d) Appeal to popularity

3. Which of the following describes a conclusion which is drawn from an inadequate number of cases or cases that have not been sufficiently analyzed? (a) Appeal to ignorance (c) Diversion (red herring)

(b) Hasty generalization (d) Circular reasoning

4. Which argument involves the fallacy of limited choice? (a) Since Paul is not at work, he must be at the hardware store. (b) Four eye doctors in town all recommend Krystal Kleer contact lenses. Therefore, all eye doctors recommend Krystal Kleer contact lenses. (c) We have never been able to communicate with beings from another planet. Therefore, the earth is the only planet with intelligent life. (d) Buy this stereo system—it’s the most popular brand! 5. Which argument involves a personal attack (ad hominem)? (a) Dad: “If you want to do well in life, you should do well in school.” Son: “Oh yeah? Well, Mom tells me your grades weren’t very good either.” (b) A driver tells a policeman, “You can’t give me a ticket. I’ve never gotten a ticket!” (c) We must raise taxes because of the children. Children are our most important resource, and we must do everything that we can to give them a brighter future. (d) If Proposition S is passed, there will be more pollution. 6. Identify the conclusion of the following argument: Roberta washed her car, and then it started to rain. Washing her car must have caused the rain to fall. (a) Roberta washed her car. (b) It started to rain. (c) Washing her car must have caused the rain to fall. (d) None of the above

Unit 1A Test 4 (continued)

Name:

7. My political opponent would like to loosen the town’s sign rules. He wants to make our beautiful town trashy looking! This argument is an example of which of the following fallacies? (a) False cause (c) Straw man

(b) Hasty generalization (d) Diversion (red herring)

8. A television commercial shows two senior citizens enjoying rock climbing and scuba diving and then drinking a certain kind of vitamin drink. This is an example of which of the following fallacies? (a) Hasty generalization

(b) Appeal to ignorance

(d) Appeal to emotion

9. We must limit immigration to the United States in order to sustain the prosperous economy. A strong economy is vital to the health and wealth of the American people and the future of our children. This argument is an example of which of the following fallacies? (a) False cause (c) Straw man

(b) Diversion (red herring) (d) Appeal to force

10. The instruction to stand back and think about whether information delivered in the media makes sense is an example of which step in Evaluating Media Information? (a) Watch for hidden agenda (c) Don’t miss the big picture

(b) Consider the source (d) Validate accuracy

Name:

Unit 1B Test 1

Date:

1. Define proposition.

2. Determine whether the following statement is a proposition. Explain. Make America great again!

3. Answer the question regarding the meaning of the given statement which contains a multiple negation. Stephen failed to avoid spoilers on the new Star Wars movie. Did Stephen see spoilers?

4. If you put the following in “If p, then q” form, what would q be? You must study if you want to pass the test.

5. State p and q, and give the truth values of each. Then state whether the entire proposition is true or false. All varieties of apples are fruit and Taylor Swift is a rap artist.

Unit 1B Test 1 (continued)

Name:

6. Does the following use an inclusive or exclusive “or”? Explain. I’m going to the movies or to a party Friday night.

7. Make a truth table for the given statement: if not p, then q.

8. Make a truth table for the given statement: (not p) and q.

9. State p and q and give their truth values. Then state whether the disjunction (or statement) is true or false. Sparrows can swim, or fish can fly.

10. Express the statement in the form of if p, then q. Siamese is a breed of cat.

Name:

Unit 1B Test 2

Date:

1. Define negation.

2. Determine whether the following statement is a proposition. Explain. Life is better after 40!

3. Answer the question regarding the meaning of the given statement which contains a multiple negation. The state legislature failed to repeal the law banning the sale of cigarettes in drug stores. Can cigarettes still be sold in drug stores?

4. If you put the following in “If p, then q” form, what would q be? You need to order now if it is going to be delivered on time.

5. State p and q, and give the truth values of each. Then state whether the entire proposition is true or false. Apple makes iPads and bananas are fruit.

Unit 1B Test 2 (continued)

Name:

6. Does the following use an inclusive or exclusive “or”? Explain. The insurance policy will cover damage to the car from weather or accidents.

7. Make a truth table for the given statement: p and q.

8. Make a truth table for the given statement: p and (not q).

9. State p and q and give their truth values. Then state whether the disjunction (or statement) is true or false. Cows have calves and chickens lay eggs.

10. Express the statement in the form of if p, then q. Male lions have manes.

Name:

Unit 1B Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following is a proposition? (a) The boy with the brown eyes. (c) Toads can sing opera.

(b) What is your IQ? (d) 15 – 12

2. Emily scored highest on the test. Which of the following is the negation of this proposition? (a) Jason scored highest on the test. (b) Emily scored lowest on the test. (c) Emily did not score highest on the test. (d) Emily did not score lowest on the test. 3. The House failed to overturn the veto banning the use of the chemical process. Choose the logical conclusion of the statement. (a) The House will vote again. (b) The use of the chemical process is destructive. (c) The use of the chemical process will continue. (d) The use of the chemical process will cease. 4. Determine the truth values of p and q in the following statements, then determine which statement is false. (a) Earth revolves around Sun and moon revolves around Earth. (b) Huskies are dogs and herring can swim. (c) Netflix requires subscription and not all movies are on Netflix. (d) Hershey’s makes candy and lima beans are fruit. 5. Which of the following most likely demonstrates an inclusive “or”? (a) I should wear a sweater or a jacket. (b) Soup or salad is included in the price of the entrée. (c) On vacation, I like to go to the beach or to the mountains. (d) I need to spend less or make more money.. 6. Determine the truth values of p or q in the following statements, then determine which statement is true. (a) Busses fly or dogs purr. (b) Dolphins are fish or trees have roots. (c) Poodles are cats or ostriches fly. (d) Rhode Island is in Europe or birds swim. 7. Use truth tables to determine which statement is logically equivalent to if p, then q. (a) p and not q

(b) (not p) and q

(d) p or not q

Unit 1B Test 3 (continued)

Name:

8. If wishes were horses, then beggars could ride. Which of the following is the inverse of this statement? (a) If beggars can’t ride, then wishes aren’t horses. (b) If wishes aren’t horses, then beggars can’t ride. (c) If beggars can’t ride, then wishes are horses. (d) If wishes aren’t horses, then beggars can ride. 9. Which of the following is logically equivalent to any conditional? (a) Inverse (c) Contrapositive

(b) Converse (d) Negation

10. You are searching for the book The Old Man and the Sea by Ernest Hemingway. Which of the following key word search combinations would not have your book on its search list? (a) (Man or Sea) and Hemingway (c) (Man or Sea) and (Hemingway or Steinbeck)

(b) (Man and Sea) or (Hemingway and Steinbeck) (d) Man and (Hemingway and Steinbeck)

Name:

Unit 1B Test 4

Date:

Choose the correct answer to each problem. 1. Which of the following is a proposition? (a) 7 + 3 – 5 (c) Alison lives here?

(b) Bring me a glass of tea. (d) Louie likes lobster less than Leslie.

2. Susie came in first in the race. Which of the following is the negation of this proposition? (a) Billy came in first in the race. (c) Susie did not come in first in the race.

(b) Susie came in second in the race. (d) Susie came in last in the race.

3. Jane will not vote for a candidate who opposes a ban on hand guns. Assuming this statement is true, which of the following is false? (a) Jane supports a ban on hand guns. (b) Jane may vote for a candidate who does not own a hand gun. (c) Jane might vote for Senator Jones who supports a ban on hand guns. (d) If Senator Jones opposes a ban on hand guns, then Jane will vote for her. 4. If p is false, q is false, and r is true, which of the following is true? (a) (p and q) and r

(b) (not p) and (q or r)

(d) p and (q or r)

5. If p is true, q is true, and r is false, which of the following is false? (a) If not p, then (q and r). (c) If not p, then (q or r).

(b) If p, then (q and r). (d) If p, then (q or not r).

6. Determine the truth values of the hypothesis and the conclusion in the following statements. Which statement is false? (a) If California is on the west coast, then Colorado is on the east coast. (b) If Colorado is on the east coast, then California is on the west coast. (c) If Colorado is on the east coast, then New York is on the west coast. (d) If California is on the west coast, then New York is on the east coast. 7. Use truth tables to determine which statement is logically equivalent to if not p, then not q. (a) p and not q

(b) (not p) and q

8. If I don’t get a job soon, then I will lose my car. Which of the following is the inverse of this statement? (a) If I lose my car, then I won’t get a job soon. (b) If I get a job soon, then I can keep my car. (c) If I can keep my car, then I’ll get a job soon. (d) If I can keep my car, then I won’t get a job soon.

(d) p or not q

Unit 1B Test 4 (continued)

Name:

9. Which of the following is logically equivalent to any conditional? (a) Inverse (c) Negation

(b) Contrapositive (d) Converse

10. You are searching for the book Little Women by Louisa May Alcott. Which of the following key word search combinations would not have your book on its search list? (a) (Little and Women) and Alcott (c) (Little or Women) and (Alcott or Bronte)

(b) Women and (Alcott and Bronte) (d) (Little and Women) or (Alcott and Bronte)

Name:

Unit 1C Test 1

Date:

1. Use set notation to write the members of the following set: odd numbers between 20 and 30.

2. Draw a Venn diagram with 2 circles to illustrate the relationship between men and surgeons. Label each part of the diagram clearly.

3. Draw a Venn diagram with 2 circles to illustrate the relationship between women and kings. Label each part of the diagram clearly.

4. Some roses are red. a) State the subject and predicate sets; b) Draw a Venn diagram to illustrate the relationship; c) Based on the diagram, can you conclude that some roses are not red?

Unit 1C Test 1 (continued)

Name:

5. No cows are plants. a) State the subject and predicate sets; b) Draw a Venn diagram to illustrate the relationship; c) Based on the diagram, is it possible that some plants are cows?

6. All Labradoodles are dogs. a) State the subject and predicate sets; b) Draw a Venn diagram to illustrate the relationship; c) Based on the diagram, can you conclude that some dogs are not labradoodles?

7. In the Venn diagram below, what does the region with the X in it tell us? Be specific. students surveyed

lefthanded 6 22

boys 4 23

Unit 1C Test 1 (continued) 8.

Name:

In the Venn diagram below, what does the region with a Y in it tell us? Be specific.

X lefthanded 6 22

boys 4 23

9. In a survey of 50 musicians, it was found that 20 people played the piano, 25 played the guitar. Additionally, it was noted that 7 played both instruments while 12 played neither. Draw a Venn diagram to represent this situation. Label each part of the diagram clearly.

Unit 1C Test 1 (continued)

Name:

10. In a survey of 20 men and 10 women, 18 were history majors and 12 were science majors. Notably, 16 of the men majored in history. Make a two-way table to represent this situation. Label each part of the table clearly.

Name:

Unit 1C Test 2

Date:

1. Use set notation to write the members of the following set: states that begin with the letter “M.”

2. Draw a Venn diagram with 2 circles to illustrate the relationship between snakes and rocks. Label each part of the diagram clearly.

3. Draw a Venn diagram with 2 circles to illustrate the relationship between celebrities and politicians. Label each part of the diagram clearly.

4. All fish live in water. a) State the subject and predicate sets; b) Draw a Venn diagram to illustrate the relationship; c) Based on the diagram, can you conclude that some fish do not live in water?

Unit 1C Test 2 (continued)

Name:

5. Some cheese is made from goat milk. a) State the subject and predicate sets; b) Draw a Venn diagram to illustrate the relationship; c) Based on the diagram, is it possible that some cheese is not made from goat milk?

6. No salamanders are mammals. a) State the subject and predicate sets; b) Draw a Venn diagram to illustrate the relationship; c) Based on the diagram, can you conclude that some mammals are salamanders?

7. In the Venn diagram below, what does the region with the X in it tell us? Be specific. athletes

basketball

volleyball 9

Unit 1C Test 2 (continued)

Name:

8. In the Venn diagram below, what does the region with the Y in it tell us? Be specific. athletes

basketball

volleyball 9

9. In a veterinary waiting room, there were a total of 12 individuals, 8 of whom brought dogs, 5 brought cats. Additionally, it was noted that three brought both dogs and cats, and two individuals had neither. Draw a Venn diagram to represent this situation. Label each part of the diagram clearly.

Unit 1C Test 2 (continued)

Name:

10. In a freshman class of 50 students, 32 of them male, 24 students are taking math, 26 students are taking history. Notably, half the men were taking each subject. Create a two-way table to represent this situation. Label each part of the table clearly.

Name:

Unit 1C Test 3

Date:

1. Which of the following sets are disjoint? (a) Aunts and uncles (c) Women and aunts

(b) Men and uncles (d) They are all disjoint

2. In a Venn diagram, if the circle for set A overlaps the circle for set B, (a) some A are B (c) all A are B

(b) no A are B (d) all B are A

3. In a Venn diagram, if the circle for set B is entirely inside the circle for set A, (a) some A are B (c) all A are B

(b) no A are B (d) all B are A

Use this Venn diagram, which describes the cars on a used car lot, to answer questions 4 and 5.

4. How many Red Fords are on the lot? (a) 10

(b) 23

(d) 3

(d) 35

5. How many cars on the lot are Fords? (a) 5

(b) 3

Unit 1C Test 3 (continued)

Name:

Use this Venn diagram, which describes the desserts people ordered at a party, to answer questions 6 and 7.

6. How many people were at the party? (a) 3

(b) 5

(d) 26

7. How many people had ice cream with their cake? (a) 3

(b) 5

Use the information below to answer questions 8, 9 and 10. Students living off-campus were asked about the electronic products they own: VCRs, DVD and MP-3 players. The table below shows the gender of students and the types of products they own. Gender male female Total

Android 4 5 9

Apple 10 7 17

Total 14 12 26

8. How many students were surveyed? (a) 9

(b) 26

(d) 78

(d) 17

9. How many men own an Apple product? (a) 4

(b) 14

10. According to the table, do students prefer Android or Apple products? (a) Android

(b) Apple

(d) Neither

Name:

Unit 1C Test 4

Date:

1. Which of the following sets are overlapping? (a) Dogs and cats (c) Pets and dogs

(b) Cats and birds (d) Birds and fish

2. Which of the following sets are not disjoint? (a) Cloudy days and holidays (c) Fords and Chevrolets

(b) Brothers and sisters (d) Democrats and Republicans

3. In a Venn diagram, overlapping circles indicate (a) Sets that share common members (c) Sets of numbers

(b) Disjoint sets (d) Subsets

4. In a Venn diagram, if the circle for set B is totally enclosed within the circle representing set A, which of the following is true? (a) some A are B (c) Se all A are B

(b) no A are B (d) all B are A

Use this Venn diagram, which describes the optional features ordered by new telephone customers in one day, to answer questions 5, 6 and 7.

5. How many customers ordered neither caller ID nor call waiting? (a) 17

(b) 21

(d) 112

(d) 98

6. How many customers ordered caller ID? (a) 17

(b) 77

7. How many customers did not order call waiting? (a) 77

(b) 35

Unit 1C Test 4 (continued)

Name:

Use this Venn diagram, which describes the types of cookies in a bakery, to answer questions 8, 9, and 10. Cookies

Chocolate Walnut Chip 10 13 15

8. How many cookies were in the bakery? (a) 7

(b) 28

(d) 45

9. How many cookies have neither chocolate chips nor walnuts in them? (a) 7

(b) 13

(d) 15

(d) 3

10. How many chocolate chip cookies also have walnuts? (a) 10

(b) 13

Name:

Unit 1D Test 1

Date:

1. Explain what is meant by a valid argument.

2. Explain what is meant by an inductive argument.

3. Give an example of a deductive argument.

4. For the following argument, state the truth of each premise and the truth of the conclusion. Premise: All birds lay eggs. Premise: Frogs lay eggs. Conclusion: Frogs are birds.

5. Identify the form of the following conditional argument. Is the argument valid? Premise: If I stay home from work, I am sick. Premise: I did not stay home from work today. Conclusion: I am not sick.

Unit 1D Test 1 (continued)

Name:

6. What can be deduced from the following argument? If Amy studies for the test, she will pass it. If Amy passes the test, she has a good chance of passing the course.

7. Premise: Most girls like to color. Premise: Emily is a girl. Conclusion: Emily might like to color. Use a Venn diagram to determine the validity of this argument.

8. Premise: Some animals are cold-blooded. Premise: My dog is an animal. Conclusion: My dog is cold-blooded. Use a Venn diagram to determine the validity of this argument.

9. Illustrate “the sum of two odd numbers is an even number” by stating four examples. Is this inductive or deductive reasoning?

10. Give an example that invalidates the mathematical rule “the difference of two negative numbers is always a negative number.”

Name:

Unit 1D Test 2

Date:

1. Explain what is meant by a sound argument.

2. Explain what is meant by a deductive argument.

3. Give an example of an inductive argument.

4. For the following argument, state the truth of each premise and the truth of the conclusion. Premise: All mammals have live births. Premise: Some snakes have live births. Conclusion: Some snakes are mammals.

5. Identify the form of the following conditional argument. Is the argument valid? Premise: If I am sick, I stay home from work. Premise: I stayed home from work today. Conclusion: I am sick.

Unit 1D Test 2 (continued)

Name:

6. What can be deduced from the following argument? If Aaron goes to bed early, he will get up early. If Aaron gets up early, he should not be late for his appointment.

7. Premise: All horses are green. Premise: Trigger is a horse. Conclusion: Trigger is green. Use a Venn diagram to determine the validity of this argument.

8. Premise: Everyone who drives faster than the speed limit is breaking the law. Premise: Gary is breaking the law. Conclusion: Gary is driving faster than the speed limit. Use a Venn diagram to determine the validity of this argument.

9. Illustrate “six times any number is an even number” by stating four examples. Is this inductive or deductive reasoning?

10. Give an example that invalidates the following mathematical rule a(b + c) = ab + c

Name:

Unit 1D Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following is a valid argument? (a) Premise: All cars have engines. Premise: Mustangs are cars. Conclusion: Mustangs have engines.

(b) Premise: All airplanes have engines. Premise: 747s have engines. Conclusion: 747s are airplanes.

(c) Premise: All Mustangs have engines. Premise: All Corvettes have engines. Premise: All Ferraris have engines. Conclusion: All cars have engines.

(d) Premise: Some cars have sun roofs. Premise: Liza’s Honda does not have a sunroof. Conclusion: Liza’s Honda is not a car.

2. Which of the following is a sound argument? (a) Premise: All birds can fly. Premise: Eagles are birds. Conclusion: Eagles can fly.

(b) Premise: All birds have wings. Premise: Ducks are birds. Conclusion: Ducks have wings.

(c) Premise: Eagles have feathers. Premise: Sparrows have feathers. Premise: Ducks have feathers. Conclusion: All birds have feathers.

(d) Premise: Some birds have feathers. Premise: Sparrows are birds. Conclusion: Sparrows have feathers.

3. If the congressman is lying, then no one will vote for him. If no one votes for the congressman, then he will not win the election. What can be deduced from these premises? (a) The congressman is lying. (b) The congressman will not win the election. (c) If the congressman does not win the election, then he was lying. (d) If the congressman is lying, then he will not win the election.

4. Premise: If I love a television show, it gets cancelled. Premise: I didn’t love that show. Conclusion: That show won’t get cancelled. This invalid argument is an example of which of the following? (a) Affirming the hypothesis (c) Affirming the conclusion

(b) Denying the hypothesis (d) Denying the conclusion

Unit 1D Test 3 (continued)

Name:

5. Some lakes always freeze in the winter. Lake Tahoe does not always freeze in the winter. What can be deduced from these premises? Use a Venn diagram to test your answer. (a) Lake Tahoe is not a lake. (c) Nothing can be deduced.

(b) Lake Tahoe sometimes freezes in the winter. (d) Some lakes do not always freeze in the winter.

6. Premise: Every musician owns a guitar. Premise: Johnny Bravo owns a guitar. Conclusion: Johnny Bravo is a musician. Which of the following describes this argument? (a) Valid and sound (c) Not valid and sound

(b) Valid and not sound (d) Not valid and not sound

7. Premise: If you were born after 1900, you were not in the Civil War. Premise: U.S. Grant was in the Civil War. Conclusion: U.S. Grant was not born after 1900. Which of the following describes this argument? (a) Valid and sound (c) Not valid and sound

(b) Valid and not sound (d) Not valid and not sound

8. Use inductive reasoning to test the following mathematical rules. Which statement do you think is true? (a) −1 × a < 0

(b) −1 × a = − a

(d) −1 × a > a

9. Which of the following is an example of inductive logic? (a) If I got an A in my last four math classes then I will get an A in this math class. (b) If I get an A on every test, then I will get an A in the class. (c) If I study very hard then I will get an A. (d) If I get an A in my math class then I will take another math class next year.

10. Which of the following is an example of deductive logic? (a) Ashley has blonde hair and blue eyes so blondes must have blue eyes. (b) Malcolm has red hair and green eyes. Most red heads have green eyes. (c) Malcolm has had vanilla yogurt every day for three days. So, he will have vanilla yogurt tomorrow. (d) All blondes have blue eyes and Ashley is a blonde so Ashley has blue eyes.

Name:

Unit 1D Test 4

Date:

Choose the correct answer to each problem. 1. Which of the following is a valid argument? (a) Premise: Bank robbers are in jail. Premise: Burglars are in jail. Premise: Extortionists are in jail. Conclusion: All criminals are in jail.

(b) Premise: Some criminals go to jail. Premise: Burglars go to jail. Conclusion: Burglars are criminals.

(d) Premise: Some bank robbers are in jail. Premise: Burt is a bank robber. Conclusion: Burt is in jail.

2. Which of the following is a sound argument? (a) Premise: All fruit grow on trees. Premise: Money doesn’t grow on trees. Conclusion: Money is not a fruit.

(b) Premise: Some trees have fruit. Premise: Peaches are fruit. Conclusion: Peaches grow on trees.

(c) Premise: Peach trees have fruit. Premise: Apple trees have fruit. Premise: Cherry trees have fruit. Conclusion: All trees have fruit.

(d) Premise: Apples grow on trees. Premise: Apples are fruit. Conclusion: Some fruit grows on trees.

3. If Lori is sick then Tony will drive. If Tony drives then Susan will not go. What can be deduced from these premises? (a) Susan will not go. (c) If Lori is sick then Susan will not go.

(b) Lori is sick. (d) If Susan does not go, then Lori is sick.

4. Premise: If a man is married, then he is happy. Premise: Tom is married. Conclusion: Tom is happy. This valid argument is an example of which of the following? (a) Affirming the hypothesis (c) Affirming the conclusion

(b) Denying the hypothesis (d) Denying the conclusion

5. Some dogs bite. Chihuahuas are dogs. What can be deduced from these premises? Use a Venn diagram to test your answer. (a) Some dogs do not bite. (c) Nothing can be deduced.

(b) Some Chihuahuas bite. (d) Some dogs are Chihuahuas.

Unit 1D Test 4 (continued)

Name:

6. Premise: Some monsters live under my bed. Premise: Cookie Monster lives on Sesame Street. Conclusion: Some monsters do not live under my bed. Which of the following describes this argument? (a) Valid and sound (c) Not valid and sound

(b) Valid and not sound (d) Not valid and not sound

7. Premise: All cats have four legs. Premise: Some cats are black. Conclusion: Some four-legged animals are black. Which of the following describes this argument? (a) Valid and sound (c) Not valid and sound

(b) Valid and not sound (d) Not valid and not sound

8. Use inductive reasoning to test the following mathematical rules. Which statement do you think is true? (a) 0 – a = a

(b) 0 – (–a) = a

(d) –a – 0 = a

9. Which of the following is an example of inductive logic? (a) If there is an accident on the freeway then we will be late for the play. (b) If you lost the last two tennis matches, you will likely lose the next one too. (c) I have to leave work earlier if the bank closes at 5:00 today. (d) If I get a raise next week then I can buy a new car.

10. Which of the following is an example of deductive logic? (a) I like Chinese food so I should like all Asian cuisine. (b) I like all Asian cuisine so I should like Chinese food. (c) Henrietta has been late every day this past week and she will probably always be late. (d) Henrietta doesn’t like spicy food and neither do I.

Name:

Unit 1E Test 1

Date:

1. I decided not to put off canceling my cable subscription. Do I still have cable? Explain.

2. I want to find the best airfare to Phoenix because my sister is getting married there next month and I want to fly to the wedding. State the conclusion of this argument.

3. Buying a new lawn mower would save me time and money. List two hidden assumptions.

4. Andy decided to buy two State Fair tickets online for $6 each plus a $3 handling fee rather than pay $8 per ticket at the gate. Does this statement make sense or not make sense? Explain your reasoning.

5. A basic yearly cellular telephone service contract is advertised as costing only $24 per month. However, there is a $15 per unused month penalty if you cancel the contract before the end of the year. Calculate the total cost of the service if you cancel at the end of three months.

6. All bills should be paid on time because a bad credit report will make it difficult to get a loan. Identify any hidden assumptions in this argument.

Unit 1E Test 1 (continued)

Name:

7. In planning a trip to Scotland, nine months in advance, you find that an airline offers two options. Plan A: You can buy a fully refundable ticket for $1900. Plan B: You can buy a $1000 ticket, but you forfeit $250 if the ticket is changed or cancelled. Describe your options and how you would decide which ticket to buy.

Use the following IRS information to answer questions 8 – 10. According to the IRS, a single person under age 65 (and not blind) must file a tax return if any of the following apply (numbers were for tax year 2012): (i) unearned income was more than $950 (ii) earned income was more than $5950 (iii) gross income was more than the larger of $950 or your earned income (up to $5650) plus $300 8. Sidney is 24, has unearned income of $650, earned income of $2400, and gross income of $3050. Assuming that Sidney is single and not blind, does Sidney need to file a return? Explain.

9. Wally is 17 and has earned income of $1750, unearned income of $200, and gross income of $2000. Assuming Wally is single and not blind, does Wally need to file a return? Explain.

10. Inga is 47 and has earned and gross income of $7560 and no unearned income. Assuming Inga is single and not blind, does Inga need to file a return? Explain.

Name:

Unit 1E Test 2

Date:

1. Consider the following ballot question: Shall there be an amendment to the state constitution to prohibit the state legislature from adopting any law which inhibits the freedom of religious expression? Explain the meaning of a no vote.

2. The stores at the mall should stay open later this month. After all, it is the holiday season and there are more shoppers. State the conclusion of this argument.

3. A dictator of a foreign country has enacted a ban on all firearms, citing accidental deaths among children as his main concern. Identify other issues that might be involved in his decision to ban firearms.

4. Andy decided to buy four State Fair tickets on-line for $6 each plus a $3 handling fee rather than pay $8 per ticket at the gate. Does this statement make sense or not make sense? Explain your reasoning.

5. You can purchase the 48-load Tide laundry detergent bottle that is on sale for $6.50 or the 64-load bottle for $15.49. Which is the better option?

Unit 1E Test 2 (continued)

Name:

6. Swimming is healthy because it improves your cardiovascular system. Identify any hidden assumptions in this argument.

7. In planning a trip to Greece, nine months in advance, you find that an airline offers two options. Plan A: You can buy a fully refundable ticket for $2100. Plan B: You can buy a $1600 ticket, but you forfeit $250 if the ticket is changed or cancelled. Describe your options and how you would decide which ticket to buy.

Use the following IRS information to answer questions 8 – 10. According to the IRS, a single person under age 65 (and not blind) must file a tax return if any of the following apply (numbers were for tax year 2012): (i) unearned income was more than $950 (ii) earned income was more than $5950 (iii) gross income was more than the larger of $950 or your earned income (up to $5650) plus $300 8. Sidney is 24, has unearned income of $650, no earned income, and gross income of $850. Assuming Sidney is single and not blind, does Sidney need to file a return? Explain.

9. Wally is 17 and has earned income of $1750 and unearned income of $200, and gross income of $1950. Assuming Wally is single and not blind, does Wally need to file a return? Explain.

Unit 1E Test 2 (continued)

Name:

10. Inga is 47 and has earned and gross income of $7560 and no unearned income. Assuming Inga is single and not blind, does Inga need to file a return? Explain.

Name:

Unit 1E Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following are stated explicitly in an argument? (a) Hidden assumptions (c) Valid premises

(b) Missing information (d) Other possible conclusions

2. Since Jerry’s birthday is coming up, I should buy him a basketball as a gift. Which of the following conclusions can be deduced from this argument? (a) Jerry plays basketball every Saturday. (c) Jerry bought me a birthday present last year.

(b) Jerry wants a basketball. (d) Jerry’s birthday is next week.

3. Neptunes are the most comfortable car on the road because they have the most elaborate suspension system. Which of the following hidden assumptions is being used in this argument? (a) Other cars on the road are not comfortable. (b) If you are going to buy a new car, then you should buy a Neptune. (c) The suspension system is the most important factor in determining car comfort. (d) The suspension system on the Neptune is better than on any other car. 4. We get two weeks of vacation this year. We are going camping for one week and skiing for one week, so we will have to visit Aunt Martha next year. Which of the following propositions is the conclusion of this argument? (a) We get two weeks of vacation this year. (b) We are going camping for one week and skiing for one week this year. (c) We will have to visit Aunt Martha next year. (d) We need more vacation time this year. 5. We should all drink 8 glasses of water a day because being properly hydrated will improve our health. Which of the following propositions is the conclusion of this argument? (a) Drinking 8 glasses of water per day will keep us properly hydrated. (b) We should all be properly hydrated. (c) We should all drink 8 glasses of water per day. (d) Drinking 8 glasses of water per day will improve our health. 6. You are leasing a summer home for twelve weeks and need to cut the grass every week. If you do it yourself you can buy a new power mower for $340 and sell it at the end of the summer for $100. Or you can rent a power mower for $20 each day. The third option is to hire a neighbor’s son will charge you $9 per hour for the 2 hours that it takes to mow the grass each time using his own equipment. Which is the least expensive option? (a) Buy a new mower. (c) Hire the neighbor’s son.

(b) Rent a mower. (d) They all cost the same.

7. To help make a complex argument clear, visual aids may include all except which of the following? (a) Written descriptions (c) Graphs

Unit 1E Test 3 (continued)

Name:

8. A box of 20 Crunchy Munchy cookies costs $2.50 and a box of 40 Crunchy Munchy cookies costs $4.00. One quart of milk costs $1.50. Which of the following is a better bargain? (a) A box of 20 cookies that comes with a free quart of milk (b) A box of 40 cookies with a quart of milk that costs $1.50 (c) The cost of each option is the same 9. Two friends are planning a vacation. It will cost $100 each way for each of them to fly to San Francisco or $400 round trip for each of them to fly to New York. If they fly to San Francisco they will also have to pay $125 a night for a hotel. If they fly to New York, they can stay with friends for free. Which of the following situations would make flying to New York the better option? (a) They want to stay for two days (c) It will cost more to eat in San Francisco

(b) They want to stay for four or more days (d) It will cost more to rent a car in New York

10. Betty has to go to New Orleans for business. If she flies there and back on the same day her round trip airfare will cost $510. If she stays overnight, her roundtrip airfare will cost $300, her hotel will cost $130, and three extra meals will cost $80. Which is the less expensive option? (a) Staying overnight in New Orleans (b) Flying there and back on the same day (c) The cost of each option is the same

Name:

Unit 1E Test 4

Date:

Choose the correct answer to each problem. 1. Alice needs to compute the average of her exam scores. She has already received scores of 60, 70, and 80 and has one more exam to take. Which of the following is not missing information? (a) Grading scale (c) Weight of each exam

(b) Number of exams to be averaged (d) Score on the last exam

2. Edith is taking her cat, Pico, to the vet next week because Pico is due for a vaccination. Cats should be vaccinated every year. Which of the following conclusions can be deduced from this argument? (a) Pico is due for a tetanus shot. (b) Pico wants to be vaccinated. (c) Edith could not get an appointment with the veterinarian until next week. (d) It has been at least one year since Pico was last vaccinated. 3. We should not vote for the incumbent because he has already been in office for three consecutive terms. Which of the following hidden assumptions is being used in this argument? (a) We should never vote for an incumbent. (b) The incumbent has already been elected three times. (c) Four consecutive terms is too many. (d) We should vote for the underdog. 4. We are all out of gasoline. Since I want to finish cutting the lawn before it rains, I need to go to town. Which of the following propositions is the conclusion of this argument? (a) We are out of gasoline. (c) I need to go to town.

(b) I need gasoline to mow the lawn. (d) The grass needs to be cut.

5. Jenny must have found a new job because I haven’t seen her in the career center for weeks. Which of the following propositions is the conclusion of this argument? (a) Jenny hasn’t been to the career center for weeks. (b) I haven’t seen Jenny in the career center for weeks. (c) Jenny needs a job. (d) Jenny must have found a new job. 6. You are leasing a summer home for twelve weeks and need to cut the grass every week. The neighbor’s son will charge you $10 per hour for the 2 hours it takes to mow the grass and will use his own equipment. If you do it yourself, you can buy a new power mower for $350 and sell it at the end of the summer for $100. Or you can rent a power mower for $18 each day. Which is the least expensive option? (a) Hire the neighbor’s son. (c) Rent a mower.

(b) Buy a new mower. (d) They all cost the same.

Unit 1E Test 4 (continued)

Name:

7. Which of the following is not a hidden danger with a calling plan that offers all calls of up to 20 minutes for just 99¢? (a) The cost of reaching a friend’s answering machine (b) The cost per minute after the first 20 minutes (c) The cost of a 20-minute call (d) Monthly service fees 8. Maternity insurance, with a $500 deductible, will cost Anne an extra $280 per month. She will need to purchase it for a total of 15 months to carry her through an eligibility period and the maternity and delivery. She would also have to pay a $900 co-pay as part of the regular insurance contract. Paying for the maternity and delivery herself should cost Anne about $5000. If an emergency occurs (such as an emergency C-section), her regular insurance would cover it. Which option should she choose? (a) Maternity insurance (b) Pay out-of-pocket herself (c) The cost of each option is the same. 9. Ben has to decide whether to drive from Los Angeles to Las Vegas or fly. If he drives it will take four hours. If he flies it will take 30 minutes to drive to the airport, one hour to check-in, one hour in the air, and 20 minutes to take a cab from the airport to his destination. Which is the faster option? (a) Driving to Las Vegas (b) Flying to Las Vegas (c) Each option takes the same amount of time. 10. Mr. Burns is going to Miami and wants to rent a car there. The price per day to rent a car is $25 and the first 100 miles are included. After 100 miles the price per mile is $0.50. The weekly rate to rent a car is $100 plus $0.20 per mile. The weekly rate is for seven days. Which of the following situations would make the weekly rate more economical? (a) Mr. Burns is staying in Miami for 3 days and plans to drive 50 miles. (b) Mr. Burns is staying in Miami for 6 days and plans to drive 200 miles. (c) Mr. Burns is staying in Miami for 4 days and plans to drive 125 miles. (d) Mr. Burns is staying in Miami for 2 days and plans to drive 250 miles.

Name:

Unit 2A Test 1

Date:

1. An airplane travels 520 miles in 1.3 hours. What is its speed in miles per hour? Please show operations and label units clearly.

2. You plan to drive to a resort that is 399 miles away. Your car presently gets 28 miles per gallon. How many gallons of gas will it take you to get to the resort? Clearly show your use of units.

3. If gas is currently $2.45 per gallon, how much will it cost you to drive to the resort and back home? Clearly show your use of units. Round your answer to the nearest cent.

4. The interior of a standard shipping container interior measures 39 feet long by 8 feet wide by 7 feet tall. What is the volume of the container? Clearly show your use of units.

5. A new concrete courtyard will be 15 feet by 25 feet and will be filled to a depth of 3 inches (¼ foot). How much concrete do you need? Clearly show your use of units.

6. Convert 4.5 hours to seconds. Clearly show your use of units.

Unit 2A Test 1 (continued)

Name:

7. Convert 7 feet to inches. Clearly show your use of units.

8. Find the area in square feet of a play area that measures 15 yards by 9 yards. Clearly show your use of units.

9. If 1 euro = $1.058, then a dinner that was 28 euros cost how much in U.S. dollars? Round your answer to the nearest cent. Clearly show your use of units.

10. If 1 CAD (Canadian dollar) = $0.7586 (U.S.), how much would a pair of jeans that sell for $50 in the United States cost in Canada? Round your answer to the nearest cent. Clearly show your use of units.

Name:

Unit 2A Test 2

Date:

1. An airplane travels 1575 miles in 3.5 hours. What is its speed in miles per hour? Please show operations and label units clearly.

2. You plan on taking a 1350 mile-long trip in your car, which averages 22.5 miles per gallon. How many gallons of gas will you use? Clearly show your use of units.

3. If gas costs $2.13 per gallon, how much do you expect to spend on gas for the trip described above? Clearly show your use of units.

4. You need to carpet a room that measures 20 feet length by 15 feet. That costs $3.49 per square foot. How much will this cost? Clearly show your use of units.

5. You plan on purchasing mulch for your yard and spreading it to a depth of 3 inches (1/4 of a foot). The area to cover is 62 feet by 45 feet. How much mulch do you need? Clearly show your use of units.

6. Convert 2.5 hours to seconds. Clearly show your use of units.

Unit 2A Test 2 (continued)

Name:

7. Convert 8.5 feet to inches. Clearly show your use of units.

8. Find the area in square feet of a kennel that measures 8 yards by 6 yards. Clearly show your use of units.

9. Since $1 = 21.86 pesos, a scarf that was purchased for 200 pesos cost how much in U.S. dollars. Round your answer to the nearest cent. Clearly show your use of units.

10. Since $1 = 0.8191 British pounds, a meal that was purchased for 28 pounds cost how much in U.S. dollars. Round your answer to the nearest cent. Clearly show your use of units.

Name:

Unit 2A Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following is a conversion factor? (a) feet per second

(b) 8 ounces = 1 cup

(d) 180 miles

2. Suppose your car gets 28 miles per gallon of gasoline, and you are driving at 55 miles per hour. Using unit analysis, find the amount of gas you use every hour. (a) 1.45 gallons

(b) 1.96 gallons

(d) 0.51 gallons

3. Suppose you drive 320 miles at a speed of 60 miles per hour. How many hours does that trip take? (a) 0.89 hour

(b) 5.3 hours

(d) 3.8 hours

4. An acre is equal to 43,560 square feet, and there are 5280 feet in a mile. If a farm has the shape of a rectangle measuring 0.9 miles by 1.5 miles, what is the area of the farm in acres? (a) 0.164 acre

(b) 11.14 acres

(d) 1050 acres

5. You need to buy a carpet that measures 7.5 yards long and 5 yards wide and costs $49.50 per square yard. How much will the carpet for the room cost? (a) $618.75

(b) $1856.25

(d) $1237.50

6. Given that 1 meter = 100 centimeters, find the number of cubic centimeters in a cubic meter. (a) 100

(b) 10,000

(d) 100,000,000

(b) 108 inches

(d) 27 inches

7. Convert 9 feet to inches. (a) 0.75 inches

8. If U.S. $1 = 7.82 Hong Kong dollars, what is the value of 25 Hong Kong dollars in U.S. dollars? (a) $195.50

(b) $3.20

(d) $31.20

9. If a Norwegian kroner is worth $0.16, what is the value of $5.00 in kroners? (a) 0.80 kroners

(b) 14.9 kroners

(d) 31.25 kroners

10. If your heart beats 70 times per minute, how many times does your heart beat in 6 days? (a) 25,200

(b) 201,600

(d) 36,288,000

Name:

Unit 2A Test 4

Date:

Choose the correct answer to each problem. 1. Which of the following is a conversion factor? (a) miles per hour (b) 60 seconds

(d) V = lwh

2. Suppose you drive 338 miles at a speed of 52 miles per hour. How many hours does it take? (a) 0.15 hour

(b) 1.76 hours

(d) 6.5 hours

3. A cubit is an ancient measurement considered to be equivalent to about 18 inches today. If Noah’s ark was 300 cubits long, how long was the ark in yards? (a) 450 yards

(b) 50 yards

(d) 150 yards

4. An acre is equal to 43,560 square feet, and there are 5280 feet in a mile. If a farm has the shape of a rectangle measuring 0.8 mile by 1.1 miles, what is the area of the farm in acres? (a) 684.3 acres

(b) 563.2 acres

(d) 13.75 acres

5. You need to buy a carpet that measures 5.5 yards long and 4.5 yards wide and costs $39.50 per square yard. How much will the carpet for the room cost? (a) $395

(b) $977.63

(d) $790

6. Given that 1 mile = 8 furlongs, find the number of cubic furlongs in a cubic mile. (a) 8 cubic furlongs (c) 512 cubic furlongs

(b) 64 cubic furlongs (d) 4096 cubic furlongs

7. Convert 9 hours to seconds. (a) 540 seconds

(b) 0.15 seconds

(d) 5400 seconds

8. If U.S. $1 = 63.44 Indian rupees, what is the value of 400 rupees in dollars? (a) $25,376

(b) $6.31

(d) $35.84

9. If U.S. $1 = 112.53 Japanese yen, what is the value of $40 in Japanese yen? (a) 0.36 Japanese yen (c) 2.81 Japanese yen

(b) 4501.2 Japanese yen (d) 89.37 Japanese yen

10. If your heart beats 68 times per minute, how many times does your heart beat in 5 days? (a) 32,400,000

(b) 540,000

(d) 22,500

Name:

Unit 2B Test 1

Date:

1. Which of the following two is the better deal? Explain why. A 96-ounce bottle for $27.99 or a 28-ounce bottle for $7.99

Use the following conversion factors to answer problems 2 – 4. Round final answers to the nearest tenth. 1 mile = 1.6093 kilometers

1 kilometer = 0.6214 miles

1 yard = 0.9144 meters

1 meter = 1.094 yards

1 quart = 0.9464 liters

1 liter = 1.057 quarts

1 gallon = 3.785 liters

1 liter = 0.2642 gallons

2. Two cities are 582 kilometers apart. Convert this distance to miles

3. A 2-liter bottle of soda is how many quarts?

4. The speed limit on the highway is 55 miles per hour. What is the speed limit in meters per second?

Unit 2B Test 1 (continued)

Name:

Use the following formulas to answer problems 5 – 7. Round your answers to a hundredth of a degree.

F − 32 1.8

F = 1.8C + 32

K = C + 273.15

C = K − 273.15

5. Convert 60° C to degrees Fahrenheit.

6. Convert 92° F to degrees Celsius.

7. Convert 40° C to degrees Kelvin.

8. North Carolina has a population of roughly 10.15 million people and is 53,819 square miles in size. What is the density of the population?

9. Suppose your utility company charges 10¢ per kilowatt-hour of electricity. How much does it cost to operate a chandelier with five 75-watt light bulbs for 90 minutes?

Name:

Unit 2B Test 2

Date:

1. Which of the following two is the better deal? Explain why. A 48-ounce bottle for $7.49 or a 10-ounce bottle for $1.79

Use the following conversion factors to answer problems 2 – 4. Round final answers to the nearest tenth. 1 mile = 1.6093 kilometers

1 kilometer = 0.6214 miles

1 yard = 0.9144 meters

1 meter = 1.094 yards

1 quart = 0.9464 liters

1 liter = 1.057 quarts

1 gallon = 3.785 liters

1 liter = 0.2642 gallons

2. Two cities are 614 kilometers apart. Convert this distance to miles. State your answer to the nearest tenth of a mile.

3. A 5-gallon cooler will hold how many liters?

4. A projectile traveling at 16 meters per second is moving at how many miles per hour?

Unit 2B Test 2 (continued)

Name:

Use the following formulas to answer problems 5 – 7. Round your answers to a hundredth of a degree.

F − 32 1.8

F = 1.8C + 32

K = C + 273.15

C = K − 273.15

5. Convert 20° F to degrees Celsius.

6. Convert 50° C to degrees Fahrenheit.

7. Convert 25° C to degrees Kelvin.

8. North Dakota has a population of roughly 757,952 people and is 70,900 square miles in size. What is the density of the population?

9. Suppose your utility company charges 8¢ per kilowatt-hour of electricity. How much does it cost to keep a 100-watt light bulb lit for one day?

Name:

Unit 2B Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following is the best deal? (a) 16 ounces for $4.99 (c) 8 ounces for $2.99

(b) 4 ounces for $1.19 (d) 5 ounces for $1.49

2. State how much larger a cubic meter is than a cubic centimeter. (a) Larger by a factor of 100 (c) Larger by a factor of 10,000

(b) Larger by a factor of 1000 (d) Larger by a factor of 1,000,000

3. A pond contains 9.4 cubic yards of water. What is the volume of the water in cubic meters to the nearest tenth? (a) 12.3 cubic meters (c) 10.3 cubic meters

(b) 8.6 cubic meters (d) 7.2 cubic meters

4. Many Australian highways have a speed limit of 110 kilometers per hour. Convert this to miles per hour. (a) 177 mph (c) 89 mph

(b) 136 mph (d) 68 mph

5. A field of grass has an area of 618,000,000 square millimeters. Convert this area to square hectometers. (a) 0.0618 square hectometers (c) 61.8 square hectometers

(b) 6.18 square hectometers (d) 6180 square hectometers

6. Wally ran 5 miles in 34.7 minutes. Find his speed in meters per second. (a) 3.7 m/s

(b) 3.9 m/s

(d) 6.1 m/s

(d) 306.15° F

(d) 58° C

7. Convert 33° C to degrees Fahrenheit. (a) 27.4° F

(b) 1.8° F

8. Convert 50 K to degrees Celsius. (a) 122° C

(b) −223.15° C

9. South Dakota has a population of roughly 865,454 people and is 78,116 square miles in size. What is the density of the population? (a) 0.091 people/mi2 (c) 11.079 mi2/person

(b) 11.079 people/mi2 (d) 91.080 people/mi2

10. What is the cost of lighting a 400-watt outdoor light for 6 hours, if electricity costs 6.5¢ per kilowatthour? (a) 26 cents

(b) 16 cents

(d) 30 cents

Name:

Unit 2B Test 4

Date:

Choose the correct answer to each problem. 1. Which of the following is the best deal? (a) 16 ounces for $14.99 (c) 8 ounces for $7.99

(b) 4 ounces for $3.99 (d) 5 ounces for $5.49

2. State how much larger a cubic centimeter is than a cubic millimeter. (a) Larger by a factor of 100 (c) Larger by a factor of 10,000

(b) Larger by a factor of 1000 (d) Larger by a factor of 1,000,000

3. A pond contains 7.2 cubic yards of water. What is the volume of the water in cubic meters to the nearest tenth? (a) 21.6 cubic meters (c) 5.5 cubic meters

(b) 64.8 cubic meters (d) 253.8 cubic meters

4. The advisory speed limit of the German autobahn is 130 kilometers per hour. Convert this to miles per hour. (a) 209 mph (c) 81 mph

(b) 105 mph (d) 40 mph

5. A field of grass has an area of 6,420,000 square centimeters. Convert this area to square decameters. (a) 0.0642 square decameters (c) 64.2 square decameters

(b) 6.42 square decameters (d) 6420 square decameters

6. Sophia ran 10 kilometers in 56 minutes. Find her speed in minutes per mile. (a) 8.7 min/mi

(b) 9.3 min/mi

(d) 11 min/mi

(d) −6.1° F

(d) 284° C

7. Convert 21° C to degrees Fahrenheit. (a) 294.15° F

(b) 5.8° F

8. Convert 140° K to degrees Celsius. (a) 413.15° C

(b) −133.15° C

9. What is the cost of lighting a 500-watt outdoor light for 8 hours, if electricity costs 7.5¢ per kilowatthour? (a) 40 cents

(b) 38 cents

(d) 30 cents

10. Connecticut has a population of roughly 3.576 million people and is 5543 square miles in size. What is the density of the population? (a) 645.138 people/mi2 (c) 645.138 mi2/person

Name:

Unit 2C Test 1

Date:

1. A traffic counter consists of a thin black tube stretched across a street or highway and connected to a “brain box” at the side of the road. The device registers one “count” each time a set of wheels (that is, wheels on a single axle) rolls over the tube. A normal automobile (two axles) registers two counts, and a light truck (three axles) registers three counts. Suppose that, during a one-hour period, a particular counter registers 41 counts on a residential street on which only two-axle vehicles (cars) and three-axle vehicles (light trucks) are allowed. Give a possible answer for the number of cars and the number of light trucks that passed over the traffic counter.

2. Tom and Silas ran a 100-meter race. When Tom crossed the finish line, Silas had run only 95 meters. Then they ran a second race, with Tom starting 10 meters behind the starting line. Assuming that both runners ran at the same pace as in the first race, who won the second race?

3. Two bicyclists, 48 miles apart, begin riding toward each other on a long straight avenue. One cyclist travels 15 miles per hour and the other 25 miles per hour. At the same time, Spot (a greyhound), starting at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 35 miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet?

4. Suppose you have 12 white socks and 5 black socks in a drawer. How many socks must you take from the drawer to be certain of having a pair of white socks?

Unit 2C Test 1 (continued)

Name:

5. Suppose that you begin with a red bucket containing 12 red marbles and a yellow bucket containing 12 yellow marbles. You move three marbles from the red bucket to the yellow bucket, and then you move any four marbles from the yellow bucket to the red bucket. Which is greater, the number of yellow marbles in the red bucket or the number of red marbles in the yellow bucket?

6. Suppose that 20 turns of a wire are wrapped around a pipe with a length of 10 inches and a circumference of 12.5 inches. What is the length of the wire?

7. You are considering buying 15 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. How can you determine the lightweight coin in a maximum of three weighings on a balance scale?

8. Suppose that China’s population policy is modified so that every family could have children until either a boy is born or two children are born, whichever comes first. Assuming that every family chooses to have as many children as possible under this policy, and that boys and girls are equally likely, what fraction of the children would be girls and what fraction would be boys?

Name:

Unit 2C Test 2

Date:

1. A traffic counter consists of a thin black tube stretched across a street or highway and connected to a “brain box” at the side of the road. The device registers one “count” each time a set of wheels (that is, wheels on a single axle) rolls over the tube. A normal automobile (two axles) registers two counts, and a light truck (three axles) registers three counts. Suppose that, during a one-hour period, a particular counter registers 43 counts on a residential street on which only two-axle vehicles (cars) and three-axle vehicles (light trucks) are allowed. Give a possible answer for the number of cars and the number of light trucks that passed over the traffic counter.

2. Steve and Karen ran a 400-meter race. When Karen crossed the finish line, Steve had run only 340 meters. Then they ran a second race, with Karen starting 60 meters behind the starting line. Assuming that both runners ran at the same pace as in the first race, who won the second race?

3. Two bicyclists, 48 miles apart, begin riding toward each other on a long straight avenue. One cyclist travels 18 miles per hour and the other 12 miles per hour. At the same time, Spot (a greyhound), starting at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 36 miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet?

4. Suppose you have 10 white socks and 6 black socks in a drawer. How many socks must you take from the drawer to be certain of having a pair of black socks?

Unit 2C Test 2 (continued) 5.

Name:

Suppose that you begin with a green bucket containing 14 green marbles and a black bucket containing 14 black marbles. You move four marbles from the green bucket to the black bucket, and then you move any three marbles from the black bucket to the green bucket. Which is greater, the number of black marbles in the green bucket or the number of green marbles in the black bucket?

6. Suppose that 8 turns of a ribbon are wrapped around a maypole that is 168 inches tall and has a circumference of 9 inches. What is the length of the ribbon?

7. You are considering buying 18 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. How can you determine the lightweight coin in a maximum of three weighings on a balance scale?

8. Suppose that China’s population policy is modified so that every family could have children until either a boy is born or three children are born, whichever comes first. Assuming that every family chooses to have as many children as possible under this policy, and that boys and girls are equally likely, what fraction of the children would be girls and what fraction would be boys?

Name:

Unit 2C Test 3

Date:

Choose the correct answer to each problem. 1. A traffic counter consists of a thin black tube stretched across a street or highway and connected to a “brain box” at the side of the road. The device registers one “count” each time a set of wheels (that is, wheels on a single axle) rolls over the tube. A normal automobile (two axles) registers two counts, and a light truck (three axles) registers three counts. Suppose that, during a one-hour period, a particular counter registers 49 counts on a residential street on which only two-axle vehicles (cars) and three-axle vehicles (light trucks) are allowed. Which of the following is a possible answer for the number of cars and the number of light trucks that passed over the traffic counter? (a) 7 cars and 11 light trucks (c) 14 cars and 7 light trucks

(b) 9 cars and 10 light trucks (d) 23 cars and 24 light trucks

2. Candi and Sandi ran an 80-meter race. When Candi crossed the finish line, Sandi had run only 72 meters. Then they ran a second race, with Candi starting 8 meters behind the starting line. Assuming that both runners ran at the same pace as in the first race, who won the second race? (a) Candi (c) They tied.

(b) Sandi (d) More information is needed.

3. Suppose you have 7 striped socks and 3 red socks in a drawer. How many socks must you take from the drawer to be certain of having a pair of striped socks? (a) 2

(b) 4

(d) 6

4. Suppose that you begin with a red bucket containing 16 red marbles and a yellow bucket containing 16 yellow marbles. You move five marbles from the red bucket to the yellow bucket, and then you move any four marbles from the yellow bucket to the red bucket. Compare the number of yellow marbles in the red bucket to the number of red marbles in the yellow bucket. (a) The number of red marbles in the yellow bucket is greater. (b) The number of yellow marbles in the red bucket is greater. (c) They are the same. (d) More information is needed. 5. Two bicyclists, 44 miles apart, begin riding toward each other on a long straight avenue. One cyclist travels 16 miles per hour and the other 17 miles per hour. At the same time, Spot (a greyhound), starting at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 39 miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet? (a) 48 mi

(b) 52 mi

(d) 64 mi

6. Suppose that 6 turns of a ribbon are wrapped around a maypole with a height of 84 inches and a circumference of 15 inches. What is the length of the ribbon? (a) 35 inches

(b) 84 inches

(d) 123 inches

7. You are considering buying 27 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. Find the least number of weighings on a balance scale that you can use to be certain you have found the counterfeit coin. (a) 2

(b) 3

(d) 5

Unit 2C Test 3 (continued)

Name:

8. Suppose that China’s population policy is modified so that every family could have children until either a boy is born or two children are born, whichever comes first. Assuming that every family chooses to have as many children as possible under this policy, and that boys and girls are equally likely, how many children would be born in a typical group of 1000 families? (a) 1500

(b) 1750

(d) 2000

Name:

Unit 2C Test 4

Date:

Choose the correct answer to each problem. 1. A traffic counter consists of a thin black tube stretched across a street or highway and connected to a “brain box” at the side of the road. The device registers one “count” each time a set of wheels (that is, wheels on a single axle) rolls over the tube. A normal automobile (two axles) registers two counts, and a light truck (three axles) registers three counts. Suppose that, during a one-hour period, a particular counter registers 54 counts on a residential street on which only two-axle vehicles (cars) and three-axle vehicles (light trucks) are allowed. Which of the following is a possible answer for the number of cars and the number of light trucks that passed over the traffic counter? (a) 7 cars and 16 light trucks (c) 13 cars and 9 light trucks

(b) 12 cars and 10 light trucks (d) 42 cars and 11 light trucks

2. Perry and Barry ran an 120-meter race. When Barry crossed the finish line, Perry had run only 105 meters. Then they ran a second race, with Barry starting 15 meters behind the starting line. Assuming that both runners ran at the same pace as in the first race, who won the second race? (a) Perry (c) They tied.

(b) Barry (d) More information is needed.

3. Two bicyclists, 13 miles apart, begin riding toward each other on a long straight avenue. One cyclist travels 16 miles per hour and the other 10 miles per hour. At the same time, Spot (a greyhound), starting at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 26 miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet? (a) 6.5 mi

(b) 13 mi

(d) 52 mi

4. Suppose you have 10 striped socks and 6 red socks in a drawer. How many socks must you take from the drawer to be certain of having a pair of red socks? (a) 4

(b) 7

(d) 12

5. Suppose that you begin with a green bucket containing 18 green marbles and a black bucket containing 18 black marbles. You move four marbles from the green bucket to the black bucket, and then you move any five marbles from the black bucket to the green bucket. Compare the number of black marbles in the green bucket to the number of green marbles in the black bucket. (a) The number of green marbles in the black bucket is greater. (b) The number of black marbles in the green bucket is greater. (c) They are the same. (d) More information is needed. 6. Suppose that 8 turns of a wire are wrapped around a pipe with a length of 48 inches and a circumference of 3 inches. What is the length of the wire? (a) 24.1 inches

(b) 64.5 inches

(d) 53.7 inches

7. You are considering buying 45 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. Find the least number of weighings on a balance scale that you can use to be certain you have found the counterfeit coin. (a) 2

(b) 3

(d) 5

Unit 2C Test 4 (continued)

Name:

8. Suppose that China’s population policy is modified so that every family could have children until either a boy is born or three children are born, whichever comes first. Assuming that every family chooses to have as many children as possible under this policy, and that boys and girls are equally likely, how many children would be born in a typical group of 5000 families? (a) 7500

(b) 8750

(d) 2500

Name:

Unit 3A Test 1

Date:

1. Of 2003 people surveyed, 560 believe in the existence of “Deep State.” What is this amount expressed as a percentage?

2. The number of students enrolled at a college increased from 17,000 to 30,000 in twelve years. What is the absolute and the relative change in the enrollment?

3. After the safety training courses were conducted, the number of people who were injured at work decreased from 276 last year to 109 this year. Find the absolute and relative change in the number of work injuries.

4. The average period of gestation for dogs (60 days) is what percent less than the average gestation period for humans (280 days)? Please show all work.

5. The number of people who voted in the last local election was down from the last local election by almost 14%. Therefore, the number of people who voted in this election was how many times the number who voted in the last election.

Unit 3A Test 1 (continued)

Name:

6. A political candidate hears that 65% of the voters are for him in the polls, up 40% since the last poll. What percentage of the voters were for the candidate based on the last poll?

7. Suppose the interest on your CD decreases from 2.4% to 1.9%. Find the absolute and relative change in your interest rate.

8. The after-tax price of your shiny new car is $25,989.60. If a 4% sales tax was charged, what was the pretax price of the car?

9. If Janie makes 200% more than Jenny, then Janie makes how many times more than Jenny?

10. If the balance in your bank account increases by 1% during the first half of the year and 2% during the second half of the year, does it follow that the balance has increased by 3% over the entire year? Explain.

Name:

Unit 3A Test 2

Date:

1. Of 1056 people surveyed, 285 believe in the existence of ghosts. What is this amount expressed as a percentage?

2. The price of gasoline dropped from $2.76 to $2.44 after the holidays. Find the absolute and relative change in the price of gas.

3. Consider the population of town that grows from 24,730, to 72,210 over a decade. Find the absolute and relative change in the population.

4. The average period of gestation for cats (66 days) is what percent more than the average gestation period for hamsters (22 days)? Please show all work.

5. The number of people who voted in the most recent local election was up from the last local election by about 24%. Therefore, the number of people who voted in this election was how many times the number who voted in the last election.

Unit 3A Test 2 (continued)

Name:

6. A political candidate knows that 40% of the voters are for him, down 25% since the last poll. What percentage of voters were for the candidate based on the last poll?

7. If the interest charged by your credit card increases from 14.9% to 19.3%, find the absolute and relative change in your interest rate.

8. The after-tax price of your new designer shirt is $96.29. If a 7% sales tax was charged, what was the pretax price of the shirt?

9. I have invested 8 times as much as Carla. This is what percentage more than her investment?

10. If the population of a city increases by 4% one year and by 6% the next, does it follow that the population has increased by 10% over the two-year period? Explain.

Name:

Unit 3A Test 3

Date:

Choose the correct answer to each problem. 1. A new scarf has a regular price of $24. It is on sale for $16. What percent discount is this? (a) 66.7% (c) 50%

(b) 33.3% (d) 1.5%

2. The price of gas dropped over the weekend by 28 cents! This statement shows the use of which of the following concepts? (a) Absolute change (c) Relative change

(b) Absolute difference (d) Relative difference

3. Sam earns a salary of $25,000 while Charlie earns a salary of $30,000. They each receive a $2000 raise. Which of the following is true? (a) Sam’s raise is larger than Charlie’s in both absolute and relative terms. (b) The raises are the same in absolute terms, but Sam’s is larger in relative terms. (c) The raises are the same in relative terms, but Sam’s is larger in absolute terms. (d) The raises are the same in absolute terms, but Charlie’s is larger in relative terms. 4. The price of a waffle maker fell from $36 to $29. Describe the change in both absolute and relative terms. (a) Absolute change = $7; Relative change = 19.4% (b) Absolute change = $7; Relative change = 24.1% (c) Absolute change = -$7; Relative change = -19.4% (d) Absolute change = -$7; Relative change = -24.1% 5. Compare the costs of Spa Treatment A ($210) and Spa Treatment B ($250). (a) Spa Treatment A is 16% more than Spa Treatment B. (b Spa Treatment A is 19% more than Spa Treatment B. (c) Spa Treatment A is 16% less than Spa Treatment B. (d) Spa Treatment A is 19% less than Spa Treatment B. 6. The governor’s approval rating dropped by 40%, to 18%. What was his approval rating before? (a) 25.2%

(b) 58%

(d) 7.2 %

7. A store is having a 20% off sale. What is the sale price of a sweater that was originally marked $80? (a) $32

(b) $48

(d) $64

8. The football game was attended by 417 people, 22% more than last week. How many people attended last week’s game? (a) 325

(b) 342

(d) 509

9. If Romeo earns 8% more than Juliet, Romeo’s salary is how many times Juliet’s salary? (a) 1.08

(b) 0.92

(d) 108

Unit 3A Test 3 (continued)

Name:

10. Suppose your stock balance increased by 5% during the first half of the year and by 3% during the second half; what was the relative change in your balance at the end of the year? (a) 8%

(b) -2%

(d) $8.15

Name:

Unit 3A Test 4

Date:

Choose the correct answer to each problem. 1. The new CD burner costs 12% less at the new electronics store. This statement shows the use of which of the following concepts? (a) Absolute change (c) Relative change

(b) Absolute difference (d) Relative difference

2. If I use my debit card at the gas pump, I get a five-cent discount. Which of the following statements is accurate? (a) The absolute change in price is the same for all grades of gas; the relative change in price for Regular (the cheapest) is the greatest. (b) The absolute change in price is the same for all grades of gas; the relative change in price for Premium (the most expensive) is the greatest. (c) The relative change in price is the same for all grades of gas; the absolute change in price for Regular (the cheapest) is the greatest. (d) The relative change in price is the same for all grades of gas; the absolute change in price for Premium (the most expensive) is the greatest. 3. If Alice earns 56% more than Wally, Alice’s salary is how many times Wally’s salary? (a) 0.44

(b) 1.44

(d) 1.56

4. Compare the length of a quarter (10 weeks) to the length of a semester (15 weeks). (a) A quarter is 50% more than a semester. (b) A quarter is 33.3% more than a semester. (c) A quarter is 50% less than a semester. (d) A quarter is 33.3% less than a semester. 5. The football game was attended by 237 people, down 40% from last week. How many people attended last week’s game? (a) 332

(b) 395

(d) 379

6. The percentage of students who take statistics is at 62%, up 78% from last year. What percentage of students took statistics last year? (a) 34.8%

(b) 16 percentage points

(d) 110.4%

7. The population of a town increased from 60,450 to 95,610 in one decade. What was the relative change of the population? (a) 58.2%

(b) 36.8%

(d) -36.8%

Unit 3A Test 4 (continued)

Name:

8. You have exactly $50 to spend on groceries. They charge 4.3% sales tax on food. What is the most you can spend on food, pre-tax? (a) $47.85

(b) $52.24

(d) $47.94

9. I paid twice as much by not waiting for a sale and not ordering on line. Which of the following statements is also true? (a) I paid 200% more than I could have online and on sale. (b) I paid 100% of what I could have online and on sale. (c) I paid 200% of what I could have online and on sale. (d) I paid 3 times what I could have online and on sale. 10. Suppose your original salary was increased by 4% one year and then 5% the next year. What was the relative change in your salary at the end of the two years? (a) 9%

(b) -1%

(d) 9.2%

Name:

Unit 3B Test 1

Date:

1. Convert 3.6 ×10−2 from scientific notation to ordinary notation.

2. Convert 5,600,000,000 to scientific notation.

3. Convert 978.62 × 103 to the correct form of scientific notation.

4. Calculate ( 2 × 106 ) × ( 7 × 109 ) . Show your work clearly. Express the final answer in scientific notation.

5. Calculate ( 8 × 1012 ) ÷ ( 4 × 105 ) without using a calculator. Show your work clearly. Express the final answer in scientific notation.

Unit 3B Test 1 (continued)

Name:

6. Energy released by metabolism of 1 average candy bar = 1×106 joules. Electrical energy used in an average home daily = 5 ×107 joules. How many candy bars would you have to eat to generate enough energy to power a home for 3 days?

7. If one inch on a map represents 50 miles, what is the scale ratio?

8. Assuming you can count 1 dollar bill per second, how many days would it take to count 400,000 dollar bills?

9. As of November 2017, the United States federal debt was $19.84 trillion. If each of the 324.5 million people in the United States paid an extra $1000 in taxes each year, every year, how many years would it take to pay off this debt?

10. Bryan is 63 years old. Find his age in seconds. State your answer in scientific notation. You may round your answer by writing only two digits (as in 3.2 ×105 ).

Name:

Unit 3B Test 2

Date:

1. Convert 5.9 ×108 from scientific notation to ordinary notation.

2. Convert 0.00000078 to scientific notation.

3. Convert 0.0097 × 10 −3 to the correct form of scientific notation.

4. Calculate ( 5 × 107 ) × ( 2 × 104 ) . Show your work clearly. Express the final answer in scientific notation.

5. Calculate ( 8 × 1011 ) ÷ ( 2 × 104 ) without using a calculator. Show your work clearly. Express the final answer in scientific notation.

6. How many years would it take a worker making $12 per hour to earn $48,000,000? Assume she works 260 8-hour days per year.

Unit 3B Test 2 (continued)

Name:

7. Energy released by burning 1 kilogram of coal = 1.6 ×109 joules. Energy released by fission of 1 kilogram of uranium-235 = 5.6 ×1013 joules. How many kilograms of coal would you have to burn to generate the same energy as 3 kg of uranium-235?

8. The diameter of the moon is about 1.1×107 feet and the diameter of Uranus is about 1.7 ×108 feet. If a scale model of the solar system is constructed so that the diameter of the moon is 3.5 feet, what will be the diameter of Uranus?

9. If one inch on a map represents 120 miles, what is the scale ratio?

10. A standard dump truck can hold 129 cubic feet of dirt and rock. Mount Shasta in California has an estimated volume of 108 cubic miles. If dump trucks worked 24 hours a day and could leave once every 15 minutes, how many years would it take to move Mount Shasta? You may round your answer by writing only two digits (as in 3.2 ×105 ).

Name:

Unit 3B Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following is equal to 5 ×10−4 ? (a) five thousandths (c) five hundred-thousandths

(b) five ten-thousandths (d) five millionths

2. Convert 78,000,000 to scientific notation. (a) 78 ×106 3. Suppose that you add 10 10

(a) 10

(b) 7.8 ×106 10

(d) 7.8 ×108

100

+ 10

. What, approximately, is the answer? 100

(b) 10

110

1000

(d) 10

(d) 2.35 ×108

(d) 2.35 ×1036

(d) 2.7 ×10−11

4. Calculate ( 9.87 × 1012 ) ÷ ( 4.2 × 10 4 ) . (a) 2.35 ×103

(b) 2.35 ×106

5. Calculate ( 9.4 × 109 ) × ( 2.5 × 104 ) . (a) 2.35 ×1013

(b) 2.35 ×1014

6. Which is the largest number? (a) 1.5 billion

(b) 1650 million

7. How many years would it take a worker making $40 per hour to earn $8,000,000, assuming she works 240 8-hour days per year? (a) 250 years

(b) 833 years

(d) 481 years

8. If one centimeter on a map represents 280 kilometers, what is the scale ratio? (a) 1 to 2.8 ×104

(b) 1 to 2.8 ×105

(d) 1 to 2.8 ×107

9. If a stack of $10 bills is worth $90 billion, what is the height of the stack in kilometers? Assume each bill is 0.2 millimeters thick. (a) 1800 km

(b) 4500 km

(d) 45,000 km

10. If you take 2000 steps to walk one mile, how many miles can you walk in one million steps? (a) 5 miles (c) 5000 miles

(b) 50 miles (d) 500 miles

Name:

Unit 3B Test 4

Date:

Choose the correct answer to each problem. 1. Which of the following is equal to 3 ×10−4 ? (a) three thousandths (c) three hundred-thousandths

(b) three ten-thousandths (d) three millionths

2. Convert 42,000,000 to scientific notation. (a) 4.2 ×106

(b) 4.2 ×107

3. Suppose that you subtract 10 (a) –10

(d) 42 ×106

– 10 . What, approximately, is the answer? 12

(b) 10

(d) 10

(d) 1.75 ×108

(d) 6.15 ×1027

(d) 8.2 ×10−11

4. Calculate ( 6.3 × 109 ) ÷ ( 3.6 × 103 ) . (a) 1.75 ×103

(b) 1.75 ×106

5. Calculate ( 7.5 × 103 ) × ( 8.2 × 106 ) ? (a) 6.15 ×108

(b) 6.15 ×109

6. Which is the largest number? (a) 2.9 billion

(b) 3021 million

7. In 2005, Bill Gates donated $3,300,000,000 to charity. Assuming you could give $10.00 per day, 365 days per year, how many years would it take you to donate this amount? (a) 1.3 ×105 years

(b) 3.8 ×104 years

(d) 2.5 ×103 years

8. If one centimeter on a map represents 50 kilometers, what is the scale ratio? (a) 1 to 5 ×104

(b) 1 to 5 ×105

(d) 1 to 5 ×107

9. If a stack of $5 bills is worth $175 billion, what is the height of the stack in kilometers? Assume each bill is 0.2 millimeters thick. (a) 1750 km

(b) 7000 km

(d) 35,000 km

10. If you take 2000 steps to walk one mile, how many miles can you walk in one billion steps? (a) 5 ×102 miles (c) 5 ×105 miles

(b) 5 ×103 miles (d) 5 ×104 miles

Name:

Unit 3C Test 1

Date:

1. The capacity of a bucket is given as 10.60 liters. State the number of significant digits and the implied precision in this number.

2. The population of the last town we passed was listed as 17,500. State the number of significant digits and the implied precision in this number.

3. The actual age of a tree is known to be 105 years old. Using scientific methods, a biologist estimates the age of the tree to be 98 years old. Find the absolute error and the relative error of the biologist’s measurement.

4. Two students measured the width of a swimming pool whose actual width is 18.500 meters. Bobby reported the width as 18.329 meters, while Carolyn reported the width as 18.6 meters. Which student reported the width more accurately? Which student reported the width more precisely?

5. Give an example of a systematic error that could occur when grading tests.

Unit 3C Test 1 (continued)

Name:

6. The finance charge on your credit card was supposed to be $12.22. Instead you were charged $19.54. Find the absolute error and the relative error in the finance charge.

7. Find the sum: 652.69 + 27.9813. Give your answer to the correct precision.

8. Find the difference: 95,400 – 295. Give your answer to the correct precision.

9. What is the per capita cost of a $4.3 million aquatic center in a city with 123,000 people? Give your answer to the correct precision.

10. Find the product: 3.0 × 7.962. Give your answer to the correct precision.

Name:

Unit 3C Test 2

Date:

1. The tolerance is given as 0.00210. State the number of significant digits and the implied precision in this number.

2. The population of the last town we passed was listed as 17,000. State the number of significant digits and the implied precision in this number.

3. A painting is known to be 525 years old. Using carbon dating, a scientist estimates that the painting is 610 years old. Find the absolute error and the relative error of the scientist’s measurement of the age of the painting.

4. Two students measured the height of a building whose actual height is 21.500 meters. Evelyn reported the height as 21.4 meters, while Priscilla reported the height as 22.375 meters. Which student reported the height more accurately? Which student reported the height more precisely?

5. Give an example of a random error that could occur when grading tests.

Unit 3C Test 2 (continued)

Name:

6. The finance charge on your credit card was supposed to be $15.22. Instead you were charged $9.54. Find the absolute error and the relative error in the finance charge.

7. Find the difference: 16,950 – 222. Give your answer to the correct precision.

8. Find the sum: 4059.81 + 46.009. Give your answer to the correct precision.

9. What is the per capita cost of a $3.2 million aquatic center in a city with 146,000 people? Give your answer to the correct precision.

10. You are driving to your cousin’s house, which is 4.3 miles past the center of the next town down the road. The highway sign lists that town as 35 miles away. How much farther do you have to drive? Give your answer to the correct precision.

Name:

Unit 3C Test 3

Date:

Choose the correct answer to each problem. 1. A problem in a math book stated “1 mile = 1.6 km,” while the actual conversion (to 4 decimal places) is 1 mile = 1.6093 km. How would you describe the way the conversion was given in the problem in the math book? (a) Accurate, but not precise (c) Both accurate and precise

(b) Precise, but not accurate (d) Neither accurate nor precise

2. Which of the following is an example of a random error? (a) In a written survey, people sometimes make errors in filling out the form. (b) A telephone survey will not accurately reflect the opinions of people who do not have telephones. (c) Measurements are taken using an inaccurate scale that always reports a smaller weight than the correct weight. (d) At a clinic, people are wearing shoes when their heights are measured. 3. The actual height of a building is 441 feet. A student reports the height to be 398 feet. Find the relative error of the student’s measurement. (a) 10.8%

(b) –10.8%

(d) –9.8%

4. Two students measured the width of a table whose actual width is 4.500 feet. Dave reported the width as 4.7 feet, while Gary reported the width as 4.932 feet. Which student reported the width more accurately? Which student reported the width more precisely? (a) Dave was more accurate and more precise. (b) Gary was more accurate and more precise. (c) Dave was more accurate, and Gary was more precise. (d) Gary was more accurate, and Dave was more precise. 5. The actual distance between the two houses is 44.1 ft. The contractor measures the distance as 46 ft. Find the relative error of the contractor’s measurement. (a) 4.3%

(b) 4.1%

(d) -4.1%

6. The height of a mountain is given as 4800 feet. State the number of significant digits and the implied precision in this number. (a) 4 significant digits; nearest hundred feet (c) 2 significant digits; nearest hundred feet

(b) 4 significant digits; nearest foot (d) 2 significant digits; nearest foot

7. Find the difference: 9.8 – 2.472. Give your answer to the correct precision. (a) 7.328

(b) 7.33

(d) 7.32

8. Find the sum: 67.4321 + 67,843.8. Give your answer to the correct precision. (a) 67,911

(b) 67,911.2

(d) 67,911.232

Unit 3C Test 3 (continued)

Name:

9. Multiply: 6.70 × 8.4662. Give your answer to the correct precision. (a) 56.7

(b) 56.72

(d) 56.7235

10. Divide the area 326.4 square feet by the length 15 feet. Give your answer to the correct precision. (a) 20 feet

(b) 22 feet

(d) 21.76 feet

Name:

Unit 3C Test 4

Date:

Choose the correct answer to each problem. 1. On a word problem, Doris used 1.5 km = 1 mile. The actual conversion factor is 1 mile = 1.6093 km. How would you describe the way she worked the problem? (a) Accurate, but not precise (c) Both accurate and precise

(b) Precise, but not accurate (d) Neither accurate nor precise

2. Which of the following is an example of a systematic error? (a) In a written survey, people sometimes make errors in filling out the form. (b) A man is measuring times with a stopwatch, but the watch is slow by 0.2 seconds every minute. (c) A telephone survey will not accurately reflect the opinions of people who do not have telephones. (d) Because people may move or have multiple residences, the census may accidentally count some people twice (or not at all). 3. The actual age of a manuscript is known to be 950 years old. Using scientific methods, an expert estimates that the manuscript is 1000 years old. Find the relative error of his measurement. (a) 5.3%

(b) 5.0%

(d) –5.0%

4. Two students measured the height of a statue whose actual height is 11.600 feet. Joyce reported the height as 11.843 feet, while Peter reported the height as 11.7 feet. Which student reported the height more accurately? Which student reported the height more precisely? (a) Joyce was more accurate and more precise. (b) Peter was more accurate and more precise. (c) Joyce was more accurate, and Peter was more precise. (d) Peter was more accurate, and Joyce was more precise. 5. On a job application, Doris gave her age as 32 years. Her actual age at the time was about 27. What is the relative error for her age? (a) 18.5%

(b) -18.5%

(d) -15.6%

6. The distance between two flagpoles is given as 1710.0 meters. State the number of significant digits and the implied precision in this number. (a) 3 significant digits; nearest tenth meter (c) 5 significant digits; nearest tenth meter

(b) 3 significant digits; nearest ten meters (d) 5 significant digits; nearest ten meters

7. Find the difference: 29.8 – 12.472. Give your answer to the correct precision. (a) 17

(b) 17.3

(d) 17.328

8. Find the sum: 5278.31232 + 26.12. Give your answer to the correct precision. (a) 5304

(b) 5304.4

(d) 5304.432

9. Find the product: 2.10 × 7.9921. Give your answer to the correct precision. (a) 16.8

(b) 16.78

(d) 16.78341

Unit 3C Test 4 (continued)

Name:

10. Divide the area 3250 square feet by the length 120 feet. Give your answer to the correct precision. (a) 27 feet

(b) 27.1 feet

(d) 27.083 feet

Name:

Unit 3D Test 1

Date:

The following table provides information about median incomes in four states for 2016. Use this information to answer Questions 1 – 4. 2016 Median Income State

Income

Index

Alabama

$46,257

86.4

Alaska

$76,440

142.7

Arizona

$53,558

100.0

Arkansas

$44,334

82.8

Source: U.S. Census Bureau

1. Identify the reference value.

2. Given that the 2016 median income for California was $67,739, find the income index for California.

3. If you make a salary of $53,200 in Arkansas, how much would you have to make in Alabama to keep the same standard of living?

4. Calculate the income index for each state in the table using the median income from California as the reference value.

Unit 3D Test 1 (continued)

Name:

5. How often is the Consumer Price Index computed and reported?

6. Given that the Consumer Price Index was 215.3 in 2008 and 229.6 in 2012, find the inflation rate from 2008 to 2012 to the nearest hundredth of a percent.

7. Given that the Consumer Price Index was 215.3 in 2008 and 214.5 in 2009, find the deflation rate from 2008 to 2009.

In Questions 8–10, use 214.5 as the Consumer Price Index in 2009 and 240.0 as its value in 2016. 8. What would be the price in 2016 of an item that cost $1.00 in 2009?

9. What would be the equivalent price in 2009 of a pair of jeans that cost $89 in 2016?

10. A salary of $45,000 in 2009 would have to be how much in 2016 to keep the same standard of living?

Name:

Unit 3D Test 2

Date:

1. What is the benefit of an index number?

2. The following table provides the average price of Regular for 4 years. 2015 as the reference value, complete the table by calculating the price index for each week. Regular Grade Gasoline Prices Date

Price

2013

$3.505

2014

$3.358

2015

$2.429

2016

$2.143

Price Index

Source: Energy Information Administration 3. The average price of Regular grade gasoline so far in 2017 is $2.415. Using the information provided in the problem above, find the index number for the price of gas so far in 2017.

4. What government agency computes and reports the Consumer Price Index?

5. Given that the Consumer Price Index was 215.3 in 2008 and 214.5 in 2009, find the deflation rate from 2008 to 2009.

Unit 3D Test 2 (continued)

Name:

6. Given that the Consumer Price Index was 237.0 in 2015 and 240.0 in 2016, find the inflation rate from 2015 to 2016.

In Questions 7–10, use 140.3 as the Consumer Price Index in 1992 and 240.0 as its value in 2016 7. To keep up with inflation, what should a standard 29 cent first class postage stamp for 1992 cost in 2016?

8. The average cost of a car in 1992 was $11,580. What would a similar car have cost in 2016?

9. What would be the equivalent price in 1992 of a pair of jeans that cost $69 in 2016?

10. The median household income in 2014 was $53,657. What would that income have to be in 2016 to maintain the same standard of living? The CPI for 2014 is 236.7.

Name:

Unit 3D Test 3

Date:

Choose the correct answer to each problem. 1. In a study of how college education costs have changed since 1980, each year’s average cost of tuition is expressed as a percentage of the 1980 cost. Which term refers to the 1980 cost? (a) Reference value

(b) Index number

(d) Price index

2. What is the primary purpose of index numbers? (a) To predict future prices (c) To measure the strength of the economy

(b) To determine interest rates (d) To facilitate comparisons

3. Who computes and reports the Consumer Price Index? (a) U.S. Bureau of the Economic Analysis (c) Wall Street Journal

(b) New York Stock Exchange (d) U.S. Bureau of Labor Statistics

4. Which price index measures consumer attitudes so that businesses can gauge whether people are likely to be spending or saving? (a) Consumer Price Index (c) Consumer Confidence Index

(b) Producer Price Index (d) Health Care Quality Index

The following table provides information about regular gasoline prices in the U.S. by region. Use this information to answer Questions 5 – 7. Regular Grade Gasoline Prices (sorted by region in the United States) Region

Price

Price Index

East Coast

$3.495

100.0

Midwest

$3.456

98.9

Gulf Coast

$3.231

Rocky Mountain

$3.586

102.6

Source: Energy Information Administration 5. Calculate the price index for the Gulf Coast to complete the table. (a) 92.4

(b) 93.5

(d) 108.2

6. Given that the retail gasoline price for the West Coast during the same week is $3.866, calculate the price index for the Gulf Coast using the West Coast price as the reference value. (a) 110.6

(b) 83.6

(d) 119.7

Unit 3D Test 3 (continued)

Name:

7. If it cost you $40.92 to fill up your tank in Iowa (Midwest), how much would it cost you to fill the same tank in Colorado (Rocky Mountain)? (a) $42.45

(b) $41.99

(d) $39.88

8. Given that the Consumer Price Index was 82.4 in 1980 and 215.3 in 2008, find the price in 2008 dollars of a used car that cost $1500 in 1980. (a) $574.08

(b) $3919.30

(d) $5549.06

9. Given that the Consumer Price Index was 215.3 in 2008 and 214.5 in 2009, find the rate of deflation from 2008 to 2009. (a) 0.8%

(b) 3.73%

(d) 0.37%

10. The Consumer Price Index was 179.9 in 2002 and 240.0 in 2016. If a person earned $59,500 in 2002, how much did he need to earn in 2016 to maintain the same standard of living? (a) $44,600.21

(b) $79,377.43

(d) $83,300.02

Name:

Unit 3D Test 4

Date:

Choose the correct answer to each problem. 1. Which quantity provides a simple way to compare measurements made at different times or in different places? (a) Reference value (c) Rate of inflation

(b) Index number (d) Price of gasoline

2. Which term refers to the rise of prices and wages over time? (a) Consumer Price Index (c) Rate of inflation

(b) Inflation (d) Adjusted value

3. How often is the Consumer Price Index computed and reported? (a) Daily

(b) Weekly

(d) Quarterly

4. Which quantity refers to the relative change in the Consumer Price Index from one year to the next? (a) Reference value

(b) Index number

(d) Price index

5. Which price index represents an average of prices in a sample of more than 60,000 goods, services, and housing costs? (a) Consumer Price Index (c) Consumer Confidence Index

(b) Producer Price Index (d) Health Care Quality Index

The following table provides information about median incomes in four states for 2016. Use this information to answer Questions 6-8. 2016 Median Income State

Income

Index

Alabama

$46,257

86.4

Alaska

$76,440

142.7

Arizona

$53,558

100.0

Arkansas

$44,334

82.8

Source: U.S. Census Bureau 6. Given that the 2016 median income for Tennessee was $48,547, find the income index for Tennessee. (a) 98.9

(b) 90.6

(d) 442.9

7. If you make a salary of $43,200 in Arkansas, how much would you have to make in Alabama to keep the same standard of living? (a) $265.73

(b) $41,400.00

(d) $45,078.26

Unit 3D Test 4 (continued)

Name:

8. Calculate the income index for Arkansas using the median income from Tennessee as the reference value. (a) 103.6

(b) 109.5

(d) 91.3

9. Given that the Consumer Price Index was 72.6 in 1979 and 82.4 in 1980, find the inflation rate from 1979 to 1980. (a) 13.5%

(b) 11.9%

(d) 12.6%

10. The Consumer Price Index was 207.3 in 2007 and 240.0 in 2016. If a person earned $39,400 in 2007, how much did he need to earn in 2016 to maintain the same standard of living? (a) $34,031.75

(b) $45,615.05

(d) $165,874

Name:

Unit 3E Test 1

Date:

Use the information below for problems 1 – 2. In trials for a new drug product, data was collected for the FDA. Some participants were given a placebo while others were given the trial drug. The data collected is shown in the table. Showed Improvement Yes No Given trial drug Given placebo

22 31

47 20

1. What percentage of the 51 participants given the placebo showed improvement? What percentage of the 69 people who received the trial drug showed improvement?

2. What percentage of those who showed improvement received the trial drug?

Use the information below for questions 3 – 6. The 366 people in a study about the correlation between coffee and violence can be split into two groups, convicted felons and non-felons. The results break down as indicated in the following table. Violent

Coffee Drinker

Yes No

Felon Yes No

Non-felon Yes No

139 15

5 6

11 1

95 94

3. For non-felons, what percentage of the 100 coffee drinkers are violent, and what percentage of the 100 non-coffee drinkers are violent?

Unit 3E Test 1 (continued)

Name:

4. For coffee-drinking felons, what percentage are non-violent, and what percentage of the 16 felon noncoffee drinkers are non-violent?

5. Do coffee drinkers or non-coffee drinkers have the higher rate of violence within each category? Do you think that this is sufficient evidence to make a conclusion about a correlation between coffee and violence? Explain.

6. Consider the results from each category, felon and non-felon, as well as the results when the categories are combined. What design flaw in the study caused Simpson’s paradox to occur?

7. Two candidates for mayor of a large city differ in their accounts of the incumbent’s record on reducing crime. The incumbent claims that during his term violent crime has decreased, citing average annual homicide rates of 2.9 per 10,000 during the previous mayor’s administration and 2.5 per 10,000 during his own administration. The challenger claims that violent crimes have actually increased, citing an average of 161 homicides per year during the previous mayor’s administration and 175 homicides per year during the present administration. Explain how both candidates can be right.

Unit 3E Test 1 (continued)

Name:

Use the information below for questions 8 – 10. Suppose that a sobriety test is 95% accurate (it will correctly detect 95% of the people who are legally intoxicated and it will correctly identify 95% of the people who are within the legal blood alcohol limit). Each of 1000 drivers pulled over by law enforcement officers for dangerous driving last month was required to take the sobriety test. The test identified 100 drivers as being legally intoxicated, when, in fact, only 75 were legally intoxicated. When this sobriety test indicates that a driver is legally intoxicated, the officers administer other tests to be more certain of intoxication before arresting the driver, but if this sobriety test indicates that the driver’s blood alcohol is within the legal limit, no further tests are given. The data are given in the table.

Test identifies driver as legally intoxicated Test identifies driver as within the legal limit Total

Legally intoxicated Within the limit Total 74 26 100 1 899 900 75

925

1000

8. What percentage of legally intoxicated drivers were not identified by the sobriety test?

9. What percentage of drivers who were not legally intoxicated were falsely identified as being legally intoxicated?

10. What percentage of drivers identified as legally intoxicated by the test were actually within the legal blood alcohol limit?

Name:

Unit 3E Test 2

Date:

Use the information below for questions 1 – 2. The rapid test given in doctor’s offices to determine if someone has the H1N1 “swine” flu is known for having a high rate of false positives. Information from a study of 500 patients is below. Tested Positive Negative Really had H1N1 Did not have H1N1

76 9

124 291

1. What percentage of the patients with H1N1 tested negative? What percentage of those who tested negative have H1N1?

2. What percentage of those with H1N1 tested positive? What percentage of those who tested positive have H1N1?

3. Two candidates for mayor of a large city differ in their accounts of the incumbent’s record on job growth. The incumbent claims that during his term the job market has improved, citing a drop in the city’s unemployment rate from 2.8% to 1.7%. The challenger claims that the job situation has actually deteriorated, citing that over 50,000 jobs were lost and not replaced during the incumbent’s administration. Explain how both candidates can be right.

Unit 3E Test 2 (continued)

Name:

Use the information below for questions 4 – 7. The 425 women in the study about the correlation between abortion and breast cancer were split into two groups according to age, those under 40 and those 40 or older. The results break down as indicated in the following table.

Abortion

Yes No

Breast Cancer Under 40 40 or older Yes No Yes No 2 173 2 48 1 99 3 97

4. For women 40 or older, what percentage of the 50 women who have had an abortion have breast cancer, and what percentage of the 100 women who have not had an abortion have breast cancer?

5. For women under 40, what percentage of the 175 women who have had an abortion do not have breast cancer, and what percentage of the 100 women who have not had an abortion have breast cancer?

6. Which group has the higher rate of breast cancer within each age category? Do you think that this is sufficient evidence to make a conclusion about the alleged correlation? Explain.

7. Consider the results from each age group as well as the results when the age groups are combined. What design flaw in the study caused Simpson’s paradox to occur?

Unit 3E Test 2 (continued)

Name:

Use the information below for questions 8 – 10. Suppose that a pregnancy test is 89% accurate (it will correctly detect 89% of the women who are pregnant and it will correctly identify 89% of the women who are not pregnant). Of 1200 women who used the test, 250 were identified as pregnant while only 200 were actually pregnant. The data is given in the table. Pregnant Test indicates pregnant 182 Test indicates not pregnant 18 Total

200

Not pregnant Total 68 250 932 950 1000

1200

8. What percentage of pregnant women were not identified as pregnant by the test?

9. What percentage of women who were not pregnant was falsely identified as being pregnant?

10. What percentage of women not identified as pregnant by the test was not pregnant?

Name:

Unit 3E Test 3

Date:

Choose the correct answer to each problem. Use the information below for questions 1 – 2. A television producer tested her theory that watching her new television program improves a child’s reading ability. She designed a reading test and gave it to 500 children. She collected the information in the table. Test Passed Failed Watches the program

Yes No

163 46

87 204

1. What percentage of the 250 children who do not watch the program passed the test, and what percentage of the 250 children who watch the program failed the test? (a) 18.4% and 34.8%, respectively (c) 34.8% and 81.6%, respectively

(b) 34.8% and 18.4%, respectively (d) 81.6 % and 34.8%, respectively

2. Which of the following claims is best supported by the data in the table? (a) The program has no effect on a child’s reading ability. (b) The program improves a child’s reading ability. (c) The program hinders a child’s reading ability. (d) The program develops a child’s sense of community. Use the information below for questions 3 – 6. The 300 children in the study about the correlation between watching a television program and reading ability can be split into two groups according to age. The results break down as indicated in the following table. Test Age 5 Passed Failed Watches the program

Yes No

7 23

43 77

Age 7 Passed Failed 35 18

65 32

3. For 5-year olds, what percentage of the 50 children who watch the program passed the test, and what percentage of the 100 children who do not watch the program passed the test? (a) 16.3% and 29%, respectively (c) 14% and 23%, respectively

(b) 16.3% and 53.8%, respectively (d) 7% and 23%, respectively

Unit 3E Test 3 (continued)

Name:

4. For 7-year olds, what percentage of the 100 children who watch the program passed the test, and what percentage of the 50 children who do not watch the program passed the test? (a) 66% and 67%, respectively (c) 35% and 18%, respectively

(b) 35% and 36%, respectively (d) 53.8% and 56.3%, respectively

5. Which of the following best describes the results? (a) Within each age group, children who watch the program read much better than children who do not watch the program. (b) Within each age group, children who do not watch the program read much better than children who watch the program. (c) Within each age group, children who watch the program do better on the test, but the difference is minor. (d) Within each age group, children who do not watch the program do better on the test, but the difference is minor. 6. Consider the results from each age group as well as the results with the age groups combined. Which of the following most likely caused Simpson’s paradox to occur? (a) The children who watch the program do better on the reading test when 5-year olds and 7-year olds take the test in the same room, but the children who do not watch the program do better when the age groups are tested separately. (b) A different television program is actually responsible for the improved reading skills, but the reading test was not designed to distinguish between the effects of the two programs. (c) The children who watch the program are mostly 7-year olds whose reading skills would be expected to be further developed, while the children who do not watch the program are mostly 5-year olds, whose reading skills would be less developed. (d) Test scores will vary for a child each time he takes a test. The results showing that children who watch the program did better in a mixed age group than when separated by age are due to the randomness in the variation of scores. Use the information below for questions 7 – 9. Suppose that a colon cancer test is 97% accurate (it will correctly detect 97% of the patients who have colon cancer and it will correctly identify 97% of the patients who do not have colon cancer). Of 1500 patients who took the test, 79 tested positive for colon cancer while only 50 actually have colon cancer. The data is given in the table. Has cancer Does not have cancer Total Test result is positive 49 30 79 Test result is negative 1 1420 1421 Total 50 1450 1500 7. What percentage of patients with colon cancer tested negative? (a) About 2%

(b) About 3%

(d) About 98%

Unit 3E Test 3 (continued)

Name:

8. What percentage of patients who tested positive do not have colon cancer? (a) About 3%

(b) About 38%

(d) About 97%

9. What percentage of patients who do not have colon cancer tested positive? (a) About 2%

(b) About 3%

(d) About 97%

10. Two candidates for governor of a state differ in their accounts of the state’s economy during the incumbent’s term. The incumbent claims that during his four-year term the economy has improved, citing a rise in the median household income from $33,000 to $34,500. The challenger claims that the economy has declined, citing that the buying power of families in the state has declined during the four years. Which of the following best explains how both candidates can be right? (a) Candidates always tell the truth by nature, so anything either candidate says is automatically true. (b) Though the median household income increased, prices increased by a greater percent, meaning that the greater income buys less goods and services. (c) The incumbent is referring to the economy within the state, while the challenger is referring to the national economy. (d) It is not possible for both candidates to be right; one of them is obviously lying.

Name:

Unit 3E Test 4

Date:

Choose the correct answer to each problem. Use the information below for questions 1 - 2. An education specialist tested her theory that home schoolers do not learn mathematics as well as students taught in the traditional classroom setting. She designed a mathematics test and gave it to 800 children. She collected the information in the table. Test Passed

Failed

176 275

224 125

Home school Traditional

1. What percentage of the 400 traditional students passed the test, and what percentage of the 400 home schoolers failed the test? (a) About 56.0% and 68.8%, respectively (c) About 68.8% and 56.0%, respectively

(b) About 68.6% and 56.0%, respectively (d) About 56.0% and 68.6%, respectively

2. Which of the following claims is best supported by the data in the table? (a) Home schoolers do better on mathematics tests than traditional students. (b) Home schoolers and traditional students do about the same on mathematics tests. (c) Traditional students do better on mathematics tests than home schoolers. (d) All students have a perfect understanding of mathematics. Use the information below for questions 3 – 6. The 800 children in the study about the correlation between home schooling and learning mathematics can be split into two groups according to grade level. The results break down as indicated in the following table. Test 8th grade Passed Failed Home school Traditional

78 25

222 75

12th grade Passed Failed 98 287

2 13

3. For 8th graders, what percentage of the 300 home schoolers failed the test, and what percentage of the 100 traditional students passed the test? (a) About 75.7% and 24.3%, respectively (c) About 74.0 % and 25.0%, respectively

(b) About 35.1% and 33.3%, respectively (d) About 19.5% and 6.3%, respectively

Unit 3E Test 4 (continued)

Name:

4. For 12th graders, what percentage of the 100 home schoolers passed the test, and what percentage of the 300 traditional students passed the test? (a) About 25.4% and 74.6%, respectively (c) About 24.5% and 71.2%, respectively

(b) About 98.0% and 95.7%, respectively (d) About 34.1% and 65.9%, respectively

5. Which of the following best describes the results? (a) Within each grade level, home schoolers do much better in mathematics than traditional students. (b) Within each grade level, traditional students do much better in mathematics than home schoolers. (c) Within each grade level, home schoolers do better on the test, but the difference is minor. (d) Within each grade level, traditional students do better on the test, but the difference is minor. 6. Consider the results from each grade level as well as the results with the grades combined. Which of the following most likely caused Simpson’s paradox to occur? (a) Home schoolers do better on math tests when 8th graders and 12th graders take the tests in separate rooms, but traditional students do better when they are in a room with both 8th graders and 12th graders. (b) A new mathematics curriculum is responsible for the dramatically higher test scores among traditional students. If home schoolers used this curriculum, they would learn mathematics just as well. (c) Test scores will vary for a child each time he takes a test. The results showing that home schoolers did better when separated by grade level are due to the randomness in the variation of scores. (d) The group of home schoolers is comprised of mostly 8th graders, while the group of traditional students is mostly 12th graders, who would be expected to do better on the test than 8th graders. Use the information below for questions 7 – 9. Suppose that a pregnancy test is 95% accurate (it will correctly detect 95% of the women who are pregnant and it will correctly identify 95% of the women who are not pregnant). Of 750 women who took the test, 129 tested positive for pregnancy while only 115 are actually pregnant. The data are given in the table. Pregnant

Not pregnant Total

Test result is positive Test result is negative

111 4

18 617

129 621

Total

115

635

750

7. What percentage of women who are not pregnant tested positive? (a) About 2.8%

(b) About 5.0%

(d) About 95%

8. What percentage of non-pregnant women tested negative? (a) About 0.6%

(b) About 97%

(d) About 95%

Unit 3E Test 4 (continued)

Name:

9. What percentage of women who tested negative are really pregnant? (a) About 0.6%

(b) About 3.5%

(d) About 86%

10. Two candidates for governor of a state differ in their claims on the quality of education over the incumbent’s term. The incumbent claims that per capita spending on education has increased during his term, so the quality of education has improved. The challenger claims that the per student spending on education has decreased during the incumbent’s term. Which of the following best explains their claims? (a) Both candidates have made up their claims in order to win the election, because all politicians are liars. (b) Only the incumbent’s claim is correct. If spending increases per capita, it must increase per student. (c) Both claims may be correct. While the per capita spending has increased, the number of students may have increased much more than the overall population. Thus, per student spending would have decreased. (d) Only one of the claims can be correct. One of the candidates must be lying.

Name:

Unit 4A Test 1

Date:

1. Compute the annual cost of each of the following expenses: $18 a week on lottery tickets; $150 per month on gasoline. Complete the sentence: On an annual basis, the first set of expenses is % of the second set of expenses.

Elise maintains an average monthly balance on her credit card of about $1220. Her credit card company charges 18% annual interest rate. How much is she spending on credit card interest per year?

3. Prorate the given expenses to find the monthly cost. Valerie is a big music fan. She downloads an album each week at a cost of about $10. She also attends two concerts each year, with a cost of about $75 for each ticket.

4. Prorate the given expenses to find the monthly cost. Fred pays $6200 for each of two semesters to attend a local college. He pays an additional $560 for books each semester, summer school tuition is $1240 and books for summer school are $110.

Unit 4A Test 1 (continued)

Name:

5. Find the net monthly cash flow. (1 month = 4 weeks, 1 year = 2 semesters) Income Job $800 per week Loan $3000 per semester

Expenses Rent $650 per month Groceries $60 per week Tuition and fees $2500 per semester Miscellaneous $150 per week

6. Allison is 29-years old and her monthly after-tax salary is $3600. She spends an average of $250 per month on entertainment. The national average, for those under 35, on entertainment spending is 5% of income. What percent of Allison’s income does she spend on entertainment? How does Allison’s spending compare with the national average?

7. You drive an average of 500 miles per week in a car that gets 22 miles per gallon. With gasoline priced at $2.40 per gallon, how much would you save each week if you had a car that got 34 miles per gallon?

8. Your automobile insurance semiannual premium is $850 and you have a $750 deductible per incident. In a particularly bad year, you had two collisions. The total repair costs were $1700 and $2400. What was your out-of-pocket expense?

Name:

Unit 4A Test 2

Date:

1. Compute the annual cost of each of the following expenses: $16 a week on soft drinks; $170 per month on renter’s insurance. Complete the sentence: On an annual basis, the first set of expenses is % of the second set of expenses.

2. Debbie maintains an average monthly balance on her credit card of about $1250. Her credit card company charges an APR of 21%. How much is she spending on credit card interest per year?

3. Prorate the given expenses to find the monthly cost. Jason loves video games. With tax, he spends about $76 each month on games. He also subscribes to two gamer magazines, each of which cost him about $40 per year.

4. Prorate the given expenses to find the monthly cost. Mike has an annual expense of $646 for life insurance, a semi-annual car insurance premium of $550, and monthly charges of $90 for health insurance.

Unit 4A Test 2 (continued)

Name:

5. Find the net monthly cash flow. (1 month = 4 weeks, 1 year = 2 semesters) Income Job $700 per week Loan $5000 per semester

Expenses Rent $750 per month Groceries $65 per week Tuition and fees $2750 per semester Miscellaneous $150 per week

6. Tom is 45 and pays $2142 on his mortgage each month while his total take-home pay is $5950 per month. The national average, for those aged 35 – 64, on housing costs is 35% of income. What percent of Tom’s income does he spend on housing? How does Tom’s housing cost compare to the national average?

7. You drive an average of 400 miles per week in a car that gets 26 miles per gallon. With gasoline priced at $2.45 per gallon, how much would you save each week if you had a car that got 37 miles per gallon?

8. According to one estimate, the average cost of having a baby is $7800, assuming there are no complications. If your health insurance has an annual premium of $2200, carries an $1800 yearly deductible, plus a one-time hospital co-payment of $300, what is your out-of-pocket expense to have the baby?

Name:

Unit 4A Test 3

Date:

Choose the correct answer to each problem. 1. Compute the annual cost of each of the following expenses: $14 a week on snacks; $125 per month on pet supplies. Complete the sentence: On an annual basis, the first set of expenses is % of the second set of expenses. (a) 6.5

(b) 3.4

(d) 44.8

2. Rob maintains an average monthly balance on his credit card of about $1500. His credit card company charges 21% annual interest. How much is Rob spending on credit card interest per year? (a) $31.50

(b) $26.26

(d) $315.00

3. Sue enjoys her coffee. She spends $7.50 per day at the coffee shop each weekday. She brews her own on the weekends and spends $40 a month on the ground coffee. How much is Sue spending annually on coffee? (a) $2430

(b) $3210

(d) $840

4. Mike has an annual expense of $846 for life insurance, a semi-annual car insurance premium of $750, and monthly charges of $90 for health insurance. Prorate the given expenses to find the monthly cost. (a) $140.50

(b) $585.50

(d) $535.50

5. Find the net monthly cash flow. (1 month = 4 weeks, 1 year = 2 semesters) Income Job $550 per week Loan $3500 per semester

(a) $805

Expenses Rent $700 per month Groceries $55 per week Tuition and fees $2750 per semester Miscellaneous $150 per week (b) -$805

(d)

-$711.25

6. Tom is 45 and pays $2042 on his mortgage each month while his total take-home pay is $5950 per month. The national average, for those aged 35 – 64, on housing costs is 35% of income. What percent of Tom’s income does he spend on housing? Compare Tom’s housing costs to the national average. (a) 0.7% more

(b) 0.7% less

(d) 32.1% less

7. You drive an average of 750 miles per week in a car that gets 28 miles per gallon. With gasoline priced at $3.40 per gallon, what would be the difference in total weekly cost for gasoline if you start driving an SUV that gets 20 miles per gallon? (a) $145.72 more

(b) $36.43 less

(d) $36.43 more

8. Your automobile insurance semiannual premium is $750 and you have a $1050 deductible per incident. In a particularly bad year, you had two collisions. The total repair costs were $2700 and $1400. What was your out-of-pocket expense? (a) $5600

(b) $4850

(d) $2850

Name:

Unit 4A Test 4

Date:

Choose the correct answer to each problem. 1. Compute the annual cost of each of the following expenses: $16 a week on snacks; $150 per month on pet supplies. Complete the sentence: On an annual basis, the first set of expenses is % of the second set of expenses. (a) 6.5

(b) 3.4

(d) 46.2

2. Rob maintains an average monthly balance on his credit card of about $1800. His credit card company charges 18% annual interest. How much is Rob spending on credit card interest per year? (a) $324

(b) $26.26

(d) $315.00

3. Sue enjoys her coffee. She spends $9.50 per day at the coffee shop each weekday. She brews her own on the weekends and spends $25 a month on the ground coffee. How much is Sue spending annually on coffee? (a) $2430

(b) $2770

(d) $840

4. Mike has an annual expense of $700 for life insurance, a semi-annual car insurance premium of $846, and monthly charges of $90 for health insurance. Prorate the given expenses to find the monthly cost. (a) $136.33

(b) $218.83

(d) $289.33

5. Find the net monthly cash flow. (1 month = 4 weeks, 1 year = 2 semesters) Income Job $250 per week Loan $3500 per semester (a) -$525

Expenses Rent $750 per month Groceries $75 per week Tuition and fees $2750 per semester Miscellaneous $150 per week (b) $525 (c) $2391.67

(d)

-$816.66

6. Tom is 45 and pays $2619 on his mortgage each month while his total take-home pay is $4950 per month. The national average, for those aged 35 – 64, on housing costs is 35% of income. What percent of Tom’s income does he spend on housing? Compare Tom’s housing costs to the national average. (a) 17.9% more

(b) 17.9% less

(d) 23.1% less

7. You drive an average of 250 miles per week in a car that gets 28 miles per gallon. With gasoline priced at $2.40 per gallon, what would be the difference in total weekly cost for gasoline if you start driving an SUV that gets 20 miles per gallon? (a) $19.20 less

(b) $8.57 less

(d) $19.20 more

8. According to one estimate, the average cost of having a baby is $9700, assuming there are no complications. If your health insurance has an annual premium of $2200, carries an $1800 yearly deductible, plus a one-time hospital co-payment of $300, what is your out-of-pocket expense to have the baby? (a) $4300

(b) $7600

(d) $9800

Name:

Unit 4B Test 1

Date:

1. Suppose that you invest $1800 in an account that earns simple interest at an APR of 5.2%. Determine the accumulated balance after 5 years.

2. Determine the accumulated balance: $5000 is invested at an APR of 1.6% compounded annually for 15 years.

3. Determine the accumulated balance: $1500 invested at an APR of 3.6%, compounded quarterly for 7 years.

4. Determine the accumulated balance: $7500 invested at an APR of 4%, compounded monthly for 18 years.

5. Suppose that your savings account earns interest at an APR of 2.8%, compounded daily. Determine the annual percentage yield (APY). State your answer to the nearest hundredth of a percent.

Unit 4B Test 1 (continued)

Name:

6. Determine the accumulated balance: $1200 invested in an account that earns interest at an APR of 3.7%, compounded continuously for 5 years.

7. Suppose that you invest in an account with an APR of 3.9%, compounded continuously. Determine the annual percentage yield (APY). State your answer to the nearest hundredth of a percent.

8. Suppose that you want to have $7200 to put toward a down payment on a house in 5 years. How much will you need to deposit now if you can obtain an APR of 5.4%, compounded semiannually? Assume that no additional deposits are to be made to the account.

9. Suppose that you want to have a $50,000 retirement fund after 40 years. How much will you need to deposit now if you can obtain an APR of 3.3%, compounded continuously? Assume that no additional deposits are to be made to the account.

Name:

Unit 4B Test 2

Date:

1. Suppose that you invest $900 in an account that earns simple interest at an APR of 5.7%. Determine the accumulated balance after eight years.

2. Determine the accumulated balance: $12,000 invested at an APR of 4.1%, compounded annually for 6 years.

3. Determine the accumulated balance: $500 invested in a bond that earns interest at an APR of 3.9%, compounded quarterly for 50 years.

4. Determine the accumulated balance: $5700 in an account that earns interest at an APR of 1.2%, compounded monthly for 10 years.

5. Suppose that your savings account earns interest at an APR of 1.8%, compounded daily. Determine the annual percentage yield (APY). State your answer to the nearest hundredth of a percent.

Unit 4B Test 2 (continued)

Name:

6. Determine the accumulated balance: $2600 invested in an account that earns interest at an APR of 6.2%, compounded continuously for 7 years.

7. Determine the annual percentage yield (APY) for an account with an APR of 6.9%, compounded monthly. State your answer to the nearest hundredth of a percent.

8. Sara needs to save $6700 in 5 years for the down payment on a house. She found a savings account that compounds interest annually at an APR of 4.8%. How much will Sara need to deposit now to meet her goal? Assume that no additional deposits are to be made to the account.

9. Suppose that you want to start a retirement fund for your newborn child so that she has one million dollars at age 65, when she retires. How much will you need to deposit now if you can obtain an APR of 9.5%, compounded continuously? Assume that no additional deposits are to be made to the account.

Name:

Unit 4B Test 3

Date:

Choose the correct answer to each problem. 1. Suppose that you invest $4200 in an account that earns simple interest at an APR of 5.2%. Determine the accumulated balance after 5 years. (a) $218.40

(b) $5292.00

(d) $1092.00

2. Suppose that you invest $23,000 in an account that earns interest at an APR of 3.2%, compounded annually. Determine the accumulated balance after 8 years. (a) $29,591.39

(b) $29,680.07

(d) $29,709.98

3. Suppose that you invest $217 in an account that earns interest at an APR of 6%, compounded quarterly. Determine the accumulated balance after 16 years. (a) $566.74

(b) $565.38

(d) $551.26

4. Suppose that you invest $5873 in an account that earns interest at an APR of 4.4%, compounded monthly. Determine the accumulated balance after 7 years. (a) $7986.90

(b) $8145.35

(d) $8160.99

5. Suppose that your savings account earns interest at an APR of 6.7%, compounded quarterly. Determine the annual percentage yield (APY), to the nearest hundredth of a percent. (a) 8.58%

(b) 7.11%

(d) 6.87%

6. Suppose that you invest $1600 in an account that earns interest at an APR of 7.4%, compounded continuously. Determine the accumulated balance after 6 years. (a) $1718.40

(b) $1722.89

(d) $2494.29

7. Suppose that you invest in an account with an APR of 6.1%, compounded continuously. Determine the annual percentage yield (APY), to the nearest hundredth of a percent. (a) 4.95%

(b) 6.29%

(d) 5.20%

8. Suppose that you want to have a $90,000 retirement fund after 35 years. How much will you need to deposit now if you can obtain an APR of 12%, compounded daily? Assume that no additional deposits are to be made to the account. (a) $1284.29

(b) $1349.60

(d) $1435.59

9. A savings account earns 4.3%, compounded continuously. How much would you need to deposit now in order to have a balance of $25,000 after 3 years? Assume that no additional deposits are to be made. (a) $1244.68

(b) $21,974.35

(d) $28,442.25

Name:

Unit 4B Test 4

Date:

Choose the correct answer to each problem. 1. Suppose that you invest $2500 in an account that earns simple interest at an APR of 6.8%. Determine the accumulated balance after 15 years. (a) $4206.70

(b) $5050.00

(d) $63,000

2. Suppose that you invest $18,000 in an account that earns interest at an APR of 3.7%, compounded annually. Determine the accumulated balance after 6 years. (a) $22,474.03

(b) $22,466.61

(d) $22,384.38

3. Suppose that you invest $500 in an account that earns interest at an APR of 2.75%, compounded quarterly. Determine the accumulated balance after 5 years. (a) $572.64

(b) $573.43

(d) $2569.46

4. Suppose that you invest $8645 in an account that earns interest at an APR of 5.4%, compounded monthly. Determine the accumulated balance after 9 years. (a) $14,038.42

(b) $14,039.73

(d) $12,846.47

5. Suppose that your savings account earns interest at an APR of 3.2%, compounded daily. Determine the annual percentage yield (APY), to the nearest hundredth of a percent. (a) 3.20%

(b) 3.25%

(d) 4.20%

6. Suppose that you invest $1429 in an account that earns interest at an APR of 7.2%, compounded continuously. Determine the accumulated balance after 8 years. (a) $2542.24

(b) $2542.06

(d) $2537.69

7. Suppose that you invest $7000 in an account with an APR of 7.4%, compounded continuously. Determine the annual percentage yield (APY), to the nearest hundredth of a percent. (a) 7.68%

(b) 7.63%

(d) 7.90%

8. Suppose that you want to have a $200,000 retirement fund after 40 years. How much will you need to deposit now if you can obtain an APR of 9%, compounded daily? Assume that no additional deposits are to be made to the account. (a) $542.57

(b) $4569.71

(d) $96367.52

9. A savings account earns 5.2%, compounded continuously. How much would you need to deposit now in order to have a balance of $8000 after 2 years? Assume that no additional deposits are to be made. (a) $7209.80

(b) $7209.10

(d) $7354.20

Name:

Unit 4C Test 1

Date:

1. Suppose you set up a new IRA (individual retirement account) that pays an APR of 5.1%, compounded monthly. If you contribute $150 per month for 15 years, how much will the IRA contain at the end of that time?

2. Brandi deposits $75 at the end of each month into an account with an APR of 7% for 10 years. (Assume that the payment period is the same as the compounding period.) How much will the account contain at the end of the period? How much did Brandi deposit?

3. Suppose you want your son’s college fund to contain $150,000 after 15 years. If you can get an APR of 4.3%, compounded monthly, how much should you deposit at the end of each month

4. Suppose you have 18 months in which to save $2900 for a vacation cruise. If you can earn an APR of 2.3%, compounded monthly, how much should you deposit at the end of each month?

Unit 4C Test 1 (continued)

Name:

5. Suppose that you are 25 years old now, and you would like to retire at the age of 55. Furthermore, you would like to have a retirement fund from which you can draw an income of $52,000 per year—forever! You plan to reach this goal by making monthly deposits into an investment plan. How much do you need to deposit each month? Assume an APR of 4.3%, both as you pay into the retirement fund and when you collect from it later.

6. Four years after paying $3500 for some shares of a risky stock, you sell the shares for $5000. Find the total and annual return (to the nearest hundredth of a percent) on your investment.

7. Johnson and Johnson closed at $145.76 with a P/E ratio of 25.33. What were the earnings per share for Johnson and Johnson?

8. Calculate the current yield on a $10,000 Treasury bond with a coupon rate of 8% that has a market value of $9200.

Name:

Unit 4C Test 2

Date:

1. Your savings account pays an APR of 2.3%. If you deposit $1200 at the end of each month for 18 years, what will be the accumulated balance in the account?

2. Suppose you set up a new IRA (individual retirement account) that pays an APR of 7%, compounded monthly. If you contribute $160 at the end of each month for 27 years, how much will the IRA contain at the end of that time? How much money did you actually deposit?

3. Suppose you want your daughter’s college fund to contain $120,000 after 16 years. If you can get an APR of 4%, compounded monthly, how much should you deposit at the end of each month?

4. Suppose you have 19 months in which to save $5200 for a vacation cruise. If you can earn an APR of 3.8%, compounded monthly, how much should you deposit at the end of each month?

Unit 4C Test 2 (continued)

Name:

5. Suppose that you are 29 years old now, and you would like to retire at the age of 59. Furthermore, you would like to have a retirement fund from which you can draw an income of $75,000 per year—forever! You plan to reach this goal by making monthly deposits into an investment plan. How much do you need to deposit each month? Assume an APR of 4.5%, both as you pay into the retirement fund and when you collect from it later.

6. Four years after paying $7500 for some shares of a risky stock, you sell the shares for $5500. Find the total and annual return (to the nearest hundredth of a percent) on your investment.

7. Suppose you own 150 shares of Procter and Gamble. If the newspaper lists a dividend of $0.17 for this stock for last quarter, what total dividend payment might you expect this year?

8. Name three investment considerations.

9. Compute the annual interest you would earn on a $5000 Treasury bond with a current yield of 3.125% that is quoted at 112 points.

Name:

Unit 4C Test 3

Date:

Choose the correct answer to each problem. 1. Suppose you set up a new IRA (individual retirement account) that pays an APR of 8.2%, compounded monthly. If you contribute $130 per month for 11 years, how much will the IRA contain at the end of that time? (a) $27,718.12

(b) $29,833.18

(d) $34,830.65

2. Suppose you want your daughter’s college fund to contain $125,000 after 14 years. If you can get an APR of 7.8%, compounded monthly, how much should you deposit at the end of each month? (a) $398.54

(b) $406.64

(d) $476.83

3. Suppose you have 15 months in which to save $1800 for a vacation cruise. If you can earn an APR of 3.7%, compounded monthly, how much should you deposit at the end of each month? (a) $117.43

(b) $121.78

(d) $132.47

4. Suppose that you are 26 years old now, and you would like to retire at the age of 63. Furthermore, you would like to have a retirement fund from which you can draw an income of $65,000 per year—forever! You plan to reach this goal by making monthly deposits into an investment plan. How much do you need to deposit each month? Assume an APR of 5%, both as you pay into the retirement fund and when you collect from it later. (a) $1015.23

(b) $1059.82

(d) $1365.40

5. In general, which of the following types of investments carries the most risk? (a) Small company stocks (c) Long-term corporate bonds

(b) Large company stocks (d) U.S. Treasury bills

6. Three years after paying $11,500 for some shares of a risky stock, you sell the shares for $7000. Find the total return (to the nearest hundredth of a percent) on your investment. (a) –15.25%

(b) -64.29%

(d) –39.13%

7. Six years after buying 250 shares of a certain stock for $38 per share, you sell the stock for $15,000. Find the annual return (to the nearest hundredth of a percent) on your investment. (a) 36.67%

(b) 170.84%

(d) 7.91%

8. Suppose you own 225 shares of Microsoft. If the newspaper lists a dividend of $.13 for this stock for last quarter, what total dividend payment might you expect this year? (a) $29.25

(b) $104

(d) $117

9. Calculate the yield on a $1000 T-bond with a coupon rate of 4.50% that has a market value of $1064. (a) 4.22%

(b) 4.23%

(d) 4.79%

Name:

Unit 4C Test 4

Date:

Choose the correct answer to each problem. 1. Suppose you set up a new IRA (individual retirement account) that pays an APR of 5.2%, compounded monthly. If you contribute $160 at the end of each month for 25 years, how much will the IRA contain at the end of that time? (a) $98,178.67

(b) $94,203.70

(d) $4215.08

2. Suppose you want your son’s college fund to contain $105,000 after 16 years. If you can get an APR of 3.7%, compounded monthly, how much should you deposit at the end of each month? (a) $6412.07

(b) $482.76

(d) $401.70

3. Suppose you have 9 months in which to save $2700 for a vacation cruise. If you can earn an APR of 4.8%, compounded monthly, how much should you deposit at the end of each month? (a) $274.79

(b) $295.23

(d) $356.32

4. Suppose that you are 38 years old now, and you would like to retire at the age of 65. Furthermore, you would like to have a retirement fund from which you can draw an income of $54,000 per year—forever! How much do you need to deposit each month to reach this goal? Assume an APR of 6%, both as you pay into the retirement fund and when you collect from it later. (a) $982.64

(b) $993.45

(d) $1115.87

5. Five years after paying $11,000 for some shares of a risky stock, you sell the shares for $6500. Find the total return (to the nearest hundredth of a percent) on your investment. (a) –9.99%

(b) –11.10%

(d) –40.91%

6. Three years after buying 500 shares of a certain stock for $23 per share, you sell the stock for $17,000. Find the annual return (to the nearest hundredth of a percent) on your investment. (a) 32.35%

(b) 47.83%

(d) 13.92%

7. Suppose you own 300 shares of General Electric. In the last year, GE paid out dividends of $1.03 per share. What total dividend payment might you expect this year? (a) $330.90

(b) $309

(d) $291.26

8. In general, which of the following types of investments carries the least risk? (a) Small company stocks (c) Long-term corporate bonds

(b) Large company stocks (d) U.S. Treasury bills

9. Calculate the yield on a $1000 T-bond with a coupon rate of 2.375% that has a market value of $1028. (a) 3.28%

(b) 2.30%

(d) 2.32%

Name:

Unit 4D Test 1

Date:

1. Consider a student loan of $42,000 with an APR of 5% for 10 years. Find: a) the monthly payment; b) the total amount paid on the loan; c) percent of total amount that went toward the principal; d) percent of the total amount paid that went toward interest.

2. Calculate the monthly payments for a home mortgage of $250,000 with a fixed APR of 4.2% for 30 years. Calculate the total amount paid for the house.

3. Calculate the monthly payments for a home mortgage of $255,000 with a fixed APR of 6.8% for 15 years. Calculate the total amount paid for the house.

4. Suppose you take out an auto loan for $25,500 over a period of six years at an APR of 7.5%. Determine your monthly payments.

Unit 4D Test 1 (continued)

Name:

5. Suppose you have just obtained a 30-year home mortgage in the amount of $74,000 at an APR of 4.3%. Find the required monthly payment and also the monthly payment that you would need to make in order to pay off the loan in 20 years. How much would you save in interest charges by paying off the loan in 20 years?

6. Suppose you have a balance of $6400 on your credit card, which charges an APR of 24%. Assume that you charge no additional expenses to the card and you want to pay off the balance in 2 years of monthly payments. What is the total amount of interest you will end up paying?

7. Consider the following pair of choices for a $153,000 mortgage. Calculate the monthly payment and total closing costs for each choice. Explain which loan you would choose and why. Choice 1: a 30-year fixed-rate loan at 4.3% with $1500 closing cost and no points Choice 2: a 30-year fixed-rate loan at 3.8% with closing costs of $1200 and 2 points

Name:

Unit 4D Test 2

Date:

1. Consider a student loan of $18,000 with an APR of 6% for 8 years. Find: a) the monthly payment; b) the total amount paid on the loan; c) percent of total amount that went toward the principal; d) percent of the total amount paid that went toward interest.

2. Calculate the monthly payments for a home mortgage of $174,000 with a fixed APR of 4.2% for 30 years. Calculate the total amount paid for the house.

3. Calculate the monthly payments for a home mortgage of $174,000 with a fixed APR of 5.3% for 15 years. Calculate the total amount paid for the house.

4. Suppose you take out an auto loan for $14,000 over a period of 4 years at an APR of 6.5%. Determine your monthly payments.

Unit 4D Test 2 (continued)

Name:

5. Suppose you have just obtained a 30-year home mortgage in the amount of $266,000 at an APR of 6.5%. Find the required monthly payment. Then compute the monthly payment that you would need to make in order to pay off the loan in 20 years. How much would you save in interest charges by paying off the loan in 20 years?

6. Suppose you have a balance of $4300 on your credit card, which charges an APR of 15%. Assume that you charge no additional expenses to the card and you want to pay off the balance in one year of monthly payments. What is the total amount of interest you will end up paying?

7. Assume you have the following loans. Compute the monthly payment and the total payoff for each loan. Loan Amount

APR

Duration

$5500

5.1%

4 years

$19,500

6.5%

9 years

$8000

7.3%

7 years

Monthly Payments

Total Payoff

8. Assume you consolidate the loans listed above into one loan with an APR of 5.9% for 6 years. Find the monthly payment, the total payoff for the consolidated loan, and how much more or less you would pay with the consolidation compared to the separate loans.

Name:

Unit 4D Test 3

Date:

Choose the correct answer to each problem. 1. Consider a typical 30-year fixed-rate mortgage. During which of the following years is the highest portion of each payment applied toward interest? (a) First year

(b) Tenth year

(d) Thirtieth year

2. Suppose you apply for a 7-year loan in the amount of $17,000 with an APR of 10%. Your monthly payment is $282.22. Determine the total amount of interest paid over the seven years. (a) $6706.48

(b) $9706.48

(d) $23,706.48

3. Calculate the monthly payments for a home mortgage of $98,000 with a fixed APR of 6.25% for 30 years. (a) $425.35

(b) $561.46

(d) $716.31

4. Suppose you take out an auto loan for $19,800 over a period of four years at an APR of 5.5%. To the nearest $100, determine the total amount of your payments over the term of the loan. (a) $22,000

(b) $22,100

(d) $22,300

5. Suppose you have just obtained a 30-year home mortgage in the amount of $292,000 at an APR of 5.75%. By finding the required monthly payment and also the monthly payment that you would need to make in order to pay off the loan in 20 years, determine the amount you would save in interest charges by paying off the loan in 20 years. (a) $83,052.00

(b) $120,392.40

(d) $124,578.00

6. Suppose you have a balance of $2600 on your credit card, which charges an APR of 20%. If you want to pay off the balance in 15 months, how much should you pay each month? Assume that you charge no additional expenses to the card. (a) $102.51

(b) $164.79

(d) $143.92

7. The following table shows the expenses and payments on a credit card for 3 months, starting with an initial balance of $630. Use the table as a guide to help you find the balance at the end of the three months, to the nearest $10. Assume that the APR for the credit card is 14%, and that the interest for a given month is based on the balance for the previous month. Month

Payment

Expenses

Interest

Balance

$630.00

$410

$180

$60

$680

$620

$340

(a) $750

(b) $760

(d) $7

Name:

Unit 4D Test 4

Date:

(b) Tenth year

(d) Thirtieth year

2. Suppose you apply for a 10-year loan in the amount of $37,000 with an APR of 7% and your monthly payment is $429.60. Determine the total amount of interest paid over the ten years. (a) $5960.00

(b) $11,962.00

(d) $24,862.40

3. Calculate the monthly payments for a home mortgage of $189,000 with a fixed APR of 5.875% for 15 years. (a) $1111.69

(b) $1265.72

(d) $1888.96

4. Suppose you take out an auto loan for $15,700 over a period of 5 years at an APR of 9%. To the nearest $100, determine the total amount of your payments over the term of the loan. (a) $19,600

(b) $19,700

(d) $19,900

5. Suppose you have just obtained a 30-year home mortgage in the amount of $84,000 at an APR of 7.9%. By finding the required monthly payment and also the monthly payment that you would need to make in order to pay off the loan in 20 years, determine the amount you would save in interest charges by paying off the loan in 20 years. (a) $43,834.40

(b) $48,280.00

(d) $74,786.50

6. Suppose you have a balance of $5400 on your credit card, which charges an APR of 18%. If you want to pay off the balance in 18 months, how much should you pay each month? Assume that you charge no additional expenses to the card. (a) $294.54

(b) $329.30

(d) $354.00

7. The following table shows the expenses and payments on a credit card for 3 months, starting with an initial balance of $820. Use the table as a guide to help you find the balance at the end of the three months, to the nearest $10. Assume that the APR for the credit card is 19%, and that the interest for a given month is based on the balance for the previous month. Month

Payment

Expenses

Interest

Balance

$820.00

$340

$740

$180

$270

$75

$530

(a) $1790

(b) $1800

(d) $1820

Name:

Unit 4E Test 1

Date:

In the following problems, assume 2021 values listed in the table of marginal tax rates below. Tax Rate 10% 12% 22% 24% 32% 35% 37% Standard deduction

Married Filing Jointly up to $9950 up to $19,900 up to $40,525 up to $81,050 up to $86,375 up to $172,750 up to $164,925 up to $329,850 up to $209,425 up to $418,850 up to $523,600 up to $628,300 above $523,600 above $628,300 $12,550 $25,100 Single

Married Filing Separately up to $9950 up to $40,525 up to $86,375 up to $164,925 up to $209,425 up to $314,150 above $314,150 $12,550

Head of Household up to $14,200 up to $54,200 up to $86,350 up to $164,900 up to $209,400 up to $523,600 above $523,600 $18,800

1. Roger is single and earned wages of $53,000 in 2021. He received $1700 interest from a savings account and contributed $3600 to a tax-deferred retirement plan. He is entitled to deductions totaling $18,000. Find his gross income, adjusted gross income, and taxable income.

2. A married couple who file jointly have the following deductions: $6600 in mortgage interest, $3000 in charitable donations, and $1686 in state income taxes. Should the couple itemize or take the standard deduction? Explain.

3. Juan is single and had a taxable income of $48,600 in 2021. Compute the marginal tax owed.

Unit 4E Test 1 (continued)

Name:

4. Robert and Mary are married and filing jointly. They have an adjusted gross income of $198,500 in 2021. Compute the marginal tax owed and their effective tax rate based on their taxable income.

5. A married couple who itemize deductions are in the 32% marginal tax bracket. How much will their marginal tax bill be reduced if they make a $3000 donation to charity?

6. Olive is single and earned $52,500 in wages in 2021. She had no other income, made no contributions to retirement plans, and took the standard deduction. How much did Olive owe in FICA (7.65%) and marginal taxes combined? Find Olive’s overall tax rate.

7. In 2021, a married retired couple’s income consisted solely of $240,000 in long term capital gains. They claimed $32,000 in itemized deductions and filed taxes jointly. How much marginal tax did they owe?

Name:

Unit 4E Test 2

Date:

In the following problems, assume 2021 values listed in the table of marginal tax rates below. Tax Rate 10% 12% 22% 24% 32% 35% 37% Standard deduction

Married Filing Separately up to $9950 up to $40,525 up to $86,375 up to $164,925 up to $209,425 up to $314,150 above $314,150 $12,550

Head of Household up to $14,200 up to $54,200 up to $86,350 up to $164,900 up to $209,400 up to $523,600 above $523,600 $18,800

1. Diana is married, but she and her husband filed separate income taxes in 2021. She earned wages of $32,000, and she received $500 in interest from savings accounts. She also contributed $1600 to a taxdeferred retirement plan, and had itemized deductions totaling $7220. Find her gross income, adjusted gross income, and taxable income.

2. Suppose a married couple filed jointly and had a taxable income of $148,700 in 2021. Compute the marginal tax owed.

3. In 2021, Jerry had an adjusted gross income of $65,800. He filed as Head of Household and claimed the standard deduction. Find the amount of his marginal tax bill and his effective tax rate based on his taxable income.

Unit 4E Test 2 (continued)

Name:

4. Penny and Irving have each computed that they owe $5600 in federal income tax. Penny installed solar panels that qualify for a nonrefundable tax credit of $6300. Irving qualifies for $6300 in child tax credit, which is refundable. Compute the final tax bill for Penny and for Irving. Explain.

5. Suppose that Eugene is single, earns well into the 32% tax bracket, and that his apartment rents for $1500 per month. He is considering a mortgage with payments of $1900 per month, of which an average of $1700 per month would be deductible interest and taxes during the first year. Including savings through the mortgage deduction, determine the actual cost of the mortgage each month and whether the monthly rent is greater than or less than the monthly house payments during the first year.

6. In 2021, Joyce was a single taxpayer whose income consisted solely of $86,000 in long term capital gains. She claimed $21,500 in itemized deductions. How much did she owe in marginal taxes?

7. Suppose that, in 2021, Rick is single and has a taxable income of $125,500. How will his monthly takehome pay be affected if he makes monthly contributions of $900 to a tax-deferred savings plan?

Name:

Unit 4E Test 3

Date:

Choose the correct answer to each problem. In the following problems, assume 2021 values listed in the table of marginal tax rates below. Tax Rate 10% 12% 22% 24% 32% 35% 37% Standard deduction

Married Filing Separately up to $9950 up to $40,525 up to $86,375 up to $164,925 up to $209,425 up to $314,150 above $314,150 $12,550

Head of Household up to $14,200 up to $54,200 up to $86,350 up to $164,900 up to $209,400 up to $523,600 above $523,600 $18,800

1. Mark is single and earned wages of $52,000 in 2021. He received $4300 in interest from savings accounts, he contributed $1200 to a tax-deferred retirement plan, and he took the standard deduction. Find his adjusted gross income. (a) $44,700

(b) $48,750

(d) $56,300

2. A married couple who itemize deductions are in the 24% marginal tax bracket. Which of the following will reduce their tax bill by $240? (a) They make a $1000 donation to charity. (c) They qualify for a $1000 tax credit.

(b) They make a $240 donation to charity. (d) They qualify for a $240 tax deduction.

3. Suppose a married couple filed jointly and had a taxable income of $102,000 in 2021. Compute the marginal tax owed. (a) $22,440

(b) $8830

(d) $16,918

4. Suppose that Perry is married filing separately and can claim two dependent children. Perry had an adjusted gross income of $56,400 in 2021. Assuming he is entitled to a $1000 tax credit for each child, compute the marginal tax bill for Perry. (a) $7716.50

(b) $4955.50

(d) $3395.50

5. Quentin is a single taxpayer who earned $54,500 from wages in 2021. He had no other income, made no contributions to retirement plans, and took the standard deduction. How much did he owe in FICA (7.65%) and marginal taxes combined? (a) $4169.25

(b) $4334.69

(d) $9146.75

6. In 2021, Zoe was a single taxpayer whose income consisted solely of $105,000 in long term capital gains. She claimed $18,000 in itemized deductions. How much did she owe in marginal taxes? (a) $13,867.50

(b) $7050

(d) $14,901

Unit 4E Test 3 (continued)

Name:

7. In 2021, Lois was single and had a taxable income of $52,000. By how much would her monthly takehome pay be reduced if she makes monthly contributions of $300 to a tax-deferred savings plan? (a) $300

(b) $300

(d) $234

8. In 2021, Theresa had an adjusted gross income of $51,500. She files as Head of Household, claiming the standard deduction. Find her effective tax rate based on her taxable income. (a) 11.1%

(b) 7.1%

(d) 11.4%

Name:

Unit 4E Test 4

Date:

Choose the correct answer to each problem. In the following problems, assume 2021 values listed in the table of marginal tax rates below. Tax Rate 10% 12% 22% 24% 32% 35% 37% Standard deduction

Married Filing Separately up to $9950 up to $40,525 up to $86,375 up to $164,925 up to $209,425 up to $314,150 above $314,150 $12,550

Head of Household up to $14,200 up to $54,200 up to $86,350 up to $164,900 up to $209,400 up to $523,600 above $523,600 $18,800

1. Walter is married, but he and his wife filed separate income taxes in 2021. He earned wages of $62,000, and he received $4200 in interest from savings accounts. He also contributed $2500 to a tax-deferred retirement plan, and he took the standard deduction. Find his adjusted gross income. (a) $63,700

(b) $53,300

(d) $46,950

2. A single man has the following deductions: $6900 in mortgage interest, $2500 in charitable donations, and $1185 in state income taxes. Should he itemize or take the standard deduction? Explain. (a) Itemize; it will save him $1965 on his marginal tax bill. (b) Take the standard deduction; it will save him $1965 on his marginal tax bill. (c) Take the standard deduction; it will reduce his taxable income by $1965. (d) Itemize; it will reduce his taxable income by $1965. 3. Phyllis is single and had a adjusted gross income of $87,300 in 2021. Compute Phyllis’ marginal tax bill. (a) $14,973

(b) $12,193.50

(d) $20,952

4. Elliot is head of household with one dependent child. He had a taxable income of $63,600 in 2021. Assuming he is entitled to a $1000 tax credit for the child, compute Elliot’s marginal tax bill. (a) $4936

(b) $7288

(d) $12,992

5. A single taxpayer who itemizes deductions is in the 32% marginal tax bracket. Which of the following will reduce her tax bill by $500? (a) She makes a $500 donation to charity. (c) She qualifies for a $500 tax credit.

(b) She makes a $165 donation to charity. (d) She qualifies for a $165 tax credit.

Unit 4E Test 4 (continued)

Name:

6. Colton is single and has $125,000 in taxable income and his apartment rents for $2000 per month. He is considering a mortgage with payments of $2400 per month, of which an average of $2050 per month would be deductible interest and taxes during the first year. Including savings through the mortgage deduction, determine the actual cost of the mortgage each month during the first year. (a) $1908

(b) $1824

(d) $350

7. In 2021, David and Karen were a retired couple whose income consisted solely of $210,000 in long term capital gains. They filed jointly and claimed $34,000 in itemized deductions. Compute the marginal tax bill. (a) $10,635

(b) $26,400

(d) $19,500

8. Suppose that, in 2021, you are single and have a taxable income of $120,000. How will your monthly take-home pay be reduced if you make monthly contributions of $800 to a tax-deferred savings plan? (a) $192

(b) $608

(d) $624

Name:

Unit 4F Test 1

Date:

1. Briefly explain the difference between deficit and debt.

2. Suppose Sylvia’s gross income is $46,000 for the year. Her expenditures are $24,000 for rent and food, $2600 for credit card payments, and $8500 on entertainment. Compute Sylvia’s net income.

Use the following table to answer questions 3 – 5. Budget Summary for the Wonderful Widget Company (in thousands of dollars) 2018 2019 2020 2021 Total Receipts 854 908 950 990 Outlays Operating Expenses 525 550 600 600 Employee Benefits 200 220 250 250 Security 275 300 320 300 Interest on Debt 0 12 26 47 Total Outlays 1000 1082 1196 1197 Surplus or Deficit -146 -174 -246 -207 Debt (Accumulated) -146 -320 -566 -773 3. Based on the accumulated debt for 2021, calculate the 2022 interest payment if the interest rate is 5.3%.

4. Assume that for 2022, operating expenses are $575,000, employee benefits are $270,000, and security costs are $290,000. Calculate the total outlays for 2022.

Unit 4F Test 1 (continued)

Name:

5. Assume that for 2022, total receipts are $925,000, operating expenses are $575,000, employee benefits are $270,000, and security costs are $290,000. Calculate the year-end surplus or deficit and the year-end accumulated debt for 2022.

6. Give two examples of federal discretionary spending.

7. Past and projected U.S. federal revenue, spending and GDP (all amounts in $ billions and rounded to the nearest billion) Year

Surplus or deficit

Debt

GDP

2005

-318

7905

12,834

2015

-442

18,120

18,100

2025 (projected)

-1174

35,448

28,473

Calculate the debt as a percentage of the GDP for all three years. Comment on the results.

8. Suppose in 2030 the federal debt is projected to be $45 trillion. If interest rates remain steady at 1.7%, how much interest will be owed on the debt?

Name:

Unit 4F Test 2

Date:

1. Briefly define gross domestic product (GDP).

Use the following table to answer questions 2 – 4. Budget Summary for the Wonderful Widget Company (in thousands of dollars) 2018 2019 2020 2021 Total Receipts 854 908 950 990 Outlays Operating Expenses 525 550 600 600 Employee Benefits 200 220 250 250 Security 275 300 320 300 Interest on Debt 0 12 26 47 Total Outlays 1000 1082 1196 1197 Surplus or Deficit -146 -174 -246 -207 Debt (Accumulated) -146 -320 -566 -773 2. Based on the accumulated debt for 2021, calculate the 2022 interest payment if the interest rate is 7.3%.

3. Assume that for 2022, operating expenses are $550,000, employee benefits are $290,000, and security costs are $310,000. Calculate the total outlays for 2022.

4. Assume that for 2022, total receipts are $995,000, operating expenses are $550,000, employee benefits are $290,000, and security costs are $310,000. Calculate the year-end surplus or deficit and the year-end accumulated debt for 2022.

Unit 4F Test 2 (continued)

Name:

5. Briefly describe the two main categories of federal spending.

6. How does the government borrow money from the public?

7. U.S. Federal Revenue for 2019 Source

Percentage of Total Receipts

Individual Income Taxes

50%

Social Security, Medicare, and other social insurance receipts

36%

Corporate Income Taxes

Excise Taxes

Other

Assuming the revenues collected in 2019 totaled $4.40 trillion, how much more (in dollars) was paid by individual income taxes than corporate income taxes?

8. In 2019, Social Security was 23% of all spending. Assuming the revenues collected in 2019 totaled $4.40 trillion and the spending totaled $5.20 trillion, compare the amount collected for social security to the amount spent on social security.

Name:

Unit 4F Test 3

Date:

Choose the correct answer to each problem. 1.

are all revenue collected. (a) Surpluses (c) Receipts

(b) Outlays (d) Debts

2. Roger’s income for last year totaled $29,600 and his expenses totaled $32,100. Find Roger’s net income. (a) $2500 surplus (c) $2500 debt

(b) $2500 deficit (d) -$2500 surplus

3. What type of spending is easiest for the government to control? (a) interest payments on the debt (c) entitlement spending

(b) Medicare (d) discretionary spending

4. If the gross federal debt at the end of 2030 is projected to be $45 billion and the interest rate is 1.7%, how much interest would be due on this debt? (a) $765 billion

(b) $7.7 trillion

(d) $77 billion

5. Suppose the federal debt is projected to be $22.5 trillion. If there are projected to be 160 million workers in the United States in 2020, what would the federal debt per laborer be? (a) $140,625

(b) $14,062.50

(d) $140.63

6. U.S. Federal Spending 2019 Expense

Percentage of Total Outlays

Social Security

23%

Medicaid, government pensions, and other mandatory spending

22%

Medicare

17%

Non-defense discretionary

15%

Defense and homeland security

15%

Interest on debt 8% Assuming the outlays for 2019 totaled $5.20 trillion, how much (in dollars) was paid toward all discretionary items? (a) $1.56 trillion

(b) $78 billion

(d) $7.8 trillion

7. Which of the following combinations will make it impossible to ever retire the federal debt? (a) Increase receipts by 1% and increase outlays by 1% (each year). (b) Increase receipts by 2% and increase outlays by 1% (each year) (c) Increase receipts by 1% and increase outlays by 0% (each year) (d) Increase receipts by 1% and decrease outlays by 1% (each year) Copyright © 2023 Pearson Education, Inc. - 144 -

Name:

Unit 4F Test 4

Date:

Choose the correct answer to each problem. 1.

are all expenses paid. (a) Surpluses (c) Receipts

(b) Outlays (d) Debts

2. Which of the following defines net income? (a) surplus – receipts

(b) receipts – outlays

(d) debt + receipts

3. Which of the following is not a way the government borrows money from the public? (a) selling bonds to investors (c) selling Treasury notes

(b) borrowing from Social Security trust fund (d) lowering taxes

4. Which term describes the actual amount the government is obligated to repay someday? (a) gross debt

(b) net deficit

(d) gross deficit

5. Which of the following is classified as a discretionary expense in the federal budget? (a) national defense (c) interest on the debt

(b) Medicaid (d) Social Security payments

6. If the gross federal debt at the end of a certain year was about $13 trillion and the interest rate was 2%, what was the interest due on this debt? (a) $26 billion

(b) $260 billion

(d) $2600 billion

7. U.S. Federal Spending 2019 Expense

Percentage of Total Outlays

Social Security

23%

Medicaid, government pensions, and other mandatory spending

22%

Medicare

17%

Non-defense discretionary

15%

Defense and homeland security

15%

Interest on debt 8% Assuming the outlays for 2019 totaled $5.20 trillion, how much (in dollars) was paid toward all nondiscretionary outlays? (a) $2.34 trillion

(b) $364 billion

(d) $3.64 trillion

Name:

Unit 5A Test 1

Date:

1. Name the population. A survey of 1200 New York City residents found that 35% own their own vehicle.

2. Name the sample. A survey of 1200 New York City residents found that 35% own their own vehicle.

3. Name the parameter. In a survey of 550 residents of rural Virginia, the average number of vehicles per household is 2.7.

4. Name the statistic. In a survey of 550 residents of rural Virginia, the average number of vehicles per household is 2.7.

5. Explain what is meant by an observational study, and when it is the appropriate choice.

Unit 5A Test 1 (continued)

Name:

6. Identify the sampling method (simple random sampling, systematic sampling, convenience sampling, stratified sampling) in the following study. Every 200th quart of ice cream off the assembly line is tested for taste and consistency.

7. Identify the sampling method (simple random sampling, systematic sampling, convenience sampling, stratified sampling) in the following study. A political website hosts a poll on the most important issues for concern for the state.

8. For the following question identify which type of statistical study is most likely to lead to an answer. If the study is an experiment, identify the control and treatment groups, and discuss any necessary blinding. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and the controls. Are more lawyers Republican or Democrat?

9. For the following question identify which type of statistical study is most likely to lead to an answer. If the study is an experiment, identify the control and treatment groups, and discuss any necessary blinding. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and the controls. Do restaurant patrons linger longer with darker lighting?

10. A survey finds that 45% of Americans spend less than 2 hours a day watching television, with a margin of error of 5 percentage points. Construct a confidence interval from these results.

Name:

Unit 5A Test 2

Date:

1. Name the population. 85% of 164 dentists surveyed own their own office.

2. Name the sample. 85% of 164 dentists surveyed own their own office.

3. Name the parameter. In a survey of 350 Alaskan residents, the average number of pets per household is 1.2.

4. Name the statistic. In a survey of 350 Alaskan residents, the average number of pets per household is 1.2.

5. Explain bias and list 2 potential sources of bias.

6. Identify the sampling method (simple random sampling, systematic sampling, convenience sampling, stratified sampling) in the following study. A computer randomly selects 80 Student ID Numbers to choose participants for a satisfaction survey.

Unit 5A Test 2 (continued)

Name:

7. Identify the sampling method (simple random sampling, systematic sampling, convenience sampling, stratified sampling) in the following study. An ad rep randomly selects 15 male and 15 female participants to study an insurance ad’s effectiveness.

10. A survey finds that 65% of Americans watched the Academy Awards, with a margin of error of 3 percentage points. Construct a confidence interval from the survey results.

Name:

Unit 5A Test 3

Date:

Choose the correct answer to each problem. 1. A survey showed that 16% of 1400 Colorado residents surveyed want the legalization of marijuana repealed. Identify the population. (a) 16% of the residents surveyed who want the law repealed (b) 1400 Colorado residents (c) All the residents of Colorado (d) The percentage of all Colorado residents who want the law repealed 2. A survey showed that 16% of 1400 Colorado residents surveyed want the legalization of marijuana repealed. Identify the statistic. (a) 16% of the residents surveyed who want the law repealed (b) 1400 Colorado residents (c) All the residents of Colorado (d) The percentage of all Colorado residents who want the law repealed 3.

In a study to determine the most popular automobile on the road, which of the following is the most biased sample? (a) The cars parked at an airport (c) The cars that drive by your house

(b) The cars parked at a local high school (d) The cars driving on the highway

4. In a study to determine the percentage of college students who read the newspaper, which of the following is the best sample? (a) Every 20th student who walks by the student center (b) The first 50 students who arrive at a movie (c) The freshman at a particular school (d) The students in a computer class 5. Which of the following describes a study in which the researchers do not attempt to change the characteristics of those being studied? (a) Single-blind experiment (c) Double-blind experiment

(b) Observational study (d) Experiment

6. Is taking herbal supplements or vitamin C more effective in reducing the number of colds caught? This question would best be answered by which of the following types of studies? (a) Single-blind experiment (c) Observational study

(b) Case-control study (d) Experiment (no blinding)

7. How many words can you write with a gel-pen? This question would best be answered by which of the following types of studies? (a) Single-blind experiment (c) Observational study

(b) Double-blind experiment (d) Case-control study

Unit 5A Test 3 (continued)

Name:

8. Does caffeine cause birth defects? This question would best be answered by which of the following types of studies? (a) Single-blind experiment (c) Double-blind experiment

(b) Case-control study (d) Observational study

9. A random sample of high school students found that 17% chose History as their favorite subject, with a margin of error of 6 percentage points. Which of the following can be stated? (a) The actual percentage of high school students whose favorite class is History is between 17% and 23%. (b) The actual percentage of high school students whose favorite class is History is between 11% and 17%. (c) The actual percentage of high school students whose favorite class is History is between 11% and 23%. (d) The actual percentage of high school students whose favorite class is History is 17%. 10. The poll suggested that between 58% and 66% of voters will vote for Senator Sam in the next election. What do you know about the sample statistics and the margin of error of the survey? (a) 58% of the voters surveyed stated that they will vote for Senator Sam, and the margin of error is 8 percentage points. (b) 62% of the voters surveyed stated that they will vote for Senator Sam, and the margin of error is 4 percentage points. (c) 58% of the voters surveyed stated that they will vote for Senator Sam, and the margin of error is 4 percentage points. (d) 66% of the voters surveyed stated that they will vote for Senator Sam, and the margin of error is 8 percentage points.

Name:

Unit 5A Test 4

Date:

Choose the correct answer to each problem. 1. A survey showed that 16% of 1400 Colorado residents surveyed want the legalization of marijuana repealed. Identify the sample. (a) 16% of the residents surveyed who want the law repealed (b) 1400 Colorado residents (c) All the residents of Colorado (d) The percentage of all Colorado residents who want the law repealed 2. A survey showed that 16% of 1400 Colorado residents surveyed want the legalization of marijuana repealed. Identify the parameter. (a) 16% of the residents surveyed who want the law repealed (b) 1400 Colorado residents (c) All the residents of Colorado (d) The percentage of all Colorado residents who want the law repealed 3. In a study to determine which airline has the most helpful flight attendants, which of the following is the best sample? (a) Flight attendants at several airlines (c) All airline passengers on a certain day

(b) All business travelers in a certain week (d) Shoppers at a grocery store

4. Which of the following describes a study in which the researchers know which group of participants is receiving a placebo? (a) Double-blind experiment (c) Single-blind experiment

(b) Observational study (d) Case-control study

5. Which of the following describes a study in which the participants naturally form groups by choice? (a) Single-blind experiment (c) Double-blind experiment

(b) Case-control study (d) Observational study

6. Choose 3 winners of the door prize by randomly drawing tickets out of a bag. Identify the sampling method. (a) Simple Random Sampling (c) Convenience Sampling

(b) Systematic Sampling (d) Stratified Sampling

7. Choose 3 students from each classroom to rate the lunch quality. Identify the sampling method. (a) Simple Random Sampling (c) Convenience Sampling

(b) Systematic Sampling (d) Stratified Sampling

8. Does tobacco smoking cause lung cancer? This question would best be answered by which of the following types of studies? (a) Single-blind experiment (c) Double-blind experiment

(b) Case-control study (d) Observational study

Unit 5A Test 4 (continued)

Name:

9. A random sample of dog owners revealed that 72% of them walked their dog at least 3 times a week, with a margin of error of 8 percentage points. Which of the following can be stated? (a) The percentage of dog owners who walk their dog at least 3 times a week is between 64% and 80% (b) The percentage of dog owners who walk their dog at least 3 times a week is between 72% and 80% (c) The percentage of dog owners who walk their dog at least 3 times a week is between 64% and 72% (d) The percentage of dog owners who walk their dog at least 3 times a week is 72% 10. The latest poll reports that between 53% and 59% of voters will vote for Congressman Bob in the next election. What do you know about the sample statistics and the margin of error of the survey? (a) 53% of the voters surveyed stated they will vote for Congressman Bob & the margin of error is 6 percentage points. (b) 56% of the voters surveyed stated they will vote for Congressman Bob & the margin of error is 6 percentage points. (c) 56% of the voters surveyed stated they will vote for Congressman Bob & the margin of error is 3 percentage points. (d) 59% of the voters surveyed stated they will vote for Congressman Bob, & the margin of error is 6 percentage points.

Name:

Unit 5B Test 1

Date:

1. Explain what is meant by participation bias.

2. Why is it important to consider the source of a study?

3. Give an example that illustrates the meaning of availability error. Explain your example.

4. Give an example of selection bias. Explain your example.

5. In what way might the following study be flawed? The National Dairy Council sponsored a study that concluded consuming milk or yogurt or cheese three times a day would help with weight loss.

6. In what way might the following study be flawed? A study concluded that video games that were twice as violent as others caused behavior problems in teens.

Unit 5B Test 1 (continued) Name: 7. How would you select an unbiased sample for the following study? Which candidate for governor is most likely to win the next election?

8. Why do you think it is sometimes difficult to define the variables of interest of a study? Give an example of a variable of interest that is difficult to define.

Name:

Unit 5B Test 2

Date:

1. Explain what is meant by selection bias.

2. Explain what is meant by availability error.

3. Give an example of participation bias. Explain your example.

4. Give an example of a study conducted by an inappropriate source. Explain your example.

5. In what way might the following study be flawed? A group of high school students are asked if they would oppose the repeal of a school policy that currently does not allow students to wear shorts to school.

6. In what way might the following study be flawed? Every day for a week, one group was given non-chocolate candy bars and another group was given candy bars with chocolate. Dermatologists analyzed the skin of the participants, determined that each group had comparable levels of acne, and concluded that chocolate does not cause acne.

Unit 5B Test 2 (continued) Name: 7. How would you select an unbiased sample for the following study? Do the citizens of Redwood County support spending $5,000,000 to construct a new school building?

8. Why do you think it is sometimes difficult to measure the variables of interest of a study? Give an example of a variable of interest that is difficult to measure.

Name:

Unit 5B Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following describes a variable not intended to be a part of the study? (a) Variable of interest (c) Confounding variable

(b) False conclusion (d) Availability error

2. Which of the following describes the bias that occurs when participants are self-selected? (a) Participation bias

(b) Availability error

(d) No bias

3. A researcher is studying end-times beliefs of Christians by surveying members of his Methodist church. This study may suffer from what type of bias? (a) Participation bias

(b) Availability error

(d) No bias

4. Every half-hour three candy bars are pulled from the assembly line and tested for quality. This study may suffer from what type of bias? (a) Participation bias

(b) Availability error

(d) No bias

5. A recent magazine article determined that the Gemini is the most popular car on the road. A TV journalist decided to test the accuracy of the article with a survey. Which of the following survey questions will give the journalist the most accurate results? (a) What kind of car do you drive? (b) What do you think is the most popular car on the road? (c) Do you agree that the Gemini is the most popular car on the road? (d) What kind of car do you recall seeing advertised most often? 6. If you wanted to determine if your customers are satisfied with the selection in your store, which of the following survey questions would give you the most accurate results? (a) Is there anything you would have purchased if our stock was not without it? (b) Are you satisfied with the selection at this store? (c) Do you agree that our selection is better than our competition? (d) Is our selection as good as the selection of our competition? 7. Which of the following study results implies that there is a problem with the quality of education at Rydell High? (a) 25% of the senior class scored was accepted at an Ivy League school. (b) 53% of the senior class was accepted for admission to Valley State College in the fall. (c) 83% of the seniors who applied for admission to Valley State College were accepted. (d) 30% of the senior class scored above average on the writing portion of a national aptitude test. 8. Which of the following quantities of interest would be the most difficult to define? (a) The levels of lead in various brands of paint (b) The least expensive brand of paint (c) The paint with the best looking finish (d) How water resistant a brand of paint is Copyright © 2023 Pearson Education, Inc. - 158 -

Unit 5B Test 3 (continued)

Name:

9. Which of the following quantities of interest would be the most difficult to measure? (a) The average height of a volleyball team (b) The team member with the highest salary (c) The team member with the longest hair (d) The most outgoing team member

Name:

Unit 5B Test 4

Date:

Choose the correct answer to each problem. 1. Which of the following describes what scientists are attempting to measure in a particular statistical study? (a) Participation

(b) Peer review

(d) Quality of life

2. Which of the following describes the bias that can occur when survey questions or choices are always presented in the same order? (a) Participation bias

(b) Availability error

(d) No bias

3. After a stay in one of their properties, Omni Hotels sends a survey to each of their guests. This study may suffer from what type of bias? (a) Participation bias

(b) Availability error

(d) No bias

4. Which of the following describes the bias that occurs when a researcher chooses a sample not representative of the population? (a) Participation bias

(b) Availability error

(d) No bias

5. A recent newspaper article stated that Snazzy’s is the most popular restaurant in the city. The city council decided to sponsor its own survey to determine the accuracy of the article. Which of the following survey questions will give them the most accurate survey results? (a) Which restaurant do you think is the most popular in the city? (b) Which restaurant in the city do you visit most often? (c) Which restaurant in the city do you think is the most crowded? (d) Do you agree that Snazzy’s is the most popular restaurant in the city? 6. Proposition EZ proposes to raise the state sales tax by one quarter of a percent. The proceeds will be earmarked for music education in the public schools. If you want to determine whether or not it will pass, which of the following survey questions will give you the most accurate results? (a) Do you know which proposition will raise state sales tax and fund music education? (b) Will you vote for proposition EZ which will raise the amount of state sales tax that you pay every year? (c) Do you believe that music education is important? (d) Are you planning to vote for Proposition EZ which will raise state sales taxes and support music education? 7. Which of the following study results implies that there may be a problem with the health of newborn babies at Doctor’s Hospital? (a) 25% of the newborns had genetic defects. (b) 53% of the newborns were born within one week of their due date. (c) 50% of the newborns were above average in weight. (d) 83% of the newborns were born with hepatitis.

Unit 5B Test 4 (continued)

Name:

8. Which of the following quantities of interest would be most difficult to define? (a) The number of children not counted in the last census (b) The number of children living below the poverty line (c) The percentage of children who brush their teeth at least twice a day (d) The percentage of second graders who read above grade level 9. Which of the following quantities of interest would be the most difficult to measure? (a) The levels of pesticides in a tomato crop (c) The largest crop of tomatoes

(b) The best tasting tomato crop (d) The crop with the highest acid level

Name:

Unit 5C Test 1

Date:

Use the following grades from a test from a math class to answer number 1 – 4. A B C C C B C B A B D D B C C C A A F F D A B 1. Is the above data qualitative data or quantitative data?

2. Make a frequency table for the data.

3. List the relative frequency for each category of data.

4. Construct a bar graph from the data. Label all parts.

Unit 5C Test 1 (continued)

Name:

Use the following quiz grades for answering 5 – 9. 88 96 98 72 55 78 84 87 92 73 47 32 66 78 94 86 89 90 33 67 92 87 5. Is the above data qualitative data or quantitative data?

6. Make a frequency distribution using 10-point bins.

7. Construct a histogram from this data. Label all parts.

Unit 5C Test 1 (continued) Name: 8. Find the relative frequency for each bin.

9. Find the cumulative frequency for each bin.

10. On April 1st, Rachel purchased 50 shares of ACME stock for $4 per share. The following is a time-series diagram showing the price of ACME stock during the month of April:

$5.50

$5.00

Stock Price

$4.50

$4.00

$3.50

$3.00

$2.50

$2.00 4/5

4/10

4/15

4/20

4/25

4/30

5/5

Use this time-series diagram to fill in the following table. April 5

April 15

April 25

Stock Price Value of Rachel’s Investment

May 5

Name:

Unit 5C Test 2

Date:

Use the following grades from a test from a math class to answer number 1 – 4. F C C B A A D F B C D C A A F F D A B B 1. Is the above data qualitative data or quantitative data?

2. Make a frequency table for the data.

3. List the relative frequency for each category of data.

4. Construct a bar graph from the data. Label all parts.

C D A

Unit 5C Test 2 (continued)

Name:

Use the following quiz grades for answering 5 – 9. 88 56 98 72 55 78 64 87 92 73 47 32 76 78 94 96 89 90 33 67 92 87 5. Is the above data qualitative data or quantitative data?

6. Make a frequency distribution using 10-point bins.

7. Construct a histogram from this data.

Unit 5C Test 2 (continued)

Name:

8. Find the relative frequency for each bin.

9. Find the cumulative frequency for each bin.

10. On June 1st, Staci purchased 40 shares of B&B stock for $7 per share. The following is a time-series diagram showing the price of B&B stock during the month of June: $8.50 $8.00 $7.50 $7.00 $6.50 $6.00 6/5

6/10

6/15

6/20

6/25

6/30

7/5

Use this time-series diagram to fill in the following table. June 5

June 15

June 25

Stock Price Value of Staci’s Investment

July 5

Name:

Unit 5C Test 3

Date:

1. Which types of graphs would most likely be used to display qualitative data? (a) bar graph or histogram

(b) bar graph or line chart

(d) pie chart or bar graph

2. Which of the following describes quantitative data? (a) The identification numbers for voters (b) The numbers on football jerseys (c) The colors of the cars in the parking lot (d) The number of commercials airing during an hour of network television The following bar graph shows the grades Ms. Muckluck gave the students in her English classes last year. Use it to answer questions 3 – 6.

Number of Students

25 20 15 10 5 0 A

Grade

3. Approximately how many students made a C or better on the test? (a) 72

(b) 15

(d) 50

4. How many more students received a C than received a D or an F? (a) 11

(b) 2

(d) 8

5. How many students were in Ms. Muckluck’s classes last year? (a) 75

(b) 23

(d) 45

(d) 20%

6. Compute the relative frequency of the grade “A”. (a) 15%

(b) 2%

Unit 5C Test 3 (continued)

Name:

Use following data to answer questions 7 and 8. 88 76 88 72 75 78 84 87 72 73 77 72 86 78 84 76 89 70 83 87 82 87 7. Which of the following describes the best decision for constructing a frequency table? (a) Use 10-point bins because the data is well spread. (b) Use 10-point bins because the data is close together. (c) Use 5-point bins because the data is well spread. (d) Use 5-point bins because the data is close together. 8. Compute the cumulative frequency for the third bin. (a) 11

(b) 22

(d) 7

Name:

Unit 5C Test 4

Date:

1. Which types of graphs might be used to display quantitative data with quantitative? (a) bar graph or histogram

(b) bar graph or line chart

(d) pie chart or bar graph

2. Which of the following describes qualitative data? (a) The numbers of voters (b) The temperature outside (c) The colors of the cars in the parking lot (d) The time it takes to drive to school The following bar graph shows the grades Mr. Mulligan gave the students in his History classes last year. Use it to answer questions 3 – 6.

Number of Students

30 25 20 15 10 5 0 A

Grade

3. How many students made a grade of C or better? (a) 6

(b) 54

(d) 44

4. How many more students received a C than received an A or a B? (a) 10

(b) 8

(d) 6

5. How many students were in Mr. Mulligan’s classes last year? (a) 60

(b) 63

(d) 70

(d) 20%

6. Compute the relative frequency of the grade “A”. (a) 9.5%

(b) 95%

Unit 5C Test 4 (continued)

Name:

Use the following to answer questions 7 and 8. 88 56 98 72 55 78 64 87 92 73 47 32 76 78 94 96 89 90 33 67 92 87 7. Which of the following describes the best decision for constructing a frequency table? (a) Use 10-point bins because the data is well spread. (b) Use 10-point bins because the data is close together. (c) Use 5-point bins because the data is well spread. (d) Use 5-point bins because the data is close together. 8. Compute the cumulative frequency for the third bin. (a) 2

(b) 4

(d) 18

Name:

Unit 5D Test 1

Date:

Use the following graph to answer 1 – 2.

1. What is the percentage difference in the earnings for a man who earns an associate degree with the earnings of a woman who earns an associate degree?

2. What is the percentage difference in the earnings for a man who earns an associate degree with the earnings of a man who is a high school graduate?

Unit 5D Test 1 (continued)

Name:

Use the following graph to answer 3 – 4.

3. List all locations whose mean score for the girls was greater than the mean score for the boys on the PISA Mathematics test.

4. Compute the percentage difference in the mean score for boys in Singapore and in Canada. Discuss the difference between the computed percentage and the visualization of that difference in the graph.

5. In a contour map displaying altitudes, explain the significance of the distances between the lines.

Unit 5D Test 1 (continued)

Name:

6. What type of data may be displayed more clearly on an exponential scale? Give an example.

7. How are the features of a line graph or histogram manipulated in order to accentuate the differences in the data?

Name:

Unit 5D Test 2

Date:

Use the following graph to answer 1 – 2.

1. What is the percentage difference in the earnings for a man who earns a master’s degree with the earnings of a woman who earns a master’s degree?

2. What is the percentage difference in the earnings for a woman who earns an associate degree with the earnings of a woman who is a high school graduate?

Unit 5D Test 2 (continued)

Name:

Use the following graph to answer 3 – 4.

3. List the country with the greatest difference between the mean score for the girls and the mean score for the boys on the PISA Mathematics test.

4. Compute the percentage difference in the mean score for girls in Finland and in the United States. Discuss the difference between the computed percentage and the visualization of that difference in the graph.

Unit 5D Test 2 (continued)

Name:

5. Explain the difference between a geographical data map and a contour map.

6. Explain what is meant by a three-dimensional graph and its common misuse.

7. Describe infographics and explain their use.

8. A set of data that only increases over time is displayed in a line graph depicting relative change. Is it possible for that graph to show both positive and negative fluctuations? Explain.

9. If you want the differences in the data to appear minimized, how do you manipulate a line graph or histogram?

Name:

Unit 5D Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following describes a statistical graph that plots three or more related quantities simultaneously? (a) Contour map (c) Multiple bar graph

(b) Three-dimensional graph (d) Pictograph

2. Which of the following describes a statistical graph where each category has its own wedge and the wedges are displayed on top of one another? (a) Stack plot

(b) Contour map

(d) Pictograph

3. Which of the following describes a statistical graph that is embellished with additional art work? (a) Stack plot

(b) Contour map

(d) Pictograph

4. Which of the following describes a statistical graph that plots two or more sets of related data on the same graph to facilitate comparison? (a) Contour map (c) Multiple bar graph

(b) Three-dimensional graph (d) Pictograph

5. You have collected multiple interrelated sets of information and data that would best be understood with a combination of words, data, and graphs. Which of the following is a common method of representing the results of this type of research? (a) Stack plot (c) Multiple bar graph

(b) Contour map (d) Infographics

6. Suppose you are given a contour map showing elevation (altitude) of a mountain and campsite A and campsite B are across several contour lines from each other. The lines around campsite A are closer together and the lines around campsite B are further apart. What can you tell about these two campsites? (a) Campsite A is uphill from B. (c) The area around B is steeper than A.

(b) The area around A is steeper than B. (d) There is not enough information given.

7. In a graph that describes the percent rise in the price of grain over 5 years, what does it mean for the value at one year to be less than that value the next year? (a) The price of grain has gone down (c) The real cost of grain has gone down

(b) The rate at which the price is rising has gone down (d) Inflation has gone down

Name:

Unit 5D Test 4

Date:

Choose the correct answer to each problem. 1. Which of the following describes a statistical graph where a quantity is represented by a curve and has the same value everywhere along the curve? (a) Stack plot

(b) Contour map

(d) Pictograph

2. The difference in strength of the last 5 major earthquakes to hit California have varied by factors of 10. If you were to display data describing the strengths of these earthquakes what could you use to make the graph more readable? (a) A three-dimensional graph (c) A color coded map

(b) A stack plot (d) An exponential scale

3. A display of multiple interrelated sets of information and data using a combination of words, data, and graphs instead of one stand-alone graphic. (a) Color coded map (c) Multiple bar graph

(b) Infographic (d) Exponential Scale

4. Which of the following types of statistical graphs are very common in the media, but are often hard to read due to their cosmetic embellishments? (a) Contour map (c) Multiple bar graph

(b) Three-dimensional graph (d) Pictograph

5. Which of the following types of graphs can be difficult to interpret because of visual distortion on a flat page? (a) Stack plot (c) Multiple bar graph

(b) Contour map (d) Three-dimensional graph

6. You are going to make a presentation to potential investors and you want to make the growth of your company’s revenue looks as dramatic as possible. What might you do to a histogram to get this effect? (a) Be sure to start the vertical scale at zero. (b) Start the vertical scale at a number above zero. (c) Use colors to highlight growth. (d) Make the bars thicker and thicker. 7. In a graph that describes the percent rise in the price of gasoline over 10 years, what does it mean for the value at one year to be greater than the value the next year? (a) The rate at which the price is rising has gone down. (b) The price of gasoline has gone up. (c) The real cost of gasoline has gone up. (d) Inflation has gone up.

Name:

Unit 5E Test 1

Date:

The following graph shows the number of absences for each student in a course and the final average that student earned for the course. Use this graph to answer questions 1 – 2.

Do Absences Influence Performance? 120

Final Average

100 80 60 40 20 0 0

Number of Absences 1. Describe the relationship. (Is there a correlation? Positive or negative? Weak or strong?)

2. Do you think that the relationship is an example of coincidence, a common underlying cause, or direct cause?

3. Would you expect a positive correlation, a negative correlation, or no correlation between the variables years spent in jail and years of education? Explain.

Unit 5E Test 1 (continued)

Name:

4. Would you expect a positive correlation, a negative correlation, or no correlation between the variables size of a real estate development and annual landscaping costs? Explain.

5. Do you think that the following correlation is an example of coincidence, a common underlying cause, or direct cause? Whenever the windmill is turning, I hear a rustling noise in the trees.

6. Do you think that the following correlation is an example of coincidence, a common underlying cause, or direct cause? People who smoke frequently have a higher instance of lung cancer.

In the following questions, refer to the data given below about average gasoline and diesel prices for the week of 11/18/17 according to region. Retail Fuel Prices (per gallon) Region Gasoline East Coast $3.282 Midwest $3.126 Gulf Coast $3.004 Rocky Mountain $3.183 West Coast $3.467 Source: Energy Information Administration

Diesel $3.841 $3.794 $3.745 $3.836 $3.954

7. Sketch a scatter diagram for the data. Use the horizontal axis for gasoline prices and the vertical axis for diesel prices.

Unit 5E Test 1 (continued)

Name:

8. Describe the relationship between gasoline prices and diesel prices. (Is there a correlation? Positive or negative? Weak or strong?)

9. Is the relationship between gasoline and diesel prices a coincidence, the result of some common underlying cause, or the result of a direct cause? Explain.

Name:

Unit 5E Test 2

Date:

Use this graph to answer questions 1 – 2.

Salary (in thousands of dollars)

How Does Age Influence Salary? 90 80 70 60 50 40 30 20 10 0 0

Age (in years) 1.

Describe the relationship. (Is there a correlation? Positive or negative? Weak or strong?)

2. Do you think that the relationship is an example of coincidence, a common underlying cause, or direct cause?

3. Would you expect a positive correlation, a negative correlation, or no correlation between the variables number of hours worked and the size of a paycheck? Explain.

Unit 5E Test 2 (continued)

Name:

4. Would you expect a positive correlation, a negative correlation, or no correlation between the variables number of cows and number of citizens who have earned a Ph.D. in a particular county? Explain.

5. Do you think that the following correlation is an example of coincidence, a common underlying cause, or direct cause? When I flip the switch, the light comes on.

6. Do you think that the following correlation is an example of coincidence, a common underlying cause, or direct cause? Whenever I wash my car, it rains.

In the following questions, refer to the data given below about height and GPA for five students. Student Maria Nancy Owen Paul Quincy

Height 68 inches 62 inches 67 inches 78 inches 72 inches

GPA 3.75 2.10 3.40 4.00 3.75

7. Draw a scatter diagram for the data. Use the horizontal axis for height and the vertical axis for GPA.

Unit 5E Test 2 (continued)

Name:

8. Describe the relationship between height and GPA. (Is there a correlation? Positive or negative? Weak or strong?)

9. Is the relationship between height and GPA a coincidence, the result of some common underlying cause, or the result of a direct cause? Explain.

Name:

Unit 5E Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following is a graph in which each point represents the values of two variables? (a) Histogram

(b) Scatter diagram

(d) Bar graph

2. Which of the following exists when two variables tend to increase together? (a) No correlation (c) Negative correlation

(b) Positive correlation (d) Nonlinear correlation

3. Which of the following pairs of variables is likely to have a negative correlation? (a) The square footage of a home and its price (b) The number of miles run and the number of calories burned (c) The temperature outside and the number of coats and gloves sold (d) The height of an adult male and his waist size 4. Which of the following is true about a weak positive correlation? (a) The points on the scatter diagram fall into a broad swath that slopes downward. (b) The points on the scatter diagram fall into a fairly tight line that slopes downward. (c) The points on the scatter diagram fall into a broad swath that slopes upward. (d) The points on the scatter diagram fall into a fairly tight line that slopes upward. 5. Which of the following is likely a coincidence? (a) Higher real estate prices in cities with more employment opportunities (b) More crime in neighborhoods with fewer streetlights (c) Higher annual rainfall in states with stricter gun control laws (d) More instances of skin cancer in regions with more sunshine 6. Which of the following is likely the result of some common underlying cause? (a) Whenever I eat dessert, my weight increases. (b) Whenever I get 8 hours of sleep at night, I don’t get sleepy during the day. (c) Whenever I get some cash at the ATM, my account balance decreases. (d) Whenever I see snowmen, I also see smoke coming out of chimneys. 7. Which of the following is likely a cause-and-effect relationship? (a) When the temperature drops, consumption of heating oil rises. (b) When the rooster crows, the morning glories open. (c) When I drive to work, the sun rises. (d) When I see stars, I also see the moon.

Unit 5E Test 3 (continued)

Name:

8. Which of the following is not a guideline for establishing causality? (a) Try to determine if the effect still remains after accounting for other potential causes. (b) Seek evidence that larger amounts of the cause produce larger amounts of the effect. (c) If possible, test the suspected cause with an experiment. (d) Ignore evidence that suggests there is no causality. 9. Which of the following best describes our level of confidence in causality when we have discovered a correlation but cannot yet determine whether the correlation implies causality? (a) Possible cause (c) Cause beyond reasonable doubt

(b) Probable cause (d) Absolute certainty

Name:

Unit 5E Test 4

Date:

Choose the correct answer to each problem. 1. When all the data points in a scatter diagram fall on a straight line, which of the following is present? (a) No correlation (c) Negative correlation

(b) Positive correlation (d) Linear correlation

2. Which of the following exists when two variables tend to change in opposite directions, with one increasing while the other decreases? (a) No correlation (c) Negative correlation

(b) Positive correlation (d) Nonlinear correlation

3. Which of the following pairs of variables is likely to have a positive correlation? (a) The airspeed of a plane and the time to its destination (b) The number of auto accidents a person causes and his auto insurance premium (c) The shoe size of an adult female and education level (d) The number of daylight hours and amount of electricity used for home lighting 4. Which of the following is true about a strong negative correlation? (a) The points on the scatter diagram fall into a broad swath that slopes downward. (b) The points on the scatter diagram fall into a fairly tight line that slopes downward. (c) The points on the scatter diagram fall into a broad swath that slopes upward. (d) The points on the scatter diagram fall into a fairly tight line that slopes upward. 5. Which of the following relationships between pairs of variables is likely a coincidence? (a) Higher energy levels among children who eat more sugar (b) Higher test scores among students who dye their hair red (c) Higher income levels among people with more education (d) Fewer medical problems among people who exercise more often 6. Which of the following is likely the result of some common underlying cause? (a) Patients who eat a lot of salt often have high blood pressure. (b) Patients who have runny noses often have watery eyes as well. (c) Patients who eat more vegetables often have better eyesight. (d) Patients who exercise regularly often have better cholesterol levels. 7. Which of the following is likely a cause-and-effect relationship? (a) I washed dishes, and then I did laundry. (b) It was hot and humid, and then it stormed. (c) The dog barked, and then the clock chimed. (d) The phone rang, and then someone knocked on the door.

Unit 5E Test 4 (continued)

Name:

8. Which of the following is a guideline for establishing causality? (a) Consider only the suspected cause, ignoring other potential causes. (b) Seek evidence that larger amounts of the cause produce larger amounts of the effect. (c) Ignore evidence that suggests there is no causality. (d) Avoid having to do an experiment as they are usually costly. 9. Which of the following best describes our level of confidence in causality when we have found a physical model that is so successful in explaining how one thing causes another that it seems unreasonable to doubt the causality? (a) Possible cause (c) Cause beyond reasonable doubt

(b) Probable cause (d) Absolute certainty

Name:

Unit 6A Test 1

Date:

1. Find the mean of the following set of data. 8, 3, 3, 17, 9, 8, 22, 19, 9, 8, 6

2. Find the median of the following set of data. 8, 3, 3, 17, 9, 8, 22, 19, 9, 8, 6

3. Find the mode of the following set of data. 8, 3, 3, 17, 9, 8, 22, 19, 9, 8, 6

4. Explain a situation when the median is a better measure of center than the mean.

5. Explain what is meant by an outlier.

6. State whether you expect the distribution of ages of students in a community college to be symmetric, left-skewed or right-skewed. Explain.

Unit 6A Test 1 (continued)

Name:

7. Consider the distribution graphed below.

B C

Determine whether each of the mean, median, and mode is represented by A, B, or C.

8. Suppose there are 300 students enrolled in the introductory geology course this semester. Each of these students is enrolled in one of three lecture sections of 100 students each and one of 15 laboratory sections of 20 students each. A student reports that the average size of his geology classes is 60 students, while the chairperson of the department claims that the average size of an introductory geology class is approximately 33 students. How can they both be right?

9. The median price of a new home is reported to be $172,400, and the mean price is reported to be $196,000. Describe the distribution of new home prices, explaining the relationship between the given median and mean.

10. How many peaks would you expect for the distribution of the weights of all students at Princeton University? Why?

Name:

Unit 6A Test 2

Date:

1. Find the mean of the following set of data. 65, 78, 53, 96, 87, 96, 34, 46, 85, 93

2. Find the median of the following set of data. 11, 8, 2, 5, 17, 39, 52, 42

3. Find the mode of the following set of data. 3, 2, 1, 1, 3, 1, 2, 1

4. Give an example of a data set that you would expect to have a symmetric distribution.

5. Explain what is meant by a uniform distribution.

6. State whether you expect the distribution of the ages of students at your college to be symmetric, leftskewed or right-skewed. Explain.

Unit 6A Test 2 (continued)

Name:

7. Consider the distribution graphed below.

B C

Determine whether each of the mean, median, and mode is represented by A, B, or C.

8. A small company has 20 employees of which 9 earn $40,000 per year, 3 earn $39,000 per year, and 8 earn $19,000 per year. The owner reports the average salary of his employees as $39,000 per year, while an unhappy employee claims the average is only $31,450 per year. How can they both be right?

9. The median score on a test is reported to be 79, and the mean score is reported to be 72. Describe the distribution of test scores, explaining the relationship between the given median and mean.

10. How many peaks would you expect for the distribution of the results of rolling a fair die 1000 times? Why?

Name:

Unit 6A Test 3

Date:

Choose the correct answer to each problem. 1. Find the mean of the following data set. 25, 26, 21, 29, 22, 24, 27, 24 (a) 24

(b) 24.5

(d) 25.25

(d) 102

(d) 39.2

2. Find the median of the following set of data. 52, 84, 94, 102, 94, 89, 73 (a) 52

(b) 84

3. Find the mode of the following set of data. 36, 38, 38, 40, 42, 44, 40, 38, 37, 39 (a) 38

(b) 38.5

4. Which measure of center would you expect to be the smallest in a left-skewed distribution? (a) Mean

(b) Median

(d) Variation

5. Which of the following distributions is most likely to be bimodal? (a) The distribution of the heights of a sample of 100 female college students (b) The distribution of the last digits of ID numbers in a sample of 100 college students (c) The distribution of the weights of 100 dogs, where 50 are poodles and 50 are huskies (d) The distribution of the shoe sizes of a sample of 100 male college students 6. Consider the distribution graphed below.

B C

Which are most likely to be the values of A, B, and C? (a) A = mode, B = median, C = mean (b) A = mode, B = mean, C = median (c) A = median, B = mean, C = mode (d) A = mean, B = median, C = mode

Unit 6A Test 3 (continued)

Name:

7. Which best describes the distribution graphed below?

(a) Uniform and left-skewed (c) Unimodal and symmetric

(b) Uniform and symmetric (d) Bimodal and right-skewed

8. Which best describes the shape of a uniform distribution? (a) No peaks (c) Two peaks

(b) One peak (d) More than two peaks

9. Which best describes the shape of a unimodal distribution? (a) No peaks (c) Two peaks

(b) One peak (d) More than two peaks

10. Which quantity describes how widely data values are spread about the center of a distribution? (a) Mean (c) Skewness

(b) Variation (d) Number of peaks

Name:

Unit 6A Test 4

Date:

Choose the correct answer to each problem. 1. Find the mean of the following set of data. 8.5, 3.1, 8.7, 4.6, 5.3, 3.1, 6.6, 7.3 (a) 3.1

(b) 4.95

(d) 5.95

2. Find the median of the following data set. 8.5, 3.1, 8.7, 4.6, 5.3, 3.1, 6.6, 7.3 (a) 3.1

(b) 4.95

3. Find the mode of the following set of data. 8.5, 3.1, 8.7, 4.6, 5.3, 3.1, 6.6, 7.3 (a) 3.1

(b) 4.95

4. Which measure of the center of a distribution is most affected by an outlier? (a) Mean

(b) Median

(d) Variation

5. Which measure of center is at the peak of a right-skewed distribution? (a) Mean

(b) Median

(d) Variation

6. Which of the following is not used to describe the shape of a distribution? (a) Number of Peaks (c) Variation

(b) Symmetry or skewness (d) Mean

7. Which measure of center would you expect to be the largest in a left-skewed distribution? (a) Mean

(b) Median

(d) Variation

8. Which of the following distributions is most likely to be uniform? (a) The distribution of the heights of a sample of 100 college students (b) The distribution of the last digits of ID numbers in a sample of 100 college students (c) The distribution of the scores on a mathematics exam taken by 100 college students (d) The distribution of the GPAs of a sample of 100 college students

Unit 6A Test 4 (continued)

Name:

9. Consider the distribution graphed below.

B C

Which are most likely to be the values of A, B, and C? (a) A = mode, B = median, C = mean (b) A = mode, B = mean, C = median (c) A = median, B = mean, C = mode (d) A = mean, B = median, C = mode 10. Which best describes the distribution graphed below?

(a) Uniform and symmetric (c) Unimodal and symmetric

(b) Unimodal and right-skewed (d) Bimodal and symmetric

Name:

Unit 6B Test 1

Date:

Use the following sets of SAT scores to answer the following questions. SAT Scores for Men

SAT Scores for Women

1059 1328 1175 1123 923 1017 1214

1226

965

841 1053 1056 1393 1312

1042 1313 1040 1100 1290 990 1300

1222 1100 1215 1300 1296

985

1350

1. Compute the mean and the median for each set of data.

2. Compute the 5-Number Summary for each set of data.

3. Sketch side-by-side boxplots for the sets of data.

4. Based on the 5-Number Summaries and the boxplots, which group had the highest median? Which group had the most consistent performance?

Unit 6B Test 1 (continued)

Name:

5. Compute the range and standard deviation for each set of data.

6. Apply the range rule of thumb to estimate the standard deviation of each set of data. How well does it work in each case? Briefly comment on why it did or did not work in each case.

7. Based on all your results, compare and discuss the two data sets in terms of their centers and variation.

Name:

Unit 6B Test 2

Date:

Use the following sets of ACT scores to answer the following questions. ACT Scores for Men

ACT Scores for Women

18 17 23

23 17 24

15 34 23

26 13 32

33 24 30 20 30 31

30 25 33 12

1. Compute the mean and the median for each set of data.

2. Compute the 5-Number Summary for each set of data.

3. Sketch side-by-side boxplots for the sets of data.

4. Based on the 5-Number Summaries and the boxplots, which group had the highest median? Which group had the most consistent performance?

Unit 6B Test 2 (continued)

Name:

5. Compute the range and standard deviation for each set of data.

6. Apply the range rule of thumb to estimate the standard deviation of each set of data. How well does it work in each case? Briefly comment on why it did or did not work in each case.

7. Based on all your results, compare and discuss the two data sets in terms of their centers and variation.

Name:

Unit 6B Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following is not part of the five-number summary? (a) High

(b) Lower quartile

(d) Mode

2. In a typical set of numerical data, what fraction of the data values lie at or above the lower quartile? 1 4 3 (c) 4

1 2

(b)

(a)

(d) 1 (i.e., all of the data)

3. Find the range of the following data set. 1.2 1.9 2.6 1.4 3.2 2.7 2.1 (a) .8

(b) 1.8

(d) 2.1

(d) 15.1

4. Find the lower quartile of the following data set. 14.1 14.9 15.0 15.2 15.5 15.8 (a) 14.9

(b) 14.95

5. Find the five-number summary for the data set. 7.25 8.75 8.5 8.25 8.5 9 10 10 (a) 7.25, 8.25, 8.5, 10, 10 (c) 7.25, 8.125, 8.625, 10, 10

8 (b) 7.25, 8, 8.625, 9, 10 (d) 7.25, 8.25, 8.75, 10, 10

6. The box plot shown represents the heights of 100 students. Approximately how many of these students are between 60.5 and 64.5 inches tall? 70

64.5 62.5 60.5 56 (a) 25 students

(b) 40 students

(d) 75 students

Unit 6B Test 3 (continued)

Name:

7. The weights, in pounds, of a group of dogs are: 34, 37, 42, 57, 64, 82. Calculate the standard deviation. (a) 16.9 pounds

(b) 18.5 pounds

(d) 343 pounds

8. The ages, in days, of a group of infants, are: 3, 3, 4, 7, 10, 19. Estimate the standard deviation of the ages using the range rule of thumb. (a) 4 days

(b) 6.2 days

(d) 7 days

Name:

Unit 6B Test 4

Date:

Choose the correct answer to each problem. 1. Which of the following is not a measure of variation? (a) Five-number summary (c) Mean

(b) Range (d) Standard deviation

2. In a typical set of numerical data, what fraction of the data values lie at or above the upper quartile? 1 4 3 (d) 4

(a) 0 (i.e., none of the data) (c)

(b)

1 2

3. Find the range of the following set of data. 74 62 93 98 89 85 (a) 11

(b) 24

4. Find the upper quartile of the following data set. 59 65 70 71 71 74 75 78 80 (a) 83.5

(b) 84

5. Find the five-number summary for the data set. 387 769 459 355 419 749 697 (a) 355, 419, 449, 599, 769 (c) 355, 449, 454, 697, 769

(d) 36 91

449

(d) 87 449

(b) 355, 419, 454, 697, 769 (d) 355, 419, 459, 723, 769

6. The box plot shown represents the heights of 160 students. Approximately how many of these students are between 43.5 and 46.5 inches tall? 50 46.5 43.5 41.5 37 (a) 40 students

(b) 60 students

(d) 120 students

Unit 6B Test 4 (continued)

Name:

7. The weights, in pounds, of a group of dogs are: 8, 14, 26, 56, 72, 90. Calculate the standard deviation. (a) 27.3 pounds

(b) 31.0 pounds

(d) 1155 pounds

8. The lengths, in inches, of ten baguettes are: 17.2, 17.9, 17.9, 18.0, 18.0, 18.0, 18.1, 18.1, 18.2, 18.6 Estimate the standard deviation of the lengths using the range rule of thumb. (a) 0.04

(b) 0.35

(d) 0.60

Name:

Unit 6C Test 1

Date:

Where appropriate, you may use the following abbreviated table of z-scores and percentiles. z-score

–3.0

–2.0

–1.5

–1.0

–0.9

–0.8

–0.7

–0.6

–0.5

percentile

0.13

2.28

6.68

15.87

18.41

21.19

24.20

27.43

30.85

z-score

–0.4

–0.3

–0.2

–0.1

0.0

0.1

0.2

0.3

0.4

percentile

34.46

38.21

42.07

46.02

50.00

53.98

57.93

61.79

65.54

z-score

0.5

0.6

0.7

0.8

0.9

1.0

1.5

2.0

3.0

percentile

69.15

72.57

75.80

78.81

81.59

84.13

93.32

97.72

99.87

1. Assume that a set of test scores is normally distributed with a mean of 78 and a standard deviation of 10. Use the 68-95-99.7 Rule to find the percentage of scores that lie between 58 and 98?

2. Assume that a set of test scores is normally distributed with a mean of 78 and a standard deviation of 10. Use the 68-95-99.7 Rule to find the percentage of scores greater than 78?

3. The average person has an IQ of 100, and scores are normally distributed with a standard deviation of 15 points. Use the 68-95-99.7 Rule to find the percentage of people that have an IQ between 85 and 115?

4. The average person has an IQ of 100, and scores are normally distributed with a standard deviation of 15 points. Use the 68-95-99.7 Rule to find the percentage of people that have an IQ less than 70?

Unit 6C Test 1 (continued)

Name:

5. Suppose a data set has a mean of 126 and a standard deviation of 4. Find the standard score for a data value of 133.

6. Prior to re-centering in 1995, the mean SAT verbal score was about 430. Assume that the standard deviation was 100 points. Find the standard score and the percentile for a student who scored 580.

7. Find the standard score and the percentile of a data value that is 0.4 standard deviations above the mean

8. About how many standard deviations above or below the mean is a data value in the 21st percentile?

9. Assume that a set of test scores is normally distributed with a mean of 820 and a standard deviation of 35. In what percentile is a score of 750?

10. Bob took a standardized test, and his score was in the 79th percentile. Explain the meaning of this statement.

Name:

Unit 6C Test 2

Date:

Where appropriate, you may use the following abbreviated table of z-scores and percentiles. z-score

–3.0

–2.0

–1.5

–1.0

–0.9

–0.8

–0.7

–0.6

–0.5

percentile

0.13

2.28

6.68

15.87

18.41

21.19

24.20

27.43

30.85

z-score

–0.4

–0.3

–0.2

–0.1

0.0

0.1

0.2

0.3

0.4

percentile

34.46

38.21

42.07

46.02

50.00

53.98

57.93

61.79

65.54

z-score

0.5

0.6

0.7

0.8

0.9

1.0

1.5

2.0

3.0

percentile

69.15

72.57

75.80

78.81

81.59

84.13

93.32

97.72

99.87

1. Assume that a set of test scores is normally distributed with a mean of 72 and a standard deviation of 12. Use the 68-95-99.7 Rule to find the percentage of scores that lie between 60 and 84?

2. Assume that a set of test scores is normally distributed with a mean of 72 and a standard deviation of 12. Use the 68-95-99.7 Rule to find the percentage of scores greater than 48?

3. The average person has an IQ of 100, and scores are normally distributed with a standard deviation of 15 points. Use the 68-95-99.7 Rule to find the percentage of people who have an IQ between 70 and 130?

4. The average person has an IQ of 100, and scores are normally distributed with a standard deviation of 15 points. Use the 68-95-99.7 Rule to find the percentage of people has an IQ greater than 130?

Unit 6C Test 2 (continued)

Name:

5. Suppose a data set has a mean of 104 and a standard deviation of 10. Find the standard score for a data value of 110.

6. After re-centering in 1995, the mean SAT math score was about 500. Assume that the standard deviation was 100 points. Find the standard score and the percentile for a student who scored 460.

7. Find the standard score and percentile of a data value that is 0.7 standard deviations below the mean.

8. About how many standard deviations above or below the mean is a data value in the 69th percentile?

9. Assume that a set of test scores is normally distributed with a mean of 630 and a standard deviation of 15. In what percentile is a score of 615?

10. Carol took a standardized test, and her score was in the 34th percentile. Explain the meaning of this statement.

Name:

Unit 6C Test 3

Date:

Choose the correct answer to each problem. Where appropriate, you may use the following abbreviated table of z-scores and percentiles. z-score

–3.0

–2.0

–1.5

–1.0

–0.9

–0.8

–0.7

–0.6

–0.5

percentile

0.13

2.28

6.68

15.87

18.41

21.19

24.20

27.43

30.85

z-score

–0.4

–0.3

–0.2

–0.1

0.0

0.1

0.2

0.3

0.4

percentile

34.46

38.21

42.07

46.02

50.00

53.98

57.93

61.79

65.54

z-score

0.5

0.6

0.7

0.8

0.9

1.0

1.5

2.0

3.0

percentile

69.15

72.57

75.80

78.81

81.59

84.13

93.32

97.72

99.87

1. Assume that a set of test scores is normally distributed with a mean of 545 and a standard deviation of 30. What percentage of scores lies between 515 and 545? (a) 34%

(b) 47.7%

(d) 95%

2. The average person has an IQ of 100, and scores are normally distributed with a standard deviation of 15 points. What percentage of people has an IQ above 115? (a) 6.68%

(b) 15.87%

(d) 93.32%

3. Assume that a set of test scores is normally distributed with a mean of 70 and a standard deviation of 10. In what percentile is a score of 65? (a) 95th percentile

(b) 69th percentile

(d) 5th percentile

4. Suppose a data set has a mean of 136 and a standard deviation of 8. Find the standard score for a data value of 121. (a) –1.875

(b) –0.75

(d) 1.875

5. Prior to re-centering in 1995, the mean SAT verbal score was about 430. Assume that the standard deviation was 100 points. Find the standard score for a student who scored 490. (a) –0.6

(b) –0.1

(d) 0.6

6. After re-centering in 1995, the mean SAT math score was about 500. Assume that the standard deviation was 100 points. Find the percentile for a student who scored 530. (a) 24th percentile

(b) 38th percentile

(d) 75th percentile

7. In what percentile is a data value that is 0.7 standard deviations above the mean? (a) 73rd percentile

(b) 24th percentile

(d) 70th percentile

Unit 6C Test 3 (continued)

Name:

8. In what percentile is a data value that is 0.7 standard deviations below the mean? (a) -70th percentile

(b) 24th percentile

(d) 70th percentile

9. About how many standard deviations above or below the mean is a data value in the 46th percentile? (a) 0.1 standard deviation below the mean (c) 0.2 standard deviation above the mean

(b) 0.1 standard deviation above the mean (d) 0.2 standard deviation below the mean

10. About how many standard deviations above or below the mean is a data value in the 54th percentile? (a) 0.1 standard deviation below the mean (c) 0.2 standard deviation above the mean

(b) 0.1 standard deviation above the mean (d) 0.2 standard deviation below the mean

Name:

Unit 6C Test 4

Date:

Choose the correct answer to each problem. Where appropriate, you may use the following abbreviated table of z-scores and percentiles. z-score

–3.0

–2.0

–1.5

–1.0

–0.9

–0.8

–0.7

–0.6

–0.5

percentile

0.13

2.28

6.68

15.87

18.41

21.19

24.20

27.43

30.85

z-score

–0.4

–0.3

–0.2

–0.1

0.0

0.1

0.2

0.3

0.4

percentile

34.46

38.21

42.07

46.02

50.00

53.98

57.93

61.79

65.54

z-score

0.5

0.6

0.7

0.8

0.9

1.0

1.5

2.0

3.0

percentile

69.15

72.57

75.80

78.81

81.59

84.13

93.32

97.72

99.87

1. Assume that a set of test scores is normally distributed with a mean of 480 and a standard deviation of 20. What percentage of scores lies between 440 and 480? (a) 34%

(b) 47.5%

(d) 95%

2. The average person has an IQ of 100, and scores are normally distributed with a standard deviation of 15 points. What percentage of people has an IQ above 130? (a) 2%

(b) 2.28%

(d) 6.68%

3. Assume that a set of test scores is normally distributed with a mean of 55 and a standard deviation of 15. In what percentile is a score of 70? (a) 68th percentile

(b) 70th percentile

(d) 95th percentile

4. Suppose a data set has a mean of 117 and a standard deviation of 10. Find the standard score for a data value of 103. (a) –7

(b) –1.4

(d) 7

5. Prior to re-centering in 2000, the mean SAT verbal score was about 440. Assume that the standard deviation was 100 points. Find the standard score for a student who scored 390. (a) –0.5

(b) 0.5

(d) 0.9

6. After re-centering in 1995, the mean SAT math score was about 500. Assume that the standard deviation was 100 points. Find the percentile for a student who scored 420. (a) 21st percentile

(b) 34th percentile

(d) 78th percentile

7. In what percentile is a data value that falls 0.6 standard deviation below the mean? (a) 60th percentile percentile

(b) 27th percentile

(d) 73rd

Unit 6C Test 4 (continued)

Name:

8.In what percentile is a data value that falls 0.6 standard deviation above the mean? (a) 60th percentile

(b) 27th percentile

(d) 73rd percentile

9. About how many standard deviations above or below the mean is a data value in the 21st percentile? (a) 0.8 standard deviation below the mean (c) 0.4 standard deviation above the mean

(b) 0.4 standard deviation below the mean (d) 0.8 standard deviation above the mean

10. About how many standard deviations above or below the mean is a data value in the 65th percentile? (a) 0.8 standard deviation below the mean (c) 0.4 standard deviation above the mean

(b) 0.4 standard deviation below the mean (d) 0.8 standard deviation above the mean

Name:

Unit 6D Test 1

Date:

1. What does it mean for an observed difference to be statistically significant at the 0.01 level?

2. What is a sampling distribution?

3. Suppose you draw a single sample of size 2500 from a large population and measure its sample proportion. What is the margin of error for 95% confidence?

4. Suppose that you take a random sample of 360 people who voted in the last election in a heavily populated county and you find that 9% of those people voted illegally. Find a 95% confidence interval for the actual percentage of people who voted illegally in that county.

5. Should a presidential candidate conclude that his popularity is dwindling because a poll shows his approval rating to be 61% one day and 59% the next day? Explain.

Unit 6D Test 1 (continued)

Name:

Use the following claim to answer questions 6 – 8. The local barbecue restaurant says that only 30% of its customers are students at the university. 6.

Construct a null hypothesis and an alternate hypothesis for the above claim.

7. Briefly describe the results expected in this study if the null hypothesis is true.

8. Briefly describe the results expected in this study if the alternative hypothesis is true.

Use the following study to answer questions 9 – 10. The local school system feels that the number of student absences in this county is lower than the published state average of 5.6 absences per year. They take a random sample of 120 students and the average number of absences is found to be 4.9. The likelihood that the local school system would observe a sample of this type assuming the state assertion is true is 0.0052. 9. Use the above to formulate a null hypothesis and an alternate hypothesis.

10. At the 5% level of significance, does the sample provide evidence for rejecting or not rejecting the null hypothesis? Explain.

Name:

Unit 6D Test 2

Date:

1. What does it mean for an observed difference to be statistically significant at the 0.05 level?

2. According to the Central Limit Theorem, what is the mean of a sampling distribution?

3. The actual proportion of students living in residence halls at a large university is 0.38. Several samples of 100 students each yield proportions of 0.28, 0.30, 0.31, and 0.39 residence hall students. According to the Central Limit Theorem, what is the mean of these sample proportions?

4. If you take samples of size 1000 from a large population, what is the standard deviation of the sampling distribution?

5. Of what are you 95% confident when you give a 95% confidence interval?

6. Suppose you draw a single sample of size 2000 from a large population and measure its sample proportion. What is the margin of error for 95% confidence?

Unit 6D Test 2 (continued)

Name:

Use the following to answer questions 7 – 8. A marine biologist believes the number of manatee deaths off the Florida coast has reduced since the beginning of a targeted awareness campaign. 7. Construct a null hypothesis an alternative hypothesis for this study.

8. Briefly describe the two possible results that can come from this study.

Use the following study to answer questions 9 – 10. The local school system feels that the number of student absences in this county is lower than the published state average of 5.6 absences per year. They take a random sample of 120 students and the average number of absences is found to be 5.2. The likelihood that the local school system would observe a sample of this type assuming the state assertion is true is 0.059. 9. Use the above to formulate a null hypothesis and an alternate hypothesis.

10. Does the sample provide evidence for rejecting or not rejecting the null hypothesis. Explain.

Name:

Unit 6D Test 3

Date:

Choose the correct answer to each problem. 1. The actual proportion of flawed computer chips manufactured at a particular plant is 0.06. Four samples of chips yield proportions with flaws of 0.03, 0.04, 0.08, and 0.05. According to the Central Limit Theorem, what is the mean of this sampling distribution? (a) 0.04

(b) 0.05

(d) 0.07

2. If you take samples of size 1500 from a large population, what is the standard deviation of the sampling distribution? (a) 0.001

(b) 0.007

(d) 0.026

3. Suppose you draw a single sample of size 100 from a large population and measure its sample proportion. What is the margin of error for 95% confidence? (a) 0.05

(b) 0.1

(d) 0.95

4. Suppose that you take a random sample of 100 bags of potato and corn chips from a grocery store and find that 14% are under filled according to weight. Find a 95% confidence interval for the actual percentage of under filled bags at this grocery store. (a) 0% to 28%

(b) 4% to 24%

(d) 9% to 19%

5. A poll of 750 registered voters shows the support for a proposed tax increase to build new schools to be 65% one week and 21% the next week. Which of the following is a reasonable explanation for the discrepancy in these sample statistics? (a) The percentage of the population who supports the tax increase didn’t change; the difference in the statistics is due to chance. (b) The margin of error is so large that the difference is not statistically significant; the two sample statistics are estimates of the same population parameter. (c) The proportion of the population who supports a tax increase dropped significantly during the week between the two polls. (d) The organization seeking the tax increase paid the polling organization 44% more for the first poll than for the second poll. 6. An organization of psychologists seeking millions of federal dollars to treat adults who were abused as children states in its report to the U.S. Congress that an estimated 45% of adults in the United States suffered some form of abuse during their childhood. The bipartisan committee reviewing the report hires an independent research group to test this claim. In a random sample of 144 adults, the independent group finds 9 adults who believe they were abused as children. Which of the following is not a reasonable explanation for the difference in the statistics? (a) The difference in the two statistics is due to chance, so that the difference is not statistically significant. (b) The organization seeking the money exaggerated in their report in order to make their cause seem more urgent. (c) The organization of psychologists used a sample of convicted felons to find its statistic, while the independent research group used a sample of the entire U.S. population. (d) The statistic of 45% reported by the organization of psychologists is wrong, and the true population parameter is close to 6.25%. Copyright © 2023 Pearson Education, Inc. - 218 -

Unit 6D Test 3 (continued)

Name:

7. In what circumstance is a result said to have high statistical significance? (a) It is very likely to have occurred by chance. (b) It is very unlikely to have occurred by chance. (c) It supports the alternative hypothesis of an experiment. (d) It supports the null hypothesis of an experiment. Use the following study to answer questions 8 – 10. The local school system feels that the number of student absences in this county is higher than the published state average of 5.6 absences per year. They take a random sample of 120 students and the average number of absences is found to be 5.9. The likelihood that the local school system would observe a sample of this type assuming the state assertion is true is 0.052. 8. Which of the following would be a reasonable null hypothesis for this study? (a) The local number of student absences is greater than 5.6. (b) The local number of student absences is 5.6. (c) The state average number of student absences is equal to 5.6. (d) The local number of student absences is equal to 5.9. 9. Which of the following would be a reasonable alternative hypothesis for this study? (a) The local number of student absences is greater than 5.6. (b) The local number of student absences is not 5.6. (c) The state average number of student absences is not equal to 5.6. (d) The local number of student absences is not equal to 5.9. 10. Which of the following describes what the sample provides evidence to do? (a) Reject the null hypothesis because we have evidence in support of the alternate hypothesis. (b) Reject the null hypothesis because we lack sufficient evidence to support the alternate hypothesis. (c) Do not reject the null hypothesis because we have evidence in support of the alternate hypothesis. (d) Do not reject the null hypothesis because we lack sufficient evidence to support the alternate hypothesis.

Name:

Unit 6D Test 4

Date:

Choose the correct answer to each problem. 1. The actual proportion of red Milk Chocolate M&Ms, out of all Milk Chocolate M&Ms produced each day for the small mixed bags, is 14.2%. Four samples of ten of these bags yield proportions of 0.124, 0.189, 0.093, and 0.13 red M&Ms. According to the Central Limit Theorem, what is the mean of this sampling distribution? (a) 0.134 (b) 0.139 (c) 0.142 (d) 0.147 2. If you take samples of size 16 from a population, what is the standard deviation of the sampling distribution? (a) 0.05

(b) 0.125

(d) 0.5

3. Suppose you draw a single sample of size 364 from a large population and measure its sample proportion. What is the margin of error for 95% confidence? (a) 5.2%

(b) 2.6%

(d) 52%

4. Suppose that you take a random sample of 259 people leaving a grocery store over the course of a day and you find that 12% of those people were overcharged. Find a 95% confidence interval for the actual percentage of shoppers who were overcharged. (a) 5.8% to 18.2% (b) 7% to 17% (c) 8.85% to 15.15% (d) 9.5% to 14.5% 5. A poll shows the approval rating of a senator to be 45% one day and 42% the next day. Which of the following is most likely the reason for the discrepancy in these sample statistics? (a) 3% of the population who approved of the senator at the time of the first poll disapproved at the time of the second poll. (b) Between the times of the polls, a news story was released alleging that the senator who claims to be “for women” is a groper. (c) The percentage of the population who approves of the senator didn’t change; the difference in the statistics is due to chance. (d) The senator’s staff paid the polling organization more for the first poll than for the second poll. 6. An environmentalist group seeking millions of federal dollars to clean up a polluted lake states in its report to the U.S. Congress that 75% of the fish in the lake have dangerous levels of toxins. The bipartisan committee reviewing the report hires an independent research group to test this claim. In a random sample of 280 fish from the lake, the independent group finds 35 fish that contain toxins. Which of the following is most likely true? (a) The difference in the two statistics is due to chance, and the population parameter is close to 75% as reported by the environmentalist group. (b) The fish with dangerous levels of toxins swim lower than other fish, so they were able to avoid being caught by the independent research group. (c) Since cleaning up the lake is a good idea, Congress should have given the group the money without questioning its claims. (d) The statistic of 75% reported by the environmentalist group is wrong, and the true population parameter is close to 12.5%.

Unit 6D Test 4 (continued)

Name:

7. In what circumstance is a result said to have low statistical significance? (a) It is very likely to have occurred by chance. (b) It is very unlikely to have occurred by chance. (c) It supports the alternative hypothesis of an experiment. (d) It supports the null hypothesis of an experiment. Use the following study to answer questions 8 – 10. The local school system feels that the number of student absences in this county is higher than the published state average of 5.6 absences per year. They take a random sample of 120 students and the average number of absences is found to be 5.9. The likelihood that the local school system would observe a sample of this type assuming the state assertion is true is 0.0052. 8. Which of the following would be a reasonable null hypothesis for this study? (a) The local number of student absences is greater than 5.6. (b) The local number of student absences is 5.6. (c) The state average number of student absences is equal to 5.6. (d) The local number of student absences is equal to 5.9. 9. Which of the following would be a reasonable alternative hypothesis for this study? (a) The local number of student absences is greater than 5.6. (b) The local number of student absences is not 5.6. (c) The state average number of student absences is not equal to 5.6. (d) The local number of student absences is not equal to 5.9. 10. Which of the following describes what the sample provides evidence to do? (a) Reject the null hypothesis because we have evidence in support of the alternate hypothesis. (b) Reject the null hypothesis because we lack sufficient evidence to support the alternate hypothesis. (c) Do not reject the null hypothesis because we have evidence in support of the alternate hypothesis. (d) Do not reject the null hypothesis because we lack sufficient evidence to support the alternate hypothesis.

Name:

Unit 7A Test 1

Date:

1. A kindergarten teacher has 17 students. In how many ways can she fill the roles of “line leader,” “door holder,” and “materials handler” with her students each day?

2. Explain the subjective method for finding probability.

3. Use the theoretical method for finding probability to determine the probability of: rolling a single die and getting an odd number.

4. Use the theoretical method for finding probability to determine the probability of: drawing an ace by drawing a single card from a standard deck.

5. Use the theoretical method for finding probability to determine the probability of: choosing a family that has a boy and a girl from families with two children. What assumption(s) must be made?

Unit 7A Test 1 (continued)

Name:

6. During the last 5 games, Erik made 27 baskets of his last 35 attempts. Based on this fact, what is the relative frequency probability that he will make his next basket?

7. State which method (theoretical, relative frequency, or subjective) should be used to answer the question: What is the probability of meeting someone who shares your birthday? (Ignore leap years)

8. If one card is drawn from a standard deck, what is the probability that the card will not be a face card (jack, queen, king)?

9. Find the odds for and the odds against rolling 2 fair dice and getting a double 1 (snake eyes).

10. Find the odds for and the odds against selecting one card from a standard deck and choosing a 4?

Name:

Unit 7A Test 2

Date:

1. A PAC executive council has 13 members. In how many ways can they elect a chair person, a vice-chair, a secretary, a historian, and a treasurer?

2. Explain the relative frequency method for finding probability.

3. Use the theoretical method for finding probability to determine the probability of: rolling a single die and getting a number greater than 4.

4. Use the theoretical method for finding probability to determine the probability of: drawing one card from a standard deck and choosing a 3.

5. During the last 12 weeks, it has rained at least once on seven of the weekends. Based on this fact, what is the relative frequency probability that it will rain at some point this weekend? What assumption(s) need to be made?

Unit 7A Test 2 (continued)

Name:

6. State which method (theoretical, relative frequency, or subjective) should be used to answer the question: What is the probability of winning the lottery?

7. Make a probability distribution for the given set of events. You may use a table or a graph (or both). The number of tails when you flip three coins.

8. If two fair dice are rolled, what is the probability that the sum will not be 10?

9. Find the odds for and the odds against selecting one card from a standard deck and choosing a club?

10. Find the odds for and the odds against rolling 2 fair dice and getting a 7 or 11.

Name:

Unit 7A Test 3

Date:

Choose the correct answer to each problem. 1. A family with three children has exactly 2 girls. Which of the following is not a possible outcome for that event? (G = girl, B = boy) (a) GGB (c) BGG

(b) BGB (d) GBG

2. If your instructor says she is 90% sure class won’t be canceled any more this semester due to weather, which method of determining probabilities did she use? (a) Theoretical method

(b) Relative frequency method

3. Sean flipped a coin 100 times and got heads 42 times. What conclusion should he correctly draw? (a) The coin is not a fair coin. (c) The probability of getting heads is not 0.5.

(b) He didn’t get 50 heads due to chance. (d) Tails is a more likely outcome than heads.

4. On a roll of two dice, Tom bets the sum will be 5. Henry bets the sum will be 8. Who has the better probability of winning the bet? (a) Tom

(b) Henry

5. In a particular class, there are 13 freshmen, 15 sophomores, 4 juniors, and 2 seniors. If the instructor randomly chooses a student to answer a question in class, what is the probability that the student chosen will be a freshman? (a) 0.382

(b) 0.691

(d) 0.857

6. Determine the probability of obtaining a sum of 9 on a single roll of two fair dice. (a)

1 6

(b)

1 9

(c)

1 11

(d)

1 12

7. A quality control agent tested 8 pints of ice cream during the past hour. She found that one of the pints was not acceptable. Using the relative frequency probability method, find is the probability that the next pint tested will be acceptable. (a) 0.875

(b) 0.125

(d) 0.50

8. What number correctly completes the following probability distribution for the number of boys in a family of 3 children? Result Probability 3 boys 0.125 2 boys 0.375 1 boy 0.375 0 boys (a) 0.05

(b) 0.125

(d) 0.5

Unit 7A Test 3 (continued)

Name:

9. The probability that a student chosen at random from your class owns an iPod is 0.45. What is the probability that a student chosen at random from your class does not own an iPod? (a) 0.45 (b) 0.55 (d) Cannot be determined from the information given.

10. The probability that our team will finish first in the relay race is 0.20. What are the odds of our team winning the race? (a) 1 to 2

(b) 1 to 4

(d) 2 to 5

Name:

Unit 7A Test 4

Date:

Choose the correct answer to each problem. 1. What are the most basic possible results of observations or experiments? (a) Events

(b) Outcomes

(d) Distributions

2. What is the probability of being dealt 3 aces in a 5-card poker hand. Which method of determining probabilities should be used? (a) Theoretical method

(b) Relative frequency method

3. Roger conducted a survey in his math class and found that 15% of the students are international students. He concludes that the probability of a student in his math class being an international student is 0.15. Which method did Roger use? (a) Theoretical method

(b) Relative frequency method

4. A family has 4 children. How many different boy/girl birth orders are possible? (a) 2

(b) 16

(d) 4

5. On a roll of two dice, Cindy bets the sum will be 6. Hillary bets the sum will be 3. Who has the better probability of winning the bet? (a) Cindy

(b) Hillary

6. There are 4 red marbles, 5 yellow marbles, and 3 blue marbles in a bag. Use the theoretical probability method to determine the probability of drawing a red marble from the bag. (a) 0.25

(b) 0.333

(d) 0.67

7. Use the theoretical probability method to determine the probability of drawing an ace from a standard deck of cards. (a) 0.0769

(b) 0.03

(d) 0.5

8. What number correctly completes the following probability distribution for the number of girls in a family of 3 children? Result Probability 3 girls 0.125 2 girls 0.375 1 girl 0 girls 0.125 (a) 0.05

(b) 0.125

(d) 0.5

9. Find the probability of not rolling a sum of 9 with a pair of dice. (a)

1 12

(b)

1 36

(c)

1 9

(d) 8 9

Unit 7A Test 4 (continued)

Name:

10. The probability that the Junior class will win Spirit Week is 0.25. What are the odds that the Junior class wins? (a) 1 to 2

(b) 1 to 3

(d) 2 to 1

Name:

Unit 7B Test 1

Date:

1. Define dependent events.

2. Give an example of mutually exclusive events.

3. What is the probability of rolling four fair dice and getting an odd number on all four dice? Are these independent or dependent events?

4. What is the probability of drawing, in order, ace, king, queen, then jack, when drawing one card at a time from a standard deck? Assume each card is place back in the deck before drawing the next. Are these independent or dependent events?

5. What is the probability of selecting 2 men from a pool of 10 men and 6 women? Are these independent or dependent events?

6. In a drawer, there are 6 pink, 5 white, 3 yellow, and 4 blue shirts. What is the probability of randomly choosing one shirts that is white or blue? Are these events overlapping or non-overlapping?

Unit 7B Test 1 (continued)

Name:

7. When drawing one card, what is the probability of drawing a 6 or an ace from a standard deck? Are these events overlapping or non-overlapping?

8. When drawing one card, what is the probability of drawing a queen or a heart from a standard deck? Are these events overlapping or non-overlapping?

9. Find the probability of at least one 3 when you roll 2 fair dice.

10. Scratch ‘N Win Fun lottery tickets advertise 1 in 50 wins. You buy 5 tickets. What is the probability that you have purchased at least one winner?

Name:

Unit 7B Test 2

Date:

1. Give an example of dependent events.

2. Define mutually exclusive.

3. Someone flips a fair coin and rolls a 6-sided die. What is the probability that a tail and a 3 will be the result? Are the events independent or dependent?

4. If two cards are drawn from a standard deck, what is the probability that the two cards are a 4 then a 5? Assume the first card drawn is placed back in the deck before the second card is drawn. Are the events independent or dependent?

5. What is the probability of randomly selecting all seniors to form a committee of three from a pool of 15 seniors, 12 juniors, and 9 sophomores? Are the events independent or dependent?

6. What is the probability of drawing either an ace or a heart from a standard deck of cards? Are these events overlapping or non-overlapping?

Unit 7B Test 2 (continued)

Name:

7. What is the probability of drawing either an ace or a three from a standard deck of cards? Are these events overlapping or non-overlapping?

8. Everyone in a literature class of 81 students bought two books by the same author. Sixty-two of the students read the first book, 54 read the second book, and 39 read both. What is the probability that a randomly selected student read at least one of the two books?

9. A little boy loses his shoe once in every three trips to the backyard. What is the probability that he will lose his shoe at least once in the next six trips?

10. A rug weaver’s thread accidentally breaks, on average, once every 42 passes. What is the probability that the thread will break at least once in the next 12 passes?

Name:

Unit 7B Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following are examples of independent events? (a) Two consecutive victories by the same army (b) Two archeological discoveries at different locations in the same country, at the same time (c) Two people in the same family falling ill in the same week (d) Two laughs by different people watching the same movie in a theater 2. A certain wrench has a 5% breakage rate in normal use. Another brand of wrench has a 2% breakage rate. What is the percent chance that a person who uses both wrenches moderately often will break both during normal use? (a) 0.096%

(b) 0.024%

(d) 0.1%

3. A music fan randomly selects 4 CDs from a stack of 35, where 6 are by the same country-western artist. What is the probability that all the CDs chosen are by that artist? (a) 0.000134

(b) 0.000212

(d) 0.000369

4. A committee of three people is to be randomly selected from a group of 20 men and 17 women. What is the probability that all three people will be women? (a) 0.0875

(b) 0.097

(d) 1.378

5. A selected person could have red hair. That person could also have blue eyes. Are these overlapping or non-overlapping? Why or why not? (a) Overlapping, because one person could have both (c) Overlapping, because one person could not have both

(b) Non-overlapping, because one person could have both (d) Non-overlapping, because one person could not have both

6. What is the probability of drawing a diamond or an ace from a standard deck of cards? (a) 0.135

(b) 0.308

(d) 0.481

7. What is the probability of drawing an ace or a king from a standard deck of cards? (a) 0.0769

(b) 0.154

(d) 0.327

8. What is the probability of drawing four hearts in a row from a standard deck when the drawn card is returned to the deck each time? (a) 0.00035

(b) 0.00264

(d) 0.0042

9. In a certain country, there is a bank failure once every 2 years, on average. What is the probability of at least one bank failure in the next 10 years? (a) 0.969

(b) 0.64

(d) 0.999

Unit 7B Test 3 (continued)

Name:

10. A plant has a pollution-control system shutdown once every 75 days, on average. What is the probability of at least one shutdown in the next year? (a) 100.0%

(b) 1.33%

(d) 99.3%

Name:

Unit 7B Test 4

Date:

Choose the correct answer to each problem. 1. Which of the following are examples of independent events? (a) Two travelers from the same family, but in different countries, catching local diseases at the same time (b) Two people in different places getting mugged by the same man on the same afternoon (c) Two baseball players getting salaries over $10 million during the same preseason negotiations (d) Two bids at an open auction, for the same painting, by different people 2. A televised debate is being taped using two independent sound systems. The first has a 0.03 probability of failure during taping; the second has a 0.05 probability of failure. What is the probability that both will fail during taping? (a) 0.08

(b) 0.02

(d) 0.0015

3. Two whirlpool spas by different manufacturers are subjected to government safety tests. The first has a 0.86 probability of passing without modification; the second has a 0.88 probability. What is the probability that both spas will pass without modification? (a) 0.757

(b) 0.781

(d) 0.847

4. Two friends compete with each other and with five other equally good violinists for first and second chair in an orchestra, in a blind competition. What is the probability that the two friends end up as first and second chair together? (a) 0.0255

(b) 0.0476

(d) 0.0784

5. What is the probability of drawing either a jack, queen, or king from a standard deck of cards? (a) 0.014

(b) 0.058

(d) 0.75

6. The soldiers in a battalion are all inspected by two inspectors, working separately. 87% of the men are passed by inspector A, 89% are passed by inspector B, and 80% are passed by both. What percent of soldiers are passed by at least one inspector? (a) 92%

(b) 94%

(d) 98%

7. A hijacked plane may land in Greece. It may also land in Cuba. Are these events overlapping? Why or why not? (a) No, because the plane might land in two places (c) Yes, because the plane might land in two places

(b) No, because the plane can only land in one place (d) Yes, because the plane can only land in one place

8. Out of 80 students on a dorm hall, 38 are taking at least English, 24 are taking at least science, and 8 are taking both English and science. What is the probability that a student chosen at random from this hall is taking English or science? (a) 0.014

(b) 0.525

(d) 0.875

Unit 7B Test 4 (continued)

Name:

9. What is the probability of getting at least one six when rolling six fair dice? (a) 0.00002

(b) 0.167

(d) 0.999

10. A bicycle rider has a spill once every 25 days, on average. What is the probability of at least one fall in the next 30 days? (a) 68.2%

(b) 70.5%

(d) 82.6%

Name:

Unit 7C Test 1

Date:

1. An insurance policy to cover damage on a Move-Me truck for the duration of a rental is $70. Based on historical data, 1 in 200 renters cause damage to a rented truck. The average cost of repair to a damaged truck is $1200. If 1000 renters buy the insurance, what is the expected profit or loss with the renter’s insurance?

2. A new style of policing is thought to give a city 3 to 5 odds of reducing crime by 15%. If the style is adopted by 30 cities, about how many can be expected to achieve that result?

3. A criminal investigation into a department of the government suggests that for any given worker, there is a chance of about 1 in 30 that this person is involved in questionable but criminally minor activities of some kind or other, while 1 in 120 is involved in a serious crime. The rest are innocent. If the department contains 5400 workers, how many may be expected to be innocent, how many involved in minor shady dealings, and how many involved in serious crime?

4. Explain the gambler’s fallacy.

5. A private pilot buys a plane with possible mechanical trouble. There is a 20% chance that the plane is in good condition and worth $43,000, there is a 50% chance that it needs a complete systems overhaul and is worth $26,000, and there is a 30% chance that the plane needs only minor repairs and is worth $35,000. What is the expected value of the plane?

Unit 7C Test 1 (continued)

Name:

6. Cold weather threatens an orange grove. If the weather passes without dropping the temperatures too far, the crop will be worth $680,000, but there is a 12% chance that the oranges will freeze and become worthless. What is the expected value of the crop?

7. A hacker breaking into a computer system has a 10% chance of breaking into a system in 3 minutes, a 30% chance after 10 minutes, and a 60% chance after 30 minutes. What is the expected time will take the hacker to get in?

8. An electronics store sells extended warranties. For a particular product they estimate 8% of those who buy the $14 warranty will use it, costing the store $110 to replace and ship the product. What is the expected flow of income from this extended warranty?

9. A casino card game takes $4 bets. Players have a 46% chance of winning back their bets plus $4, and they have a 54% chance of losing their bets. What is the house edge?

10. A game consists of laying a bet of $1 and taking a single card from a dealer (the house). If the card is a face card, the player wins and collects $3.00 plus the original bet; otherwise, the player loses the $1. What is the house edge in this game?

Name:

Unit 7C Test 2

Date:

1. A surgical procedure has a 46% chance of helping the average cancer patient it is performed on. If the operation is done on 43,500 patients, how many may it be expected to help?

2. A new hairstyle is all the rage, and a hairstylist figures that about one in six women coming into the salon request this style. If the salon expects about 300 women during the next week, how many times will the hairstyle be recreated at the salon that week?

3. A particular kind of loan has an estimated 15% chance of not being repaid, a 25% chance of being repaid with difficulty, and a 60% chance of being repaid without incident. If this kind of loan is granted to 38,000 people, how many people in each category may one expect?

4. A smoker whose friend urges him to quit refuses, saying “My grandfather and father both died of lung cancer; I figure my family’s run of bad luck is due to change.” What is this mindset called?

5. A recently excavated skull is being bought, sight unseen, by an antiquities dealer. There is a 30% chance that the skull is in good condition and worth $5900; there is a 20% chance that it is heavily damaged and worth only $850, and there is a 50% chance that it suffers from only minor damage and is worth $3400. What is the expected value of the skull?

Unit 7C Test 2 (continued)

Name:

6. Hurricane season threatens to cause a loss of tourist revenue to a coastal town. If the season looks pretty clear, the locals expect tourist revenues of $2.4 million. However, there is a 15% chance that several hurricanes will threaten the area and cause tourist revenue to plunge to $320,000. What are the expected revenues for the season?

7. A piece of antique furniture has an 80% chance of being a genuine article, 300 years old, a 10% chance of being a 150-year-old forgery, and a 10% chance of being a 50-year-old forgery. What is the expected age of the piece?

8. A lawyer considering taking a case figures that there is a 40% chance of winning the case in court and earning his firm $400,000, a 50% chance of losing and costing his firm $150,000, and a 10% chance of settling out of court and bringing in $200,000. What is the expected payoff of the case for the firm?

9. A casino card game takes $5 bets. Players have a 48% chance of winning back their bets plus $5, and they have a 52% chance of losing their bets. What is the house edge?

10. A game consists of laying a $1 bet and taking a single card from a dealer (the house) working with a 54card deck, which includes two jokers. If the card is hearts or spades, the player wins and gets the $1 back plus another $1; otherwise, the player loses the $1. What is the house edge in this game?

Name:

Unit 7C Test 3

Date:

Choose the correct answer to each problem. 1. A magazine auto critic gives a single star (worst rating) to about one car in twelve that he reviews. If he expects to review 216 cars during the next season, how many one-star cars can the readers expect? (a) 14

(b) 16

(d) 20

2. A certain religious denomination sends one out of every seven of its missionaries to Asia. If the denomination is sending 476 missionaries next year, how many are likely to go to Asia? (a) 55

(b) 68

(d) 91

3. Suppose a motorcycle rider has 1 chance in 6 of falling sometime during a year of driving. If there are 2,700 motorcycle riders in a certain area, about how many will fall in the next year? (a) 450

(b) 900

(d) 1300

4. A woman, buying a computer of the same brand her friends have had trouble with, figures that the company is overdue to have a satisfied customer, and she figures to be it. This is a case of the gambler’s fallacy because (a) the satisfied customer could be someone else. (c) her experiences will probably match her friends’.

(b) she is relying on chance, which is unwise. (d) her friends aren’t a large sample of users.

5. Fifteen people gather for a hot dog eating contest. In the past, eight of these contestants have eaten 37 hot dogs during the competition, three ate 43, three ate 47, and one ate 49. What is the expected number of hot dogs eaten by a randomly chosen contestant today? (a) 39 hot dogs

(b) 40 hot dogs

(d) 42 hot dogs

6. Of eight goldfish in a tank, two are 1 inch long, five are 2 inches long, and one is a 3 inches long. What is the expected length of a goldfish selected from this tank?

5 (a) 1 inches 8

1 (b) 1 inches 2

3 (c) 1 inches 4

7 (d) 1 inches 8

7. A CD has a 5% chance of being a smash hit and profiting $5.2 million, a 50% chance of being a modest success and profiting $0.9 million, and a 45% chance of being a flop and breaking even. What is the expected earnings value of the CD? (a) $305,000

(b) $500,000

(d) $915,000

8. A child has a 35% chance of being sent to a day-care facility that charges $400 per month and a 65% chance of being sent to one that charges $700. What is the expected cost of the child’s day care? (a) $520

(b) $595

(d) $550

9. A casino card game takes $3 bets. Players have a 45% chance of winning and winning back their bets plus $3, and they have a 55% chance of losing their bets. What is the house edge? (a) 3.33 cents per dollar

(b) 10 cents per dollar

Unit 7C Test 3 (continued)

Name:

10. A game consists of laying a $1 bet and taking a single card from a dealer (the house) working with a 54card deck, which includes two jokers. If the card is clubs, the player wins and gets the $1 back plus another $3; otherwise, the player loses the $1. What is the house edge in this game? (a) 2.95 cents per dollar (c) 3.70 cents per dollar

(b) 3.28 cents per dollar (d) 4.22 cents per dollar

Name:

Unit 7C Test 4

Date:

Choose the correct answer to each problem. 1. A movie critic gives a single star (worst rating) to one movie in eight that he reviews. If he expects to review 160 movies during the summer season, how many one-star movies can the readers expect? (a) 20

(b) 24

(d) 48

2. A certain college tries to accept the top 3 percent of applicants. If the college expects 8100 applicants for next year, how many students should it plan on accepting? (a) 234

(b) 243

(d) 297

3. A copier jams about once in 45 copies. If a person is planning to copy 630 pages, how many jams can she expect? (a) 12

(b) 14

(d) 18

4. A soldier takes cover in a shell hole based on the belief that the chances of another shell striking in the same place are astronomically small. This is a case of the gambler’s fallacy because (a) the enemy is obviously aiming for the hole. (c) the soldier hasn’t seen enough shells to know.

(b) he is relying on chance, which is unwise. (d) the hole is just as likely to be hit as any spot is.

5. A silicon wafer is produced by a process that has a 15% chance of producing material of 100% purity, a 40% chance of producing material of 99% purity, and a 45% chance of producing material of 96% purity. What is the expected purity of a randomly selected wafer? (a) 97.8%

(b) 98.5%

(d) 99.5%

6. A chimp learning sign language is judged by the trainer to have 1 chance in 4 of learning 50 words, 1 chance in 2 of learning 35, and 1 chance in 4 of learning only 20. What is the expected number of words the chimp will learn? (a) 32

(b) 35

(d) 41

7. An insurance company is about to collect a one-time premium of $25,000 to insure an object for $1.5 million. The object has a 0.015 probability of being stolen. What is the value of the transaction to the insurer? (a) $1900

(b) $2100

(d) $2500

8. A credit card company issues a credit card to a person for whom there is a likelihood of 0.8 that he will borrow on the card and pay a steady flow of interest of $24 per month, and a likelihood of 0.2 that he will pay all his borrowings promptly and incur no interest. What is the expected flow of interest payments to the company? (a) $4.80 per month (c) $19.20 per month

(b) $5.60 per month (d) $19.40 per month

Unit 7C Test 4 (continued)

Name:

9. A casino card game takes $10 bets. Players have a 42% chance of winning and winning back their bets plus $10, and they have a 58% chance of losing their bets. What is the house edge? (a) 8 cents per dollar (c) 16 cents per dollar

(b) 12 cents per dollar (d) 26 cents per dollar

10. A game consists of laying a $1 bet and taking a single card from a dealer (the house) working with a 52card deck. If the card is clubs, the player wins and gets the $1 back plus another $2; otherwise, the player loses the $1. What is the house edge in this game? (a) 10 cents per dollar (c) 18 cents per dollar

(b) 13 cents per dollar (d) 25 cents per dollar

Name:

Unit 7D Test 1

Date:

Use the following table to answer questions 1 – 2. Year

Accidents

Fatalities

2000 2005 2010 2015

49 34 28 27

89 22 0 0

Hours flown (millions) 16.7 18.7 17.2 17.4

Miles flown (billions) 7.1 7.8 7.3 7.6

1. For each year, compute the number accidents per million of hours flown. Comment on the results.

2. For each year, compute the number fatalities per billion of miles flown. Comment on the results.

Use the following table to answer question 3 – 5. Leading Causes of Death in the United States (2015) Cause Deaths Cause Heart Disease 614,300 Alzheimer’s Disease Cancer 591,700 Diabetes Chronic Respiratory Diseases 147,100 Pneumonia/Influenza Accidents (including car crashes) 136,100 Kidney Disease Stroke 133,100 Suicide Source: Centers for Disease Control and Prevention

Deaths 93,500 76,500 55,200 48,100 42,800

3. If the population of the United States in 2015 was 325 million, find the relative frequency probability of death due to an accident.

Unit 7D Test 1 (continued)

Name:

4. How much greater is the risk of death due to Alzheimer’s disease than pneumonia/influenza?

5. If you live in a city with a population of 750,000 people, how many cases of cancer would you expect?

In the following problems, consider the following table, showing firearm deaths among Americans in 2010. The total number of Americans that year was about 317 million. Type of death

Total number

Accident

600

Suicide

19,308

Homicide

11,015

6. Compute the firearm homicide rate per 100,000.

7. Compute the relative frequency probability of an American dying by a firearm suicide.

8. Compute the relative frequency probability that an American is killed by a firearm.

Name:

Unit 7D Test 2

Date:

Use the following table to answer questions 1 – 2. Year

Accidents

Fatalities

2000 2005 2010 2015

49 34 28 27

89 22 0 0

Hours flown (millions) 16.7 18.7 17.2 17.4

Miles flown (billions) 7.1 7.8 7.3 7.6

1. For each year, compute the number accidents per billion of miles flown. Comment on the results.

2. For each year, compute the number fatalities per million of hours flown. Comment on the results.

Deaths 93,500 76,500 55,200 48,100 42,800

3. If the population of the United States in 2015 was 325 million, find the relative frequency probability of death due to chronic respiratory diseases.

Unit 7D Test 2 (continued)

Name:

4. How much greater is the risk of death due to heart disease than stroke?

5. If you live in a city with a population of 150,000 people, how many cases of diabetes would you expect?

In the following problems, consider the following table, showing firearm deaths among Americans in 2010. The total number of Americans that year was about 317 million. Type of death

Total number

Accident

600

Suicide

19,308

Homicide

11,015

6. Compute the firearm accident rate per 100,000.

7. Compute the relative frequency probability of an American dying through a firearm homicide.

8. Compute the relative frequency probability that an American is killed by a firearm.

Name:

Unit 7D Test 3

Date:

1. Suppose that in a country of 72 million people, about 3600 die from drowning each year. What is the percent chance that a person will drown in a given year? (a) 0.002%

(b) 0.003%

(d) 0.005%

2. In South Africa, a country of 49 million people, roughly 350,000 died from AIDS in 2007. What is the percent chance that a person will die of AIDS in South Africa in a given year? (a) 0.007%

(b) 0.071%

(d) 7.143%

Deaths 93,500 76,500 55,200 48,100 42,800

3. If the population of the United States in 2015 was 325 million, find the relative frequency probability of death due to kidney diseases. (a) 0.000148

(b) 0.0248

(d) 0.0148

4. How much greater is the risk of death due to accident than suicide? (a) 0.314 times

(b) 318 times

(d) 31.4 times

5. If you live in a city with a population of 250,000 people, how many cases of Alzheimer’s disease would you expect? (a) 12,059

(b) 72

(d) 72,000

Unit 7D Test 3 (continued)

Name:

For the following problems, consider the following table, showing some infant mortality data for America in 2005. Maternal Ethnicity Number of deaths under Total number of births 1 year of age White

18,500

3,229,494

African-American

8393

633,152

Hispanic

5537

985,513

6. What was the relative frequency probability that an infant born to an Hispanic woman died before one year of age? (a) 0.00006

(b) 0.00114

(d) 0.00562

7. What was the relative frequency probability of an infant born to either a white or African-American died before one year of age? (a) 0.00007

(b) 0.00555

(d) .0533

8. How many deaths per 100,000 births occurred in these three ethnic groups? (a) 555

(b) 572

(d) 861

Name:

Unit 7D Test 4

Date:

1. Suppose that in a country of 64 million people, about 3200 die from drowning each year. What is the percent chance that a person will drown in a given year? (a) 0.002%

(b) 0.003%

(d) 0.007%

2. In Haiti, a country of 9 million people, roughly 7500 died from AIDS in 2007. What is the percent chance that a person will die of AIDS in Haiti in a given year? (a) 0.0008%

(b) 0.083%

(d) 8.333%

Use the following table to answer question 3 – 5. Leading Causes of Death in the United States (2015) Cause Deaths Heart Disease 614,300 Cancer 591,700 Chronic Respiratory Diseases 147,100 Accidents (including car crashes) 136,100 Stroke 133,100 Source: Centers for Disease Control and Prevention

Cause Alzheimer’s Disease Diabetes Pneumonia/Influenza Kidney Disease Suicide

Deaths 93,500 76,500 55,200 48,100 42,800

3. If the population of the United States in 2015 was 325 million, find the relative frequency probability of death due to heart disease. (a) 0.00189

(b) 0.317

(d) 0.00261

4. How much greater is the risk of death due to chronic respiratory diseases than diabetes? (a) 52 times

(b) 1.92 times

(d) 192 times

5. If you live in a city with a population of 200,000 people, how many cases of death due to pneumonia/influenza would you expect? (a) 3

(b) 5695

(d) 34

Unit 7D Test 4 (continued)

Name:

For the following problems, consider the following table, showing some infant mortality data for America in 2005. Maternal Ethnicity Number of deaths under 1 year of age

Total number of births

White

18,500

3,229,494

African-American

8393

633,152

Hispanic

5537

985,513

6. What was the relative frequency probability that an infant born to an African-American woman died before one year of age? (a) 0.01326

(b) 0.00562

(d) 0.00001

7. What was the relative frequency probability of an infant born to a white woman died before one year of age? (a) 0.00382

(b) 0.00572

(d) 0.01326

8. How many deaths per 100,000 births occurred in the African-American and Hispanic groups? (a) 555

(b) 572

(d) 861

Name:

Unit 7E Test 1

Date:

Evaluate the expression

15! without using the factorial key on a calculator. 11!

2. Evaluate the expression

8! without using the factorial key on a calculator. 2!3!

3. A frozen yogurt shop offers eight flavors and twelve toppings. How many ways of choosing one flavor and two different topping are there?

4. A five-character computer password can be formed from three digits, followed by two lower-case letters of the alphabet. No digit nor letter may repeat. How many different passwords are possible?

5. Virginia non-personalized license plates can be any three capital letters of the alphabet, followed by any four digits. How many different license plates are possible?

Unit 7E Test 1 (continued)

Name:

6. A brand of ballpoint pen comes in four colors, with fine or regular point, and with standard, deluxe, or executive styling. How many different versions of the pen are there?

7. A committee of 4 people needs to be selected from twenty members of an organization. How many different committees are possible?

8. From a normal deck of 52 playing cards, five cards are drawn and placed face up on a table, left to right. How many possible results are there of this procedure?

9. How many different ways are there to order a medium three-topping pizza, given that there are eight toppings from which to choose?

10. A scholar is choosing four books to take on vacation, from a stack of 12. How many different combinations of books are there?

Name:

Unit 7E Test 2

Date:

1. Evaluate the expression

18! without using the factorial key on a calculator. 12!

2. Evaluate the expression

7! without using the factorial key on a calculator. 2!5!

3. An auto dealer offers a compact car, a midsize, a sport utility vehicle, and a light truck, each either in standard, custom, or sport styling, a choice of manual or automatic transmission, and a selection from 7 colors. How many ways of buying a vehicle from this dealer are there?

4. A corporate password consists of four digits, followed by three lower-case letters of the alphabet. How many different passwords are possible if no characters may repeat?

5. A seven-character insurance account number must be five lower-case letters of the alphabet followed by a two-digit number. How many different account numbers of this kind are possible?

Unit 7E Test 2 (continued)

Name:

6. A 12-person jury needs to be selected from a pool of 25 community members. How many different juries are possible?

7. Fifteen people on an amateur sports team are choosing a captain, a vice-captain, and a social media coordinator from among their ranks. How many ways are there to do this?

8. From a normal deck of playing cards, four cards are drawn and placed face up on a table, left to right. How many possible results are there of this procedure?

9. How many different ways are there to order a three-flavor hot fudge sundae, given that there are fifteen flavors to choose from and you do not want to repeat flavors?

10. A customer at a bookstore is choosing four paperback novels to take on a trip, from a shelf containing 22 books. How many different combinations of books are there?

Name:

Unit 7E Test 3

Date:

Choose the correct answer to each problem. 1. Without using the factorial key on a calculator, evaluate (a) 2

(b) 380

2. Without using the factorial key on a calculator, evaluate (a) 35

(b) 48

20! . 18! (c) 11

(d) 6840

7! . 4!3! (c) 72

(d) 154

3. A manufacturer’s automobile serial number consists of two lower-case letters of the alphabet followed by six numerical digits. How many different serial numbers are possible? (a) 362 million

(b) 676 million

(d) 2.53 billion

4. A local magazine mailing code consists of two numerical digits, followed by four capital letters of the alphabet. How many different mailing codes of this type are possible if repeated characters are not permitted? (a) 248,483,900

(b) 873,800,000

(d) 4,569,760,000

5. A type of flowering tree comes in normal, giant, and dwarf sizes, and each size produces four different colors of flower. How many varieties of the tree are there? (a) 8

(b) 12

(d) 22

6. Using 31 flavors, how many different double-scoop cones can you create with two different flavors? Assume placement of each scoop is not a factor. (a) 465

(b) 930

(d) 2790

7. You are giving out door prizes at your annual Super Bowl party. Twenty people are attending and have their names “in the hat” for five identical prizes. How many ways can the twenty party-goers get five prizes? (a) 100

(b) 3003

(d) 1,860,480

8. From a selection of sixteen courses fulfilling a humanities requirement, a student must pick any four to take, one in each of the next four terms. How many different sequences of courses are possible? (a) 1820

(b) 23,220

(d) 97,300

9. From a normal deck of 52 playing cards, four cards are drawn and placed face up on a table, left to right. How many possible results are there of this procedure? (a) 208

(b) 1,624,350

(d) 6,497,400

10. In a state-run lottery, a player has to pick six numbers out of 40, and the order that the numbers are selected does not matter. What is the probability that a player will pick all six numbers correctly? (a) 0.00000026

(b) 0.0000016

(d) 0.0000104

Name:

Unit 7E Test 4

Date:

Choose the correct answer to each problem. 1. Without using the factorial key on a calculator, evaluate (a) 4

(b) 4080

2. Without using the factorial key on a calculator, evaluate (a) 27

(b) 45

17! . 14! (c) 64,260

(d) 24

8! . 4!4! (c) 70

(d) 124

3. A wood products company produces paper in newsprint, standard bond, and glossy finish styles, each in one of four weights (thicknesses) and each in either white, yellow, pink, or powder blue. How many selections of paper are available? (a) 12

(b) 27

(d) 84

4. A mail-order catalog lists its products using a catalog number consisting of four numerical digits followed by three capital letters of the alphabet. How many different catalogue numbers are possible if characters may not repeat? (a) 78,624,000

(b) 398,663,000

(d) 1,255,716,000

5. A corporate bank account code consists of a lower-case letter of the alphabet, followed by five numerical digits, followed by a capital letter. How many different account numbers of this type are possible? (a) 87,444,500

(b) 67,600,000

(d) 1,262,821,400

6. Papa John’s currently offers 16 toppings. How many different three-topping pizzas could you create with 16 unique toppings? (a) 48

(b) 560

(d) 3360

7. There are ten children at a pirate theme birthday party. You are going to draw four names from a hat and the first child’s name drawn will play the Captain, the second will play the First Mate, the third will play the Navigator, and the fourth will play the Helmsman. How many possible results are there? (a) 40

(b) 210

(d) 10,080

8. A teacher wants to choose five students to go to the board. If there are 23 students in class, how many different sets of five could be chosen? (a) 8568

(b) 33,649

(d) 4,037,880

9. From a selection of sixteen courses fulfilling a humanities requirement, a student must pick any four to take. How many different combinations of courses are possible? (a) 1820

(b) 23,220

(d) 97,300

10. There are 12 horses in a race. What is the probability you could randomly guess correctly which horses would place 1st, 2nd, and 3rd? (a) 0.000758

(b) 0.00231

(d) 0.252

Name:

Unit 8A Test 1

Date:

1. The price of a certain product is increasing at a rate of $2.30 per year. Does this statement describe a linear or exponential relationship? Explain.

2. The value of farm land in a certain state is increasing at a rate of 4% per year. Does this statement describe a linear or exponential relationship? Explain.

3. The Board of Directors of a neighborhood Home Owner’s Association has decided they need to raise dues by 10% every year to help pay for pool improvements. If dues are $60 per month this year, how much will they be in 6 years?

4. Enrollment at a certain institution has been increasing by about 150 students each year. If the enrollment this year is 4800 students, how many students are expected to be enrolled 8 years from now?

5. The value of Bobby’s car depreciates at a rate of 16% per year. If he paid $19600 for it 4 years ago, what is the value of the car now?

Unit 8A Test 1 (continued)

Name:

6. The number of locally owned businesses in our town seems to be decreasing at a rate of 20 per year. If there are 986 locally owned businesses today, what number can we expect to have in 4 years?

7. Suppose a chess board has one grain of wheat on the first square, two grains on the second square, four grains on the third square, eight grains on the fourth square, and so on, up to and including the 18th square. Find the total number of grains on the board. If each grain of wheat weights 1/7000 pound, also find the weight of the wheat on the 18th day.

8. Suppose a leprechaun gives you a magic penny (on day 0) that doubles every night. How much money would you have after 20 days?

9. Suppose that a single bacterium is in a bottle at 11:00 am. It divides into two bacteria at 11:01, and the population continues to double every minute until the bottle is completely full at 12:00 noon. Find the population of bacteria at 11:25 am.

10. The population of a certain city is now 74,000 people. If the population doubles every 25 years, what will the population be after 125 years?

Name:

Unit 8A Test 2

Date:

1. The population of a certain city is decreasing at the rate of 17% per year. Does this statement describe a linear or exponential relationship? Explain.

2. The price of gasoline is increasing at the rate of $0.06 per week. Does this statement describe a linear or exponential relationship? Explain.

3. The Board of Directors of a neighborhood Home Owner’s Association has decided they need to raise dues by 8% every year to help pay for pool improvements. If dues are $65 per month this year, how much will they be in 8 years?

4. Enrollment at a certain institution has been increasing by about 200 students each year. If the enrollment this year is 3300 students, how many students are expected to be enrolled 6 years from now?

5. The value of Erica’s computer system depreciates at a rate of 26% per year. If she paid $1750 for it 2 years ago, what is the value of the system now?

Unit 8A Test 2 (continued)

Name:

6. The number of locally owned businesses in our town seems to be decreasing at a rate of 35 per year. If there are 860 locally owned businesses today, what number can we expect to have in 5 years?

7. Suppose a chess board has one grain of wheat on the first square, two grains on the second square, four grains on the third square, eight grains on the fourth square, and so on, up to and including the 16th square. Find the total number of grains on the board. If each grain of wheat weights 1/7000 pound, also find the weight of the wheat on the 16th day.

8. Suppose a leprechaun gives you a magic penny (on day 0) that doubles every night. How much money would you have after 18 days?

10. Suppose the population of a certain city has been doubling every 30 years, and the population was 48,000 in 1900. What will the population be in the year 2020?

Name:

Unit 8A Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following statements describes a relationship that is linear? (a) The price of houses in this neighborhood is increasing at the rate of 12% per year. (b) The number of bacteria is increasing at the rate of 18% per minute. (c) The temperature is increasing at the rate of 7° per hour. (d) The number of cars in the parking lot is decreasing at the rate of 15% per hour.

2. Which of the following statements describes an exponential relationship? (a) The population of a certain city is increasing at the rate of 600 people per year. (b) The value of this rental property can be depreciated at the rate of $4300 per year. (c) The number of dogs is increasing at the rate of 40 dogs per year. (d) The price of a widget is increasing at the rate of 34% per year.

3. The price of milk is increasing by 9 cents per week. If the price is $2.99 per gallon today, what will milk cost in six weeks? (a) $3.52

(b) $3.53

(d) $15.05

4. The cost of DVD players has dropped by $20 each year. If a DVD player cost $189 four years ago, how much does it cost today?

(a) $109.00

(b) $269.00

(d) $77.41

5. The population of a small town is growing at the rate of 3% per year. If the town had 39,800 residents at the last census, how much will the population be (to the nearest hundred) when the next census is taken, 10 years later?

(a) 39,800

(b) 51,700

(d) 53,500

6. The number of new cases of a certain disease is decreasing by 8% per year. If there were 2600 new cases worldwide this year, how many will there be in three years? (a) 1976

(b) 2025

(d) 3276

7. Suppose a chess board has one grain of wheat on the first square, two grains on the second square, four grains on the third square, eight grains on the fourth square, and so on. How many grains are on the 17th square? (a) 65,536

(b) 131,072

(d) 34

8. Suppose a leprechaun gives you a magic penny (on day 0) that doubles every night. How much money would you have after 10 days? (a) $0.20

(b) $5.12

(d) $10.24

Unit 8A Test 3 (continued)

Name:

(b) 2

(d) 2

10. Suppose that a single bacterium is in a bottle at 11:00 am. It divides into two bacteria at 11:01, and the population continues to double every minute until the bottle is completely full at 12:00 noon. Find the fraction of the bottle that is full at 11:53 am. (a)

1 32

(b)

1 64

(c)

1 128

(d)

1 512

Name:

Unit 8A Test 4

Date:

Choose the correct answer to each problem. 1. Which of the following statements describes a relationship that is linear? (a) The value of this rental property can be depreciated at the rate of $4300 per year. (b) The number of cats is decreasing at the rate of 8% per year. (c) The population of a certain city is increasing at the rate of 40% per year. (d) The price of a gizmo is increasing at the rate of 14% per year. 2. Which of the following statements describes an exponential relationship? (a) The temperature is increasing at the rate of 3° per hour. (b) The population of your home town is decreasing at a rate of 7% per year. (c) The number of cars in the parking lot is decreasing at the rate of 5 cars per hour. (d) The price of houses in this neighborhood is increasing at the rate of $15,000 per year. 3. Your credit card balance is increasing at a rate of 15% per year. If the balance is $9500 this year, what will it be in 15 years? (a) $14,448.31

(b) $21,375

(d) $77,302.09

4. The number of traffic fatalities due to alcohol in a town has dropped by 45 every year. If there were 205 traffic fatalities due to alcohol 3 years ago, how many are expected this year?

(a) 19

(b) 70

(d) 0

5. A company hopes to hire 25 new employees each year. If the company employs 430 people today, how many do they hope to employ in 5 years? (a) 460

(b) 555

(d) 9,766,055

6. The value of farm equipment depreciates by 18% each year. If a piece of equipment cost $1200 new six years ago, how much is that equipment worth now?

(a) $2496

(b) $3239.46

(d) $364.80

7. Suppose a chess board has one grain of wheat on the first square, two grains on the second square, four grains on the third square, eight grains on the fourth square, and so on, up to and including the 20th square. Find the total number of grains on the board. (a) 524,287

(b) 1,048,575

(d) 2,097,152

8. Suppose a leprechaun gives you a magic penny (on day 0) that doubles every night. How much money would you have after 12 days? (a) $0.24

(b) $1.44

(d) $40.96

Unit 8A Test 4 (continued)

Name:

(b) 2

(d) 2

(a)

1 32

(b)

1 64

(c)

1 128

(d)

1 512

Name:

Unit 8B Test 1

Date:

1. Suppose that a population of a small town has a doubling time of 23 years. By what factor will it grow in 92 years?

2. If the doubling time of a state’s population is 58 years, how long does it take for the population to increase by a factor of 8?

3. Suppose you deposit $1500 in a bank account that has a doubling time of 12 years. What will your balance be after 40 years?

4. A city doubles its population every 75 years. If the population of the city is 87,000 today, what will the population be in 100 years?

5. The price of a certain commodity rises by 4% every year. If the product costs $17 today, use the approximate doubling time formula to estimate the price of the commodity in 25 years?

Unit 8B Test 1 (continued)

Name:

6. The population of an endangered species of turtle has a half-life of 5.3 years. If at most 5000 of these turtles are alive today, estimate the population of these turtles that will still be alive in 20 years if nothing is done.

7. If the half-life of a drug in the bloodstream is 15 hours, how much drug is left in the bloodstream 36 hours after a 400-milligram dose?

8. Suppose that the consumer price index of a country is decreasing at the rate of 4.3% per year. If the CPI for this year is 214.9, use the approximate half-life formula to estimate the CPI in 5 years.

9. A family of 10 fruit flies invade your home and the population grows at a rate of 25% per day. Estimate the population of fruit flies in your house in a week by using the approximate formula to find the doubling time.

10. A family of 10 fruit flies invade your home and the population grows at a rate of 25% per day. Estimate the population of fruit flies in your house in a week by using the exact formula to find the doubling time. Compare to the answer you computed in problem 9.

Name:

Unit 8B Test 2

Date:

1. Suppose that a population has a doubling time of 10 years. By what factor will it grow in 60 years?

2. If the doubling time of a state’s population is 15 years, how long does it take for the population to increase by a factor of 32?

3. Suppose you deposit $2000 in a bank account that has a doubling time of 9 years. What will your balance be after 35 years?

4. The population of a certain town has a doubling time of 30 years. If the town has a population of 128,000 now, what will the population be in 70 years?

5. The price of a certain commodity rises by 5% every year. If the product costs $700 today, use the approximate doubling time formula to estimate the price of the commodity in 20 years?

Unit 8B Test 2 (continued)

Name:

6. The population of an endangered species of salamander has a half-life of 6.8 years. If at most 7000 of these salamanders are alive today, estimate the population of these salamanders that will still be alive in 25 years if nothing is done.

7. If the half-life of 1000 milligrams of aspirin in the bloodstream is 5 hours, how much aspirin is left in the bloodstream 12 hours later?

8. Suppose that the consumer price index of a country is decreasing at the rate of 6.1% per year. If the CPI for this year is 510.6, use the approximate half-life formula to estimate the CPI in 15 years.

9. A colony of 100 ants invade your home and the population grows at a rate of 25% per week. Estimate the population of ants in your house in a year by using the approximate formula to find the doubling time.

10. A colony of 100 ants invade your home and the population grows at a rate of 25% per week. Estimate the population of ants in your house in a year by using the exact formula to find the doubling time. Compare to the answer you computed in problem 9.

Name:

Unit 8B Test 3

Date:

Choose the correct answer to each problem. 1. Suppose that a population has a doubling time of 15 years. By what factor will it grow in 105 years? (a) 64

(b) 128

(d) 512

2. If the doubling time of a state’s population is 42 years, how long does it take for the population to increase by a factor of 16? (a) 84 years

(b) 126 years

(d) 672 years

3. Suppose you deposit $2000 in a bank account that has a doubling time of 19 years. To the nearest $100, what will your balance be after 5 years? (a) $2400

(b) $2500

(d) $27,900

4. The population of a certain town has a doubling time of 20 years. If the town has a population of 112,000 now, to the nearest thousand, what will the population be in 70 years? (a) 15,000

(b) 137,000

(d) 1,267,000

5. The price of a certain commodity rises by 2.5% every year. If the product costs $200 today, use the approximate doubling time formula to estimate the price of the commodity in 20 years? (a) $6400

(b) $51,200

(d) $527.80

6. Suppose that your Home Owner’s Association dues increase by 8% each year. Use the approximate doubling time formula to estimate the time it will take for your dues to double. (a) 7 years

(b) 8.25 years

(d) 11 years

7. If the half-life of ibuprofen in the bloodstream is 1.9 hours, how much ibuprofen is left in the bloodstream 8 hours after a 400-milligram dose? (a) 0.82 mg

(b) 21.6 mg

(d) 339.3 mg

8. The population of an endangered species of turtle has a half-life of 7.3 years. If at most 5000 of these turtles are alive today, estimate the population of these turtles that will still be alive in 20 years if nothing is done. (a) 33.397

(b) 749

(d) 3882

9. Suppose that the consumer price index of a country is decreasing at the rate of 2.8% per year. Use the appropriate formula to estimate the half-life of the CPI. (a) 25 years

(b) 24 years

(d) 28 years

10. Suppose that the consumer price index of a country is decreasing at the rate of 2.8% per year. Use the appropriate to calculate the exact half-life of the CPI. (a) 25 years

(b) 24 years

(d) 28 years

Name:

Unit 8B Test 4

Date:

Choose the correct answer to each problem. 1. Suppose that a population has a doubling time of 14 years. By what factor will it grow in 112 years? (a) 64

(b) 128

(d) 512

2. If the doubling time of a city’s population is 18 years, how long does it take for the population to increase by a factor of 8? (a) 24 years

(b) 36 years

(d) 144 years

3. Suppose you deposit $5000 in a bank account that has a doubling time of 9 years. To the nearest $1000, what will your balance be after 40 years? (a) $28,000

(b) $109,000

(d) $610,000

4. The population of a certain town has a doubling time of 13 years. If the town has a population of 78,000 now, to the nearest thousand, what will the population be in 30 years? (a) 105,000

(b) 386,000

(d) 638,976,000

5. The price of a certain commodity rises by 3.5% every year. If the product costs $300 today, use the approximate doubling time formula to estimate the price of the commodity in 10 years? (a) $1200

(b) $303.66

(d) $338.69

6. Suppose that a savings account increases its value by 4.7% per year (APY). Use the approximate doubling time formula to estimate the doubling time of the account. (a) 13 years

(b) 14 years

(d) 16 years

7. If the half-life of 10 milligrams of Ritalin in the bloodstream is 3 hours, how much Ritalin is left in the bloodstream 8 hours after a 10-milligram dose? (a) 1.6 mg

(b) 2.4 mg

(d) 7.7 mg

8. The population of an endangered species of salamander has a half-life of 8.8 years. If at most 7500 of these salamanders are alive today, estimate the population of these salamanders that will still be alive in 25 years if nothing is done. (a) 1047

(b) 5876

(d) 53,735

9. Suppose that the consumer price index of a country is decreasing at the rate of 2.1% per year. Use the appropriate formula to estimate the half-life of the CPI. (a) 33.3 years

(b) 35 years

(d) 32 years

10. Suppose that the consumer price index of a country is decreasing at the rate of 2.1% per year. Use the appropriate formula to calculate the exact half-life of the CPI. (a) 33.3 years

(b) 35 years

(d) 32.7 years

Name:

Unit 8C Test 1

Date:

1. Define carrying capacity.

2. Starting with a 2021 world population of 7.8 billion, use the growth rate of 0.9% to find the approximate doubling time and to predict the world population in 2060.

The table gives the birth and death rates for Greece between 1979 and 2019. Use this table to answer 3 – 6. Year

Birth Rate (per 1000)

Death Rate (per 1000)

1979

15.5

8.6

1999

9.4

9.6

2019

7.8

11.7

3. Describe the general trend in the birth rate between 1979 and 2019.

4. Describe the general trend in the death rate between 1979 and 2019.

Unit 8C Test 1 (continued)

Name:

5. Complete the table to show the country’s net growth rate due to births and deaths in 1979, 1999, and 2019. Neglect the effects of immigration.

6. Based on your answers to questions 3 – 5, predict how the country’s population will change over the next 20 years. Do you think your prediction is reliable? Explain.

7. Consider a population that begins growing at a base rate of 3.0% per year, then follows a logistic growth pattern. If the carrying capacity is 55 million, find the actual fractional growth rate when the population is 10 million and when it is 25 million.

Name:

Unit 8C Test 2

Date:

1. Explain the meaning of logistic growth.

2. Starting with a 2021 world population of 7.8 billion, use the growth rate of 1.3% to find the approximate doubling time and to predict the world population in 2060.

The table gives the birth and death rates for France between 1980 and 2019. Use this table to answer 3 – 6. Year

Birth Rate (per 1000)

Death Rate (per 1000)

1980

14.0

10.2

1995

12.9

9.1

2019

11.2

9.1

3. Describe the general trend in the birth rate between 1980 and 2019.

4. Describe the general trend in the death rate between 1980 and 2019.

Unit 8C Test 2 (continued)

Name:

5. Complete the table to show the country’s net growth rate due to births and deaths in 1980, 1999, and 2019. Neglect the effects of immigration.

6. Based on your answers to questions 3 – 5, predict how the country’s population will change over the next 20 years. Do you think your prediction is reliable? Explain.

7. Consider a population that begins growing at a base rate of 5.0% per year, then follows a logistic growth pattern. If the carrying capacity is 65 million, find the actual fractional growth rate when the population is 10 million and when it is 25 million.

Name:

Unit 8C Test 3

Date:

Choose the correct answer to each problem. 1. Real populations sometimes increase beyond their environment’s carrying capacity in a relatively short period of time. What is the name of this phenomenon? (a) Logistic growth (c) Overshoot

(b) Collapse (d) Annual growth rate

2. The population growth rate of India has been estimated at 1.5% per year. What is the approximate doubling time? (a) 33.3 years

(b) 46.7 years

(d) 66.7 years

3. If the population of India is now 1.17 billion and the population growth rate is 1.5% per year, what will the approximate population be in 50 years? (a) 1.27 billion

(b) 2.46 billion

(d) 59.4 billion

The table gives the birth and death rates for Japan between 1979 and 2019. Use the information to answer questions 4 – 6. Year

Birth Rate (per 1000)

Death Rate (per 1000)

1980

14.1

5.9

1995

9.3

7.8

2016

7.0

11.1

4. Examine the birth and death rate patterns. Choose the most accurate description of what you see. (a) Both the birth and death rates are rising. (b) The birth rates are rising as the death rates are falling. (c) The birth rates are falling as the death rates are rising. (d) Both the birth and death rates are falling. 5. What was Japan’s growth rate due to births and deaths in 2019? (Neglect the effects of immigration.) (a) -0.0041%

(b) -0.41%

(d) 0.41%

6. Determine the net growth rate due to births and deaths from 1979 to 2019. Observe the general trend in the net growth rate. Which of the following descriptions would be most accurate? (a) The population is increasing dramatically. (b) The population was increasing slightly and is now decreasing slightly. (c) The population is fluctuating between growth and loss. (d) The population is decreasing dramatically.

Unit 8C Test 3 (continued)

Name:

7. Suppose a country currently has a population of 24 million and an annual growth rate of 3.4%. If the population growth follows a logistic growth model with a carrying capacity of 90 million, calculate the actual fractional growth rate when the population is 32 million. (a) 2.2%

(b) 2.6%

(d) 3.4%

Name:

Unit 8C Test 4

Date:

Choose the correct answer to each problem. 1. If a population has exceeded the carrying capacity of its environment, it may suffer a rapid and severe decrease in the population. What is the name of this type of population decrease? (a) Logistic growth (c) Overshoot

(b) Collapse (d) Annual growth rate

2. The population growth rate of Ireland has been estimated at 1.1% per year. What is the approximate doubling time? (a) 5 years

(b) 62 years

(d) 91 years

3. If the population of a state is now 1,690,000 and the population growth rate is 2.6% per year, what will the approximate population be in 40 years? (a) 4,600,000

(b) 4,700,000

(d) 69,400,000

The table gives the birth and death rates for Germany between 1979 and 2019. Use the information to answer questions 4 – 6. Year

Birth Rate (per 1000)

Death Rate (per 1000)

1979

10.5

12.1

1999

9. 4

10.3

2019

9.4

11.3

4. Examine the birth and death rate patterns. Choose the most accurate description of what you see. (a) Both the birth and death rates are rising. (b) The direction of the birth rates is uncertain, but the death rate is rising. (c) The direction of the birth rates is uncertain, but the death rate is falling. (d) The direction of the birth rates and death rates are uncertain, but the birth rates are consistently lower than the death rates. 5. What was Germany’s growth rate due to births and deaths in 2019? (Neglect the effects of immigration.) (a) -1.9%

(b) -0.19%

(d) 0.19%

6. Determine the net growth rate due to births and deaths in 1979 and 1999. Observe the general trend in the net growth rate. If the trend continues, which of the following predictions would be accurate? (a) The population will increase dramatically. (b) The population will continue to grow exponentially forever. (c) The population will level off in the next decade or two, and then may begin to decrease. (d) The population is decreasing and will continue to do so.

Unit 8C Test 4 (continued)

Name:

7. Suppose a country currently has a population of 28 million and an annual growth rate of 2.2%. If the population growth follows a logistic growth model with a carrying capacity of 74 million, calculate the actual fractional growth rate when the population is 32 million. (a) 1.9%

(b) 2.0%

(d) 1.2%

Name:

Unit 8D Test 1

Date:

1. How much energy, in joules, is released by an earthquake of magnitude 5?

2. How much more energy is released by an earthquake of magnitude 8 as by one of magnitude 6?

3. What is a sound of 0 decibels defined to be?

4. Suppose that a sound is 150 times as loud as (more intense than) a whisper. What is its loudness, in decibels?

5. How much louder (more intense) is a 115-dB sound than a 65-dB sound?

6. How many times greater is the intensity from a speaker 5 meters away than the intensity of the speaker 20 meters away?

Unit 8D Test 1 (continued)

Name:

7. The sound level from a television 1 meter away is 130 dB. How far away from the television should you be to avoid risking damage to your ears?

8. Name something in a refrigerator that probably has a pH value lower than 7.

9. What is the hydrogen ion concentration of a solution that has a pH of 5.5? Is this solution an acid or a base?

10. What is the pH of a solution with a hydrogen ion concentration of 10-11 mole per liter?

Name:

Unit 8D Test 2

Date:

1. How much energy, in joules, is released by an earthquake of magnitude 6?

2. How much more energy is released by an earthquake of magnitude 6 as by one of magnitude 3?

3. What is a sound of -10 decibels defined to be?

4. Suppose that a sound is 24 times as loud as (more intense than) a whisper. What is its loudness, in decibels?

5. How much more intense is a 140-dB sound than a 90-dB sound?

6. How many times greater is the intensity from a speaker 2 meters away than the intensity of the speaker 20 meters away?

Unit 8D Test 2 (continued)

Name:

7. The sound level from a siren 30 meters away is 100 dB. How close can you get to the siren before there is a strong risk of damage to your ears?

8. Name something that probably has a pH value greater than 7.

9. What is the hydrogen ion concentration of a solution that has a pH of 8.7? Is this solution an acid or a base?

10. What is the pH of a solution with a hydrogen ion concentration of 10-2 mole per liter?

Name:

Unit 8D Test 3

Date:

Choose the correct answer to each problem. 1. How much energy, in joules, was released by the 1994 Northridge earthquake of magnitude 6.7? 6 (a) 5.3×10 joules

(b) 1.1×10 joules

14 (c) 2.8 ×10 joules

(d) 1.1×10 joules

2. Earthquakes of what magnitude occur most frequently? (a) less than 3

(b) 5

(d) 8 and up

3. Earthquakes usually cause damage in all but which one of the following related ways? (a) Tsunamis (c) Collapsed building due to inferior construction

(b) Fires caused by heat from the earth’s interior. (c) Landslides

4. Which of the following sounds would you expect to have the lowest decibel measurement? (a) Arena during college basketball game (c) Ordinary conversation

(b) Television commercial (d) Afternoon traffic in New York City

5. What is the loudness, in decibels, of a sound that is 500 times as intense as the softest audible sound? (a) 3 dB

(b) 27 dB

(d) 60 dB

6. A sound of what loudness, in decibels, is 100 times as intense as a 40-dB sound? (a) 20 dB

(b) 60 dB

(d) 140 dB

7. If you are 2 meters away from a sound of 90 dB, how far away should you move so that the intensity is decreased by a factor of 25? (a) 10 meters

(b) 8 meters

(d) 6 meters

8. Which of the following probably has a pH value lower than 6? (a) orange juice

(b) tap water

(d) antacid tablets

9. What is the hydrogen ion concentration of a solution with a pH of 7? −1 (a) 10 mole per liter −7

mole per liter

−6

mole per liter

−10

mole per liter

(b) 10 (d) 10

−6

10. What is the pH of a solution with a hydrogen ion concentration of 10 (a) 6 (c) 7

(b) 4 (d) -6

mole per liter?

Name:

Unit 8D Test 4

Date:

Choose the correct answer to each problem. 1. How much energy, in joules, was released by the 1906 San Francisco earthquake of magnitude 8.0? 6 (a) 6.3×10 joules

12 (b) 2.5 ×10 joules

16 (c) 1.0 ×10 joules

16 (d) 2.5 ×10 joules

2. Approximately how many times per year is there a major earthquake of magnitude 7-8? (a) more than 1 (c) more than 500

(b) more than 50 (d) more than 1000

3. Which of the following are factors in the amount of damage caused by an earthquake? (a) The type of surface bedrock near the quake (b) The amount of energy released in surface waves as compared to interior waves (c) The economy of the region hit by the earthquake (d) All of the above 4. Which of the following decibel measurements corresponds to an inaudible sound? (a) 100 dB

(b) 0 dB

(d) 140 dB

5. If a sound measures 60 dB, that sound is how many times as intense as the softest audible sound? (a) 100

(b) 10,000

(d) 10 million

6. A 120-dB sound is 70 times as intense as a sound of what loudness? (a) 10.1 dB

(b) 50 dB

(d) 101.5 dB

7. If you are 15 meters away from a sound of 10 dB, how much more intense is the sound if you move 10 meters closer to it? (a) 3 times more intense (c) 10 times more intense

(b) 9 times more intense (d) 25 times more intense

8. Which of the following probably has a pH value greater than 8? (a) lye

(b) pure water

(d) vinegar

9. What is the hydrogen ion concentration of a solution with a pH of 8? −1 (a) 10 mole per liter −8

−12

mole per liter

−3

mole per liter

(b) 10

(d) 10

mole per liter

−3

10. What is the pH of a solution with a hydrogen ion concentration of 10 (a) 1.5

(b) 10

mole per liter? (d) -3

Name:

Unit 9A Test 1

Date:

1. Name the three basic ways to represent a function.

2. In a function involving the altitude, over time, of a ball thrown into the air, identify the variables.

3. Use the notation (independent variable, dependent variable) to characterize the function in the previous question.

Depth under water in meters is related to the water pressure at that depth in atmospheres. The following data points represent this relationship. Use this table for problems 4 – 6. Depth

Atmospheres

1.1

1.2

1.4

4. When a diver is experiencing 2 atmospheres of pressure, what is his depth?

5. Identify the independent and dependent variables.

Unit 9A Test 1 (continued)

Name:

6. Identify the domain and range based on the table.

Use this graph to answer questions 7 – 8.

stamp price (in cents)

Price of First Class Postage 50 45 40 35 30 25 20 15 10 5 0 2000

2002

2004

2006

2008

2010

2012

2014

Year

7. Use the notation (independent variable, dependent variable) to characterize the function in the graph.

8. List the domain and the range of the graph.

Name:

Unit 9A Test 2

Date:

1. What is a mathematical model?

2. In a function involving the temperature, over time, of water being heated on a stove, identify the variables.

3. Use the notation (independent variable, dependent variable) to characterize the function in the previous question.

The following table compares the cost of an automobile to the yearly cost of repair. Use the table to answer questions 4 – 6. Cost of car

$8,209

$15,456

$16,299

$18,910

$14,678

$15,963

$15,988

$14,424

$8,164

Repair Cost

$2114

$4171

$4150

$4317

$4327

$3793

$2742

$4213

$2442

4. What is the yearly repair cost for the most expensive car on the list?

5. Identify the independent variable and the dependent variable.

Unit 9A Test 2 (continued)

Name:

6. Identify the domain and the range.

The following table compares the average cost of maintenance to the average cost of repair for the least expensive automobiles to maintain. Use this graph to answer questions 7 – 8.

Cost of Car Ownership Repair Cost (in dollars)

800 700 600 500 400 300 200 100 0 2500

2550

2600

2650

2700

2750

2800

2850

Maintenance Cost (in dollars) 7. Use the notation (independent variable, dependent variable) to characterize the function in the graph.

8. List the domain and the range of the graph.

Name:

Unit 9A Test 3

Date:

Choose the correct answer to each problem. 1. Which of the following is the most compact mathematical representation of a function? (a) Data table

(b) Graph

(d) Domain

(d) Periodic

2. The domain of a function is the set of _____ values. (a) All numeral

(b) Dependent variable

3. Which of the following most likely describes a periodic function? (a) (age of my 2001 truck, its value) (c) (age of a child, her height)

(b) (date, time of sunrise) (d) (distance traveled, time elapsed)

4. Is the following a function: “The size of a pool, measured in square feet”? Why or why not? (a) Yes, because it relates two variables. (b) No, because only one variable is mentioned. (c) Yes, because the area can change . (d) No, because the units are wrong. 5. Use the notation (independent variable, dependent variable) to characterize the relationship between time and the elevation of a flying object. (a) (time and elevation, duration) (c) (elevation, time)

(b) (duration, time and elevation) (d) (time, elevation)

6. Consider a function that describes how the height of a child relates to age. An appropriate domain for this function would be (a) a list of the child’s weights in pounds (c) a list of the child’s ages in years

(b) a list of the child’s heights in inches (d) the child’s gender

7. Consider a function that describes pay and the number of hours worked in a weekly pay period for a full time employee. An appropriate range for this function would be (a) $0 to $600 (c) $0 to $50

(b) 0 to 600 hours (d) 0 to 50 hours

8. If you were to graph the function described in question 7, which variable would be plotted on the horizontal axis? (a) Pay (c) Domain

(b) Hours (d) Range

Name:

Unit 9A Test 4

Date:

Choose the correct answer to each problem. 1. Which of the following is a mathematical representation of a function that provides detailed information but can become unwieldy? (a) Data table

(b) Graph

(d) Domain

(d) Periodic

2. The range of a function is the set of _____ values? (a) All numerical

(b) Dependent variable

3. Which of the following most likely describes a periodic function? (a) (age of my computer, its value) (c) (date, number of days until Friday)

(b) (date, your age) (d) (Tom’s age, his shoe size)

4. Is the following a function: “The volume of a soup can, measured in cubic ounces”? Why or why not? (a) No, because the units are wrong. (c) No, because only one variable is mentioned.

(b) Yes, because the mass cannot change. (d) Yes, because it relates two variables.

5. Use the notation (independent variable, dependent variable) to characterize the relationship between time and the temperature of a cooling object. (a) (temperature, time) (c) (temperature and time, rate of cooling)

(b) (time, temperature) (d) (rate of cooling, temperature and time)

An experiment is conducted relating the time in hours and the amount of a drug remaining in the bloodstream. The following data points were recorded: (1, 10), (3, 9), (5, 7), (6, 5), (7, 3), (9, 1) 6. How many milligrams of the drug remain in the bloodstream after 5 hours? (a) 3 milligrams (c) 6 milligrams

(b) 7 milligrams (d) 9 milligrams

7. After how many hours should the concentration of the drug be 3 milligrams? (a) 3 hours (c) 7 hours

(b) 5 hours (d) 9 hours

8. If you were to graph this relationship, which variable would be plotted on the vertical axis? (a) Drug concentration (c) Range

(b) Time (d) Weight

Name:

Unit 9B Test 1

Date:

For questions 1 through 6, use the graph shown, which shows the concentration of a substance, in parts per million (ppm), as a function of time, in days.

Concentration (ppm)

7 6 5 4 3 2 1 0 0

Time (days)

1. What is the concentration on day 9?

2. List the rate of change with correct units.

3. Find the initial value of the concentration.

4. By how much does the concentration drop over the space of 6 days?

Test 9B Test 1 (continued)

Name:

5. Write an equation representing concentration, c, as a function of time, t.

6. Use the equation to predict the concentration on day 15.

7. Enrollment at a day care is 135 children and increases at a constant rate of 26 children each year. Write the equation that models this situation. Use the equation to find the expected enrollment in 3 years.

8. A new computer costs $2350 today and decreases in value at a constant rate of $425 per year. Write the equation that models this situation. Use the equation to find the value of this computer in 3.5 years.

9. According to Kelley Blue Book, the value of a car drops from $10,200 when new to $7,350 in four years. Write the equation that models this situation. Use the equation to find the value of this car that is 6 years old.

10. The cost of a vacation package in 2013 was $3200. In 2015, it cost $4000. Write the equation that models this situation. Use the equation to predict the cost of this vacation in 2018.

Name:

Unit 9B Test 2

Date:

For questions 1 through 6, use the graph shown, which shows the concentration of a substance, in parts per million (ppm), as a function of time, in days. 7

Concentration (ppm)

6 5 4 3 2 1 0 0

Time (days)

1. What is the concentration on day 9?

2. List the rate of change with correct units.

3. Find the initial value of the concentration.

4. By how much does the concentration rise over the space of 6 days?

Test 9B Test 2 (continued)

Name:

5. Write an equation representing concentration, c, as a function of time, t.

6. Use the equation to predict the concentration on day 18.

7. The fare for a taxi out of LAX is $3.17 for the first tenth of a mile and $2.70 for each additional mile. Write the equation that models this situation. Use the equation to find the cost to be driven 16.5 miles.

8. Alicia weighs 162 pounds, but has been losing about 0.8 pounds per day with her new eating/exercise regimen. Write the equation that models this situation. Use the equation to find what Alicia can expect to weigh after 3 weeks.

9. According to Kelley Blue Book, the value of a car drops from $12,200 when new to $9,500 in four years. Write the equation that models this situation. Use the equation to find the value of this car that is 6 years old?

Unit 9B Test 2 (continued)

Name:

10. The cost of a vacation package in 2012 was $4100. In 2015, it cost $5000. Write the equation that models this situation. Use the equation to predict the cost of this vacation in 2018.

Name:

Unit 9B Test 3

Date:

For questions 1 through 6, use the graph shown, which shows the concentration of a substance, in parts per million (ppm), as a function of time, in days. 7

Concentration (ppm)

6 5 4 3 2 1 0 0

Time (days)

1. What is the concentration on day 12? (a) 0.5 ppm

(b) 2 ppm

(d) 5 ppm

2. What is the rate of change? (a) −

1 ppm/ day 4

(b)

1 ppm/ day 6

1 ppm/ day 3

(d)

1 ppm/day 5

3. Find the initial value of the concentration. (a) 6 ppm

(b) 7.5 ppm

(d) 10 ppm

4. Which is an equation representing concentration, c, as a function of time, t? 1 (a) c = 8 − t 4

1 (b) c = 6 − t 3

1 (c) c = 5 + t 5

1 (d) c = 3 + t 6

(d) 2.5 ppm

5. Use the equation to predict the concentration on day 18. (a) 0 ppm

(b) 1.5 ppm

6. A computer initially worth $2,000 depreciates by about $275 per year. Find a linear function that describes how the value of the computer depends on time. (a) V = 2000 + 275t (c) V = 2000 – 275t

(b) V = 275 + 2000t (d) V = 275 – 2000t

7. Use the function from question 6 to find the value of the equipment 6 years after its initial purchase. (a) $3650

(b) $12,275

(d) $350

8. A collectible baseball card is worth $120 this year and might gain about $30 in value each year. What will be the value of the card in 5 years? (a) $125

(b) $150

(d) $370

Unit 9B Test 3 (continued)

Name:

9. Restaurant equipment initially worth $22,000 has depreciated to $16,200 eight years later. Find a linear function that describes how the value of the equipment depends on time. (a) V = 16,200 + 725t (c) V = 22,000 + 725t

(b) V = 16,200 – 725t (d) V = 22,000 – 725t

10. Use the function from question 9 to find the value of the equipment 12 years after its initial purchase. (a) $7500

(b) $13,300

(d) $30,700

Name:

Unit 9B Test 4

Date:

For questions 1 through 6, use the graph shown, which shows the concentration of a substance, in parts per million (ppm), as a function of time, in days. 7

Concentration (ppm)

6 5 4 3 2 1 0 0

Time (days)

1. What is the concentration on day 6? (a) 2.5 ppm

(b) 4 ppm

(d) 7 ppm

2. What is the rate of change? (a) −

1 ppm/day 4

(b)

1 ppm/day 6

1 ppm/day 3

(d)

1 ppm/day 5

3. Find the initial value of the concentration. (a) 3 ppm

(b) 4.5 ppm

(d) 8 ppm

4. Which is an equation representing concentration, c, as a function of time, t?

1 (a) c = 8 − t 4

1 (b) c = 6 − t 3

1 (c) c = 5 + t 5

1 (d) c = 3 + t 6

(d) 7.5 ppm

5. Use the equation to predict the concentration on day 18. (a) 0 ppm

(b) 3.5 ppm

6. A country club charges a $30,000 initiation fee as well as a fixed $4800 yearly fee. Find a linear function that describes the cost of membership as a function of time (a) C = 30,000 + 4800t (c) C = 4800 + 30,000t

(b) C = 30,000 – 4800t (d) C = 4800 – 30,000t

7. According to the function in question 6, what would the total charges for membership be over 6 years? (a) $28,800

(b) $34,800

(d) $58,800

8. A car is worth $12,000 this year. With normal usage and good maintenance, the value of the car should depreciate by about $900 each year. What will be the value of the car in 5 years? (a) $11,100

(b) $7500

(d) $16,500

Unit 9B Test 4 (continued)

Name:

9. Farm equipment initially worth $26,000 has depreciated to $12,800 eight years later. Find a linear function that describes how the value of the equipment depends on time. (a) V = 26,000 + 1650t (c) V = 12,800 + 1650t

(b) V = 26,000 – 1650t (d) V = 12,800 – 1650t

10. Use the function from question 9 to find the value of the equipment 12 years after its initial purchase. (a) $6200

(b) $0

(d) $32,600

Name:

Unit 9C Test 1

Date:

Use the following information to answer questions 1 – 3. The average price of a home in Sunnyville was $86,000 in 2017, but home prices have been falling by 4% per year. 1. Create an exponential function of the form Q = Q0 × (1 + r ) to model this situation. Be sure to clearly t

identify each of the variables in your function.

2. Create a table showing the value of the quantity Q for the first 10 units of time.

0 1 2 3 4 5 6 7 8 9 10 3. Sketch a graph of the exponential function. Make sure to label your axes.

Unit 9C Test 1 (continued)

Name:

Use the following information to answer questions 4 – 6. In 2015, the enrollment at a certain university was 5200 students and enrollment increases by 9% per year. 4. Create an exponential function of the form Q = Q0 × (1 + r ) to model this situation. Be sure to clearly t

identify each of the variables in your function.

5. Create a table showing the value of the quantity Q for the first 10 units of time.

0 1 2 3 4 5 6 7 8 9 10 6. Sketch a graph of the exponential function. Make sure to label your axes.

Unit 9C Test 1 (continued)

Name:

7. If prices increase at a monthly rate of 0.35%, how much do they increase in a year?

8. A certain drug breaks down in the body at a rate of 18% per hour. If an initial dosage is 500 milligrams, after how many hours will the amount in the bloodstream be 120 milligrams?

9. Suppose that poaching reduces the population of an endangered animal by 12% per year. Further, suppose that when the population of this animal falls below 45, its extinction is inevitable (owing to the lack of reproductive options without severe in-breeding). If the current population of this animal is 1400, in how many years will it face extinction?

Name:

Unit 9C Test 2

Date:

Use the following information to answer questions 1 – 3. The average price of a home in Smalltown town was $74,000 in 2016, but home prices have been falling by 8% per year. 1. Create an exponential function of the form Q = Q0 × (1 + r ) to model this situation. Be sure to clearly t

identify each of the variables in your function.

2. Create a table showing the value of the quantity Q for the first 10 units of time.

0 1 2 3 4 5 6 7 8 9 10 3. Sketch a graph of the exponential function. Make sure to label your axes.

Unit 9C Test 2 (continued)

Name:

Use the following information to answer questions 4 – 6. In 2015, the enrollment at a certain community college was 5800 students and enrollment increases by 7% per year. 4. Create an exponential function of the form Q = Q0 × (1 + r ) to model this situation. Be sure to clearly t

identify each of the variables in your function.

5. Create a table showing the value of the quantity Q for the first 10 units of time.

0 1 2 3 4 5 6 7 8 9 10 6. Sketch a graph of the exponential function. Make sure to label your axes.

Unit 9C Test 2 (continued)

Name:

7. If prices increase at a monthly rate of 0.5%, how much do they increase in a year?

8. A certain drug breaks down in the human body at a rate of 8% per hour. If an initial dosage is 200 milligrams, after how many hours will the amount in the bloodstream be 50 milligrams?

9. Suppose that poaching reduces the population of an endangered animal by 9% per year. Further, suppose that when the population of this animal falls below 15, its extinction is inevitable (owing to the lack of reproductive options without severe in-breeding). If the current population of this animal is 1800, in how many years will it face extinction?

Name:

Unit 9C Test 3

Date:

Choose the correct answer to each problem. 1. In 1990, the population of a certain city was 75,000, and it has been growing at a steady rate of 4% per year since then. If this rate of growth continues, what will the population of this city be in 2020? (a) 164,000

(b) 183,000

(d) 2,340,000

2. Carl placed $900 in a brokerage account that has been increasing its value by 16% per year. At the same time, Brad began placing $900 under a mattress at the beginning of each year. Who had more money after 22 years, and by how much? (a) Carl, by about $1600 (c) Brad, by about $1600

(b) Carl, by about $3800 (d) Brad, by about $3800

3. The average price of a home in a certain town was $78,000 in 1990, but home prices have been falling by t 10% per year. Create an exponential function of the form Q = Q0 × (1 + r ) to model this situation, where t

is the number of years since 1990 and Q is the average home price in thousands. (a) Q = 78(1.1)

(b) Q = 10(0.78)

(d) Q = 78(0.9)

4. In 2005, the enrollment at a certain university was 2300 students. If the enrollment increases by 6% per year, what will the enrollment be (to the nearest hundred students) in the year 2020? (a) 3100 students

(b) 5500 students

(d) 8,570 students

5. Suppose that the average price for a certain product was $14.25 in 1990 and $18.75 in 1998. With an inflation rate of 3% per year, compare the inflation-adjusted prices of this product. (a) The price fell by $0.70 (as measured in 1998 dollars). (b) The price fell by $4.50 (as measured in 1998 dollars). (c) The price increased by $0.70 (as measured in 1998 dollars). (d) The price increased by $4.50 (as measured in 1998 dollars). 6. If prices increase at a monthly rate of 2.1%, how much do they increase in a year? (a) 25.2%

(b) 28.3%

(d) 41.5%

7. Between 2005 and 2009, Russia’s average rate of inflation has been 11.4% per year. If a cart of groceries cost $110 in 2005, what did it cost in 2009? (a) $160.16

(b) $169.41

(d) $185.79

8. Suppose that poaching reduces the population of an endangered animal by 12% per year. Further, suppose that when the population of this animal falls below 45, its extinction is inevitable (owing to the lack of reproductive options without severe in-breeding). If the current population of this animal is 1500, in how many years will it face extinction? (a) 27 years

(b) 33 years

(d) 55 years

Unit 9C Test 3 (continued)

Name:

9. A toxic radioactive substance with a density of 7 milligrams per square centimeter is detected in the ventilating ducts of an old nuclear processing building. If the half-life of the substance is 17 years, what was the density of the substance when it was deposited 41 years ago? 2

(a) 37.2 mg/cm

(b) 46.4 mg/cm

(d) 153.2 mg/cm

10. A fossilized bone contains about 68% of its original carbon-14. To the nearest hundred years, how old is the bone? (The half-life of carbon-14 is about 5700 years.) (a) 2700 years

(b) 3200 years

(d) 4200 years

Name:

Unit 9C Test 4

Date:

Choose the correct answer to each problem. 1. In 2000, the population of a certain town was 35,000, and it has been growing at a steady rate of 4.5% per year since then. If this rate of growth continues, what will the population of this city be in 2025? (a) 140,000

(b) 105,000

(d) 39,000

2. Celene placed $600 in a brokerage account that has been increasing its value by 12% per year (i.e., APY = 12%). At the same time, Dottie began placing $600 under a mattress at the beginning of each year. Who had more money after 25 years, and by how much? (a) Celene, by about $2500 (c) Dottie, by about $2500

(b) Celene, by about $4800 (d) Dottie, by about $4800

3. The average price of a home in a certain town was $92,000 in 1990, but home prices have been falling by t 6% per year. Create an exponential function of the form Q = Q0 × (1 + r ) to model this situation, where t

is the number of years since 1990 and Q is the average home price in thousands. t

(a) Q = 60(0.92)

(b) Q = 92(0.06)

(d) Q = 92(1.06)

4. In 2000, the enrollment at a certain university was 24,500 students. If the enrollment increases by 1% per year, what will the enrollment be (to the nearest hundred students) in the year 2018? (a) 28,900

(b) 29,300

(d) 44,100

5. Suppose that the average price for a certain product was $15.40 in 1990 and $17.25 in 1998. With an inflation rate of 3% per year, compare the inflation-adjusted prices of this product. (a) The price fell by $1.85 (as measured in 1998 dollars). (b) The price fell by $2.26 (as measured in 1998 dollars). (c) The price increased by $1.85 (as measured in 1998 dollars). (d) The price increased by $2.26 (as measured in 1998 dollars). 6. If prices increase at a monthly rate of 1.8%, how much do they increase in a year? (a) 11.5%

(b) 16.9%

(d) 23.9%

7. A city has a current population of 140,000 and does not want to grow any larger than to a total population of 275,000 within 35 years. What limit should they set for their annual percentage growth? (a) 1% years

(b) 2% years

(d) 4% years

8. Suppose that poaching reduces the population of an endangered animal by 18% per year. Further, suppose that when the population of this animal falls below 50, its extinction is inevitable (owing to the lack of reproductive options without severe in-breeding). If the current population of this animal is 2500, in how many years will it face extinction? (a) 2 years

(b) 20 years

(d) 28 years

Unit 9C Test 4 (continued)

Name:

9. A toxic radioactive substance with a density of 9 milligrams per square centimeter is detected in the ventilating ducts of an old nuclear processing building. If the half-life of the substance is 7 years, what was the density of the substance when it was deposited 52 years ago? 2

(a) 501.6 mg/cm

(b) 841.2 mg/cm 2

(d) 1550.5 mg/cm

10. A fossilized bone contains about 65% of its original carbon-14. To the nearest hundred years, how old is the bone? (The half-life of carbon-14 is about 5700 years.) (a) 2600 years

(b) 2900 years

(d) 3500 years

Name:

Unit 10A Test 1 Circle Square Rectangle Parallelogram

Date: Perimeter

Area

2π r 4l

π r2

2l + 2 w 2l + 2 w

lw lh

1 bh 2 1. Find the perimeter and area of a square city park that measures 90 yards on a side.

Triangle

a+b+c

2. Find the perimeter and area of a rectangular garden plot that has a length of 7 ft and a width of 6 ft.

3. Find the perimeter and area of the figure below.

12 inches

13 inches

5 inches

4. Find the perimeter and area of the figure below.

9 cm

7 cm 11 cm

6 cm

Unit 10A Test 1 (continued) 5.

Name:

How much paving material (in square meters) is needed to pave the parking lot illustrated below. 120 m 80 m

Surface Area Sphere

4π r 2

Cube Right Rectangular Prism

6l 2 2 ( lw + lh + wh )

Right Circular Cylinder

2π r + 2π rh

Volume

4 3 πr 3 l3 lwh

π r 2h

6. Find the volume of a regulation blocker dodge ball with diameter 8.5 inches.

7. A grain silo in the shape of a right circular cylinder is 12 meters tall and has a radius of 5 meters. Find the volume of grain the silo will hold. The farmer wants to paint the outside of the silo (not the top or bottom). Find the surface area he needs to cover so that he can estimate how much paint he needs to buy.

8. A swimming pool measures is 50 yards long, 20 yards wide, and 3 yards deep. How much water does it take to fill the pool (in cubic yards)? The pool needs to be repainted. Compute the surface area of the bottom and sided of the pool in order to estimate the amount of paint needed.

Unit 10A Test 1 (continued)

Name:

Use the following information to answer questions 9 – 10. You build an architectural model of the Lincoln Memorial using a scale factor of 50. 9. How does the height of the actual Lincoln Memorial compare to the height of the scale model?

10. How does the surface area of the actual Lincoln Memorial compare to the surface area of the scale model? (Assume the simplified shape of a right rectangular prism).

Name:

Unit 10A Test 2 Circle Square Rectangle Parallelogram

Date:

Perimeter

Area

2π r 4l

π r2

2l + 2 w 2l + 2 w

lw lh

1 bh 2 1. Find the perimeter and area of a square city park that measures 60 yards on a side.

Triangle

a+b+c

2. Find the area of the shaded region below. 8m 11 m

18 m

3. Find the perimeter and the area of the triangle below. 42 mm

112 mm 52 mm 76 mm

Unit 10A Test 2 (continued)

Name:

4. How much mulch (in square meters) is needed to cover the playground illustrated below. 70 m 50 m

Surface Area Sphere

4π r 2

Cube Right Rectangular Prism

6l 2 2 ( lw + lh + wh )

Right Circular Cylinder

2π r + 2π rh

Volume

4 3 πr 3 l3 lwh

π r 2h

5. Find the volume and surface area of a ball with a radius of 5 inches.

6. A grain silo in the shape of a right circular cylinder is 40 feet tall and has a radius of 13 feet. How many cubic feet of grain will the silo hold?

7. How much sand would it take to fill a cube with sides measuring 4 inches? How much contact paper would it take to cover the cube?

Unit 10A Test 2 (continued)

Name:

Use the following information to answer questions 8 – 10. You build an architectural model of a new apartment building using a scale factor of 40. 8. How does the height of the actual apartment building compare to the height of the scale model?

9. How does the surface area of the actual apartment building compare to the surface area of the scale model?

10. How does the volume of the actual apartment building compare to the volume of the scale model?

Name:

Unit 10A Test 3

Date:

Choose the correct answer to each problem. 1. A point has (a) 0 dimensions.

(b) 1 dimension.

(d) 3 dimensions.

(d) space.

2. In Euclidean geometry, two distinct points determine (a) a line.

(b) a plane.

3. Which polygon has the greatest area? (a) a circle with radius 2 (c) a rectangle with sides of 6 and 7

(b) a square with side length 6. (d) a triangle with base 3 and height 8

4. Which solid has the greatest volume? (a) A cube with sides of length 4 (b) A sphere with a radius of 4 (c) A right cylindrical cylinder with radius 4 and height 4 (d) A right rectangular prism with sides measuring 3, 4, and 5 5. Which solid has the greatest surface area? (a) A cube with sides of length 4 (b) A sphere with a radius of 4 (c) A right cylindrical cylinder with radius 4 and height 6 (d) A right rectangular prism with sides measuring 3, 4, and 5

Circle Square Rectangle Parallelogram Triangle

Perimeter

Area

2π r 4l

π r2

2l + 2 w 2l + 2 w

lw lh

a+b+c

1 bh 2

Surface Area Sphere

4π r 2

Cube Right Rectangular Prism

6l 2 2 ( lw + lh + wh )

Right Circular Cylinder

2π r + 2π rh

Volume

4 3 πr 3 l3 lwh

π r 2h

Unit 10A Test 3 (continued)

Name:

Use the following information to answer questions 6 – 8. You build an architectural model of a new apartment building using a scale factor of 60. 6. How does the height of the actual apartment building compare to the height of the scale model? (a)

1 times 60

(b) 60 times

(d) 216,000

7. How does the surface area of the actual apartment building compare to the surface area of the scale model? (a)

1 times 60

(b) 60 times

(d) 216,000

8. How does the volume of the actual apartment building compare to the volume of the scale model? (a)

1 times 60

(b) 60 times

(d) 216,000

Name:

Unit 10A Test 4

Date:

Choose the correct answer to each problem. 1. A line has (a) 0 dimensions.

(b) 1 dimension.

(d) 3 dimensions.

2. Which of the following do not determine a plane? (a) 2 points (c) 3 non-collinear points

(b) a line and a point not on the line (d) all of these determine a plane

3. Which polygon has the greatest perimeter (or circumference)? (a) a circle with radius 5 (c) a rectangle with sides of 3 and 7

(b) a square with side length 5 (d) a triangle with base 5 and height 8

4. Which right cylindrical cylinder has the greatest volume? (a) A can with radius 3 centimeters and height 8 centimeters (b) A can with radius 9 centimeters and height 3 centimeters. (c) A can with radius 6 centimeters and height 6 centimeters (d) A can with radius 8 centimeters and height 5 centimeters 5. Which solid has the least surface area? (a) A cube with a side of length 4 inches (b) A sphere with a radius of 4 inches (c) A right cylindrical cylinder with a radius of 4 inches and a height of 4 inches (d) A right rectangular prism with sides measuring 9, 3, and 2

Circle Square Rectangle Parallelogram Triangle

Perimeter

Area

2π r 4l

π r2

2l + 2 w 2l + 2 w

lw lh

a+b+c

1 bh 2

Surface Area Sphere

4π r 2

Cube Right Rectangular Prism

6l 2 2 ( lw + lh + wh )

Right Circular Cylinder

2π r + 2π rh

Volume

4 3 πr 3 l3 lwh

π r 2h

Unit 10A Test 4 (continued)

Name:

6. Find the perimeter of the triangle below. 12 mm

38 mm 14 mm 26 mm

(a) 156 mm

(b) 102 mm

(d) 78 mm

(d) 78 mm2

(d) 105 m

7. Find the area of the triangle below. 12 mm

38 mm 14 mm 26 mm

(a) 156 mm2

(b) 102 mm2

8. Find the area of the shaded region below. 6m 9m

15 m (a) 135 m2

(b) 26 m

Name:

Unit 10B Test 1 1.

Date:

Convert 163.18° into degrees, minutes, and seconds of arc.

2. Convert 9° 27′ 54′′ into decimal form.

3. A wall clock has a diameter of 1 foot. What is the angular size if viewed from a distance of 15 feet?

4. Find the slope of each surface, then determine which is steeper. A road with a 12% grade or a sidewalk with a pitch of 1 in 6

5. What is the slope of a driveway with a pitch of 3 in 4? How much does the driveway rise in 20 horizontal feet?

6. A jogger running around a park runs 3 miles east, then turns and runs 1 mile north. To return to the starting point, she then cuts diagonally back across the park. What is her total distance?

Unit 10B Test 1 (continued)

Name:

7. A property has stream frontage of 400 feet in length and the property line is 600 feet in length. Find the area in acres of the property. (1 acre = 43,560 ft2) property line stream frontage

8. Find x and y. 8

2 8

9. Solar Access Policy: On the shortest day of the year, a house cannot cast a noontime shadow that reaches farther than the shadow that would be cast by a 12-foot fence on the property line. A 12-foot fence casts a 20-foot shadow on the shortest day of the year and the north side of the house is planned to be set back 25 feet from the property line. Find the maximum allowed height for the house. Is the placement of the house reasonable?

10. There is 180 meters of fencing material. Find the area that can be enclosed by a circular enclosure and the area that can be enclosed by a square enclosure. Compare the areas and comment.

Name:

Unit 10B Test 2

Date:

1. Convert 142.52° into degrees, minutes, and seconds of arc.

2. Convert 12° 6′ 54′′ into decimal form.

3. A wall clock in the back of a classroom has a diameter of 1.5 feet. If the professor is standing 25 feet away from the clock, what is the angular size?

4. Find the slope of each surface, then determine which is steeper. A road with a 7% grade or a sidewalk with a pitch of 1 in 8

5. Find the slope of a roof that has a pitch of 8 to 12. How far will the roof rise from the edge to the peak, 18 feet away?

Unit 10B Test 2 (continued)

Name:

6. A jogger and his dog are running at a park. They run 2 miles west, then turn and run 3 miles north. To return to the starting point, they then cut diagonally back across the park. What is the total distance of their run?

7. A property has stream frontage of 90 feet in length and the property line is 600 feet in length. Find the area in acres of the property. (1 acre = 43,560 ft2) property line stream frontage

8. Find x and y. 4

1 6

9. Solar Access Policy: On the shortest day of the year, a house cannot cast a noontime shadow that reaches farther than the shadow that would be cast by a 12-foot fence on the property line. A 12-foot fence casts a 25-foot shadow on the shortest day of the year and the north side of the house is planned to be set back 30 feet from the property line. Find the maximum allowed height for the house. Is the placement of the house reasonable?

Unit 10A Test 2 (continued)

Name:

10. There is 120 meters of fencing material. Find the area that can be enclosed by a circular enclosure and the area that can be enclosed by a square enclosure. Compare the areas and comment.

Name:

Unit 10B Test 3

Date:

Choose the correct answer to each problem. 1. Convert 65.43° into degrees, minutes, and seconds of arc. (a) 65° 25′ 8′′

(b) 65° 25′ 13′′

(d) 65° 26′ 0′′

(d) 12.5822°

2. Convert 12° 34′ 56′′ into decimal form. (a) 12.3456°

(b) 12.1500°

3. A wall clock has a diameter of 1 foot. What is the angular size if viewed from a distance of 27 feet? (a) 2.12°

(b) 4.2°

(d) 9.8°

4. If a road has a grade of 20%, what is the pitch of the road? (a) 1 to 5

(b) 1 to 20

(d) 5 to 1

(d) 1

5. What is the slope of a roof that has a pitch of 9 to 12? (a) 0.25

(b) 0.5

6. Amy rides her bicycle due north for 5 miles, then due east for 12 miles. She turns and rides straight back to her starting point. What is the total distance of her bicycle ride? (a) 13 miles

(b) 27.9 miles

(d) 34 miles

(d) 20

7. What is the length of side x? 5

2 x

8 (a) 1.25

(b) 3.2

8. Solar Access Policy: On the shortest day of the year, a house cannot cast a noontime shadow that reaches farther than the shadow that would be cast by a 12-foot fence on the property line. A 12-foot fence casts a 15-foot shadow on the shortest day of the year and the north side of the house is planned to be set back 10 feet from the property line. Find the maximum allowed height for the house. (a) 37.5 feet

(b) 31.25 feet

(d) 20 feet

9. What is the area of a square enclosure that uses 320 meters of fencing? (a) 1280 m2

(b) 6400 m2

(d) 25,600 m2

Name:

Unit 10B Test 4

Date:

Choose the correct answer to each problem.

1. Convert 41.9° into degrees, minutes, and seconds of arc. (a) 41° 9′ 0′′

(b) 41° 15′ 0′′

(d) 41° 30′ 0′′

(d) 109.45°

2. Convert 108° 15′ 36′′ into decimal form. (a) 108.26°

(b) 108.51°

3. A wall clock has a diameter of 1 foot. What is the angular size if viewed from a distance of 36 feet? (a) 1.59°

(b) 2.5°

(d) 3.18°

4. Which is steeper? A road has a grade of 8% or a roof that has a pitch of 20 to 12? (a) The road

(b) The roof

5. A jogger and his dog are running at a park. They run 1.8 miles west, then turn and run 2.4 miles north. To return to the starting point, they then cut diagonally back across the park. What is the total distance of their run? (a) 5.8 miles

(b) 3 miles

(d) 4.2 miles

6. A property has stream frontage of 100 feet in length and the property line is 600 feet in length. Find the area in acres of the property. (1 acre = 43,560 ft2) property line

stream frontage (a) 67.9 acres

(b) 1.36 acres

(d) 814.9 acres

7. What is the length of side x? 4

3 x

15 (a) 8

(b) 12

(d) 14

8. What is the area of a circular enclosure that uses 312 meters of fencing? (a) 7746.4 m2

(b) 30,985.6 m2

(d) 305,815.2 m2

Name:

Unit 10C Test 1

Date:

1. Give an example of fractals found in nature.

2. Explain how a boundary between two countries can have different lengths, yet both still be valid.

3. Explain why there is an upper limit to the amount of area of an island, but there is not an upper limit to the length of coastline of an island.

4. Explain what it means to have a fractal dimension between 1 and 2.

5. Find the dimension of the object, and state whether or not it is a fractal. In measuring the length of the object, when you reduce the length of your ruler by a factor of 2, the number of elements increases by a factor of 8.

6. Find the dimension of the object, and state whether or not it is a fractal. In measuring the length of the object, when you reduce the length of your ruler by a factor of 2, the number of elements increases by a factor of 10.

Name:

Unit 10C Test 2

Date:

1. What does iteration mean?

2. What makes a fractal self-similar?

3. Describe what it means for an object to have a fractal dimension between 2 and 3.

4. Draw your own simple fractal, advancing as far as L2.

5. Find the dimension of the object, and state whether or not it is a fractal. In measuring the length of the object, when you reduce the length of your ruler by a factor of 3, the number of elements increases by a factor of 8.

6. Find the dimension of the object, and state whether or not it is a fractal. In measuring the length of the object, when you reduce the length of your ruler by a factor of 3, the number of elements increases by a factor of 27.

Name:

Unit 10C Test 3

Date:

Choose the correct answer to each problem. 1. In fractal geometry, the shorter the ruler (a) the longer the perimeter. (c) the shorter the perimeter.

(b) the less accurate the measurement. (d) the more difficult the procedure.

2. Fractal geometry has applications in (a) imitating nature. (c) finding parallel lines.

(b) creating music. (d) repairing broken objects.

3. In fractal geometry, (a) the perimeter of a region is limited, but the area is unlimited. (b) the perimeter of a region is unlimited, but the area is limited. (c) the perimeter and the area of a region are limited. (d) the perimeter and the area of a region are unlimited. 4. A fractal object is an object (a) with many jagged edges. (c) that reveals new features at smaller scales.

(b) that can be magnified. (d) that has been broken into pieces.

5. For the area of a square, increasing the ruler length by a factor of 4 (a) reduces the number of elements by a factor of 16. (b) reduces the number of elements by a factor of 8. (c) increases the number of elements by a factor of 4. (d) has no effect on the number of elements. 6. The Sierpinski sponge has a fractal dimension (a) between 0 and 1. (c) between 2 and 3.

(b) between 1 and 2. (d) between 3 and 4.

7. Suppose that you are measuring an object such that when you reduce the ruler length by a factor of 2.8, the number of elements increases by a factor of 6. What is the fractal dimension of the object? (a) 0.4667

(b) 0.5746

(d) 2.1429

Name:

Unit 10C Test 4

Date:

Choose the correct answer to each problem. 1. The fractal dimension of a coastline (a) between 0 and 1. (c) between 2 and 3.

(b) between 1 and 2. (d) between 3 and 4.

2. To create the Snowflake curve, the first step is to (a) divide the line segment into three equal pieces. (c) use a smaller ruler.

(b) find the fractal dimension. (d) count the number of elements.

3. A self-similar fractal (a) looks similar to itself when examined at different scales. (b) can be created by finding the fractal dimension. (c) has a fractal dimension between 0 and 1. (d) has a limited number of iterations. 4. The process of repeating a rule over and over to generate a self-similar fractal is called (a) repetition.

(b) iteration.

(d) logarithm.

5. A random iteration (a) is an iteration with slight variations in every iteration. (b) is an iteration that doesn’t produce a fractal. (c) is an iteration that is self-similar. (d) is an iteration with no variation in any iteration. 6. Website A states the North Carolina coastline is 301 miles long. Website B states it is 352 miles long. Why might they disagree? (a) Website A is using a shorter ruler than Website B. (b) Website A is using a longer ruler than Website B. (c) They didn’t use the same number of iterations when measuring. (d) One of the websites is attempting to deceive. 7. Suppose that you are measuring an object such that when you reduce the ruler length by a factor of 9, the number of elements increases by a factor of 14. What is the fractal dimension of the object? (a) 0.8326

(b) 1.2011

(d) 0.7266

Name:

Unit 11A Test 1

Date:

1. Explain how sound is produced.

2. Explain what the frequency of a string is.

3. Explain the dilemma of temperament.

4. Explain what happens to the frequency when you pluck one-eighth the length of a string.

5. If you have a tone with a frequency of 390 cps, find the frequency of the tone one octave lower.

6. For a 12-tone scale, starting at a tone with a frequency of 267 cps, find the frequency of the note 6 halfsteps higher.

Name:

Unit 11A Test 2

Date:

1. Explain the concept of fundamental frequency for a stringed instrument?

2. Explain the relationship between frequency and pitch.

3. Explain what is meant by harmonics.

4. What is the effect on the frequency when you pluck one-fourth of a string’s length?

5. If you have a tone with a frequency of 1200 cps, find the frequency of the tone 2 octaves lower.

6. For a 12-tone scale, starting with a frequency of 292 cps, find the frequency of the note 9 half-steps higher.

Name:

Unit 11A Test 3

Date:

Choose the correct answer to each problem. 1. One of the most basic qualities of sound is (a) pitch.

(b) string.

(d) harmony

2. All the following are true of the fundamental frequency of a string except: (a) Fundamental frequency is the lowest possible frequency for a particular string. (b) Fundamental frequency occurs when the string vibrates up and down its full length. (c) Fundamental frequency depends on the length, density, and tension of the string. (d) Fundamental frequency always begins at 100 cps. 3. What are the most pleasing combinations of notes? (a) fifths

(b) first harmonics

(d) pitches

4. The frequency of C one octave below middle C is (a) twice the frequency of middle C. (b) one-half the frequency of middle C. (c) one-eighth the frequency of middle C. (d) The same frequency as middle C. 5. The ancient Greeks invented the musical scale with how many notes? (a) 19

(b) 12

(d) 7

6. If you start middle A at 440 cps and raise it by a sixth to F, what is the resulting frequency? (a) 622 cps

(b) 740 cps

(d) 733 cps

7. For a 12-tone scale, starting at a tone with a frequency of 260 cps, find the frequency of the note that is 5 half-steps higher. (a) 312 cps

(b) 347 cps

(d) 194 cps

Name:

Unit 11A Test 4

Date:

Choose the correct answer to each problem. 1. How many half-steps does it take to raise a tone by a sixth? (a) nine

(b) eleven

(d) six

(d) twelve

2. In a 19-tone scale, how many tones are in one octave? (a) one

(b) eight

3. If a strings fundamental frequency is 50 cps, when you pluck only half the string the resulting frequency is (a) 25 cps.

(b) 50 cps.

(d) 150 cps.

4. Which music principle did the Greeks discover? (a) The shorter the string, the lower the pitch. (b) The shorter the string, the higher the pitch. (c) The longer the string, the higher the pitch. (d) String-length does not change pitch. 5. Consonant tones are produced by (a) many strings vibrating at once. (b) a variety of instruments being place at the same time. (c) only instruments with reeds instead of strings. (d) frequencies that have a simple ratio. 6. If middle C has a frequency of 260 cps, the frequency of G (fifth) is (a) 347 cps.

(b) 156 cps.

(d) 433 cps.

7. For a 12-tone scale, starting at a tone with frequency 437 cps, find the frequency of the note that is 6 halfsteps higher. (a) 546 cps.

(b) 618 cps.

(d) 780 cp

Name:

Unit 11B Test 1

Date:

1. List three uppercase letters that do not exhibit either reflection or rotation symmetries.

2. What three aspects of the visual arts relate directly to mathematics?

3. Give an example of symmetry in the everyday world.

4. Explain what aperiodic tiling is.

5. Draw a three-dimensional object using the point P as the principal vanishing point. Use the given object as the front face of your three-dimensional object.

•P

Unit 11B Test 1 (continued)

Name:

6. Reflect the given object over the given line. Does the object have symmetry over the vertical line?

7. How many reflection symmetries does the following shape have? How many rotational symmetries does the following shape have?

8. Explain why tilings of regular polygons can only be done with triangles, squares, and hexagons.

9. Draw an object with reflection symmetry.

10. Draw an example of translation symmetry.

Name:

Unit 11B Test 2

Date:

1. List three uppercase letters that exhibit right/left reflection symmetry.

2. List three uppercase letters that exhibit top/bottom reflection symmetry.

3. Draw an object with four rotational symmetries.

4. Explain tiling.

5. Define translating mathematically.

6. Define symmetry is in mathematical terms.

Unit 11B Test 2 (continued)

Name:

7. Draw a three-dimensional object using the point P as the principal vanishing point. Use the given object as the front face of your three-dimensional object.

•P

8. Reflect the given object over the given line. Does the object have symmetry over the horizontal line?

9. Draw a translation of the following object.

Name:

Unit 11B Test 3

Date:

Choose the correct answer to each problem. 1. An aspect of the visual arts that does not relate directly to mathematics is (a) symmetry.

(b) pitch.

(d) proportion

2. The first principle of perspective is (a) All lines that are parallel in the real scene and perpendicular to the canvas must intersect at the principal vanishing point of the painting. (b) All shapes and sizes must remain equal, regardless of their distance from the viewer. (c) All parallel lines never intersect; they remain the same distance apart. (d) Every aspect must show balance. 3. On a painting using perspective there is a row of 6-story buildings extending from the foreground, all the way to the vanishing point. The buildings in the background (a) appear smaller than the ones in the foreground. (b) appear larger than the ones in the foreground. (c) appear to be the same size as the ones in the foreground. (d) appear two-dimensional. 4. Which of the following is not a definition of symmetry? (a) a kind of balance (b) property of an object remains unchanged under certain operations (c) repetition of pattern (d) a line divides into two equal parts 5. Which letter is not an example of reflective symmetry? (a) M

(b) R

(d) B

6. When an object can be shifted, say to the left or right, and remains the same, this is an example of (a) reflection symmetry. (c) translation symmetry.

(b) rotation symmetry. (d) principal vanishing point

7. Which regular polygon cannot be used to make a tiling? (a) hexagon

(b) octagon

8. The number of different tilings with irregular polygons is (a) unlimited; you can make many different tilings using irregular polygons. (b) limited; you can only make 3 different tilings using irregular polygons. (c) zero; you cannot make a tiling using irregular polygons. (d) six

(d) square

Name:

Unit 11B Test 4

Date:

Choose the correct answer to each problem. 1. The vanishing point of a picture with perspective is (a) the point where you cannot see anything on the picture. (b) the point where parallel lines meet. (c) the point where two perpendicular lines intersect. (d) the point where the picture meets the frame. 2. Which of the following is not a type of symmetry? (a) rotation

(b) reflection

(d) translation

3. In mathematics and physics, translating an object means unchanged when (a) rewriting it as a mathematical expression. (c) moving it in a straight line, without rotating it.

(b) finding the vanishing point for the object. (d) rotating through an angle about a point.

4. In mathematics, reflection symmetry of an object means the object remains unchanged when (a) reflected across some straight line. (b) it retains a kind of balance. (c) moving it in a straight line, without rotating it. (d) rotating through some angle about some point. 5. Which letter is not an example of rotation symmetry? (a) N

(b) M

(d) O

6. Periodic tilings (a) cannot be made from regular polygons. (b) are only made from regular polygons. (c) do not have a pattern that repeats throughout the tiling. (d) have a pattern that repeats throughout the tiling. 7. Which regular polygon can be used to make a tiling with a single polygon? (a) triangle

(b) dodecahedron

(d) octagon

8. When making a tiling using only regular hexagons (a) the tiles do not fill all the space; there are gaps between the hexagons. (b) the tiles fill all the space, but there is some overlap of the tiles. (c) the tiles fill all the space, with no overlaps and no gaps. (d) the tiles do not fill all the space; there are some overlap of the tiles. 9. Which of the following is an example of how projective geometry differs from Euclidean geometry? (a) Triangles have more than 4 sides. (c) Parallel lines intersect.

(b) Perpendicular lines never intersect. (d) Two points do not make a line.

Name:

Unit 11C Test 1

Date:

1. What does the golden ratio purport to do?

2. Suppose a line segment is divided according to the golden ratio. If the length of the longer piece is 24 cm, how long is the entire line segment?

3. Suppose a piece of string is divided according to the golden ratio. If the length of the shorter piece is 6 m, how long is the entire string?

4. If the ratios of the larger to smaller sides of two rectangles are different, then is it possible that each rectangle is a golden rectangle? Explain.

5. The length of the short side of a golden rectangle is 4 inches. Find the length of the long side.

6. The length of the long side of a golden rectangle is 11 m. Find the length of the short side.

Unit 11C Test 1 (continued)

Name:

7. What is the relationship between the Fibonacci Sequence and the golden ratio?

Name:

Unit 11C Test 2

Date:

1. What question does the golden ratio claim to answer?

2. Suppose a piece of string is divided according to the golden ratio. If the length of the shorter piece is 18 cm, how long is the entire string?

3. Suppose a line segment is divided according to the golden ratio. If the length of the longer piece is 12 inches, how long is the entire line segment?

4. Is it possible to have two golden rectangles of different sizes? Explain

5. The length of the short side of a golden rectangle is 11 m. Find the length of the long side.

6. A manufacturer wants to build golden rectangle coffee tables. They know they want the longer side to be 4 ft long. What should be the length of the shorter side of the table?

Unit 11C Test 2 (continued) 7. Name a place in nature where Fibonacci numbers are encountered.

Name:

Unit 11C Test 3

Date:

Choose the correct answer to each problem. 1. The golden ratio is best described mathematically as (a) an equation.

(b) a proportion.

(d) a reflection.

2. The golden ratio is a(n) (a) irrational number.

(b) transcendental number. (c) rational number.

(d) whole number.

3. The golden ratio can be expressed as all the following except: (a) 1.6

(b)

8 5

(c)

1+ 5 2

(d)

3 5

4. Suppose a piece of string is divided according to the golden ratio. If the length of the shorter piece is 15 cm, how long is the entire string? (a) 9.3 inches

(b) 24.3 inches

(d) 30 inches

5. Suppose a piece of string is divided according to the golden ratio. If the length of the longer piece is 15 cm, how long is the entire string? (a) 9.3 inches

(b) 24.3 inches

(d) 30 inches

6. If the shorter side of a poster is 18 inches, about how long (to the nearest inch) should the longer side be so that the poster is a golden rectangle? (a) 18 inches

(b) 29 inches

(d) 11 inches

7. If the longer side of a photo is 5 inches, about how long (to the nearest inch) should the shorter side be so that the photo is a golden rectangle? (a) 5 inches

(b) 8 inches

(d) 3 inches

Name:

Unit 11C Test 4

Date:

Choose the correct answer to each problem. 1. What question led Greek scholars to formulating the golden ratio? (a) What is the square root of 2? (b) How are pitch and vibration related? (c) What is the best way to divide a line? (d) What are harmonics? 2. The golden ratio divides a line into how many pieces? (a) one

(b) two

(d) four

3. Aesthetics can best be described as (a) the art of painting. (b) research in harmony. (c) line division. (d) the study of beauty. 4. If a 6-inch long line segment is divided according to the golden ratio, the two pieces (a) have equal length. (b) are 2.3” and 3.7” long. (c) are 3.1” and 2.9” long. (d) are 2” and 4” long. 5. Suppose a piece of string is divided according to the golden ratio. If the length of the shorter piece is 9 cm, how long is the entire string? (a) 5.6 inches

(b) 14.6 inches

(d) 27 inches

6. If one side of a laptop screen is 13 inches, which of the following should not be the length of the other side if a golden rectangle is desired. (a) 8 inches

(b) 19.5 inches

(d) any will work

7. If the longer side of a photo is 14 inches, about how long (to the nearest inch) should the shorter side be so that the photo is a golden rectangle? (a) 5 inches

(b) 8 inches

8. The Fibonacci Sequence can be seen in (a) the number of petals on flowers. (b) the pattern of tiles in the Capitol floor. (c) the number of leaves on trees. (d) the years of the summer Olympics.

(d) 3 inches

Name:

Unit 12A Test 1

Date:

Suppose there are two candidates in a hypothetical U.S. Presidential election. The results are shown below. Candidate Rizzoli Isles Total Popular Votes

Electoral Votes 283 255

Popular Votes 52,684,510 53,847,684 106,532,194

1. Compute each candidate’s percentage of the popular vote. Did either candidate receive a popular majority?

2. Compute each candidate’s percentage of the electoral vote. Was the electoral winner also the winner of the popular vote?

3. Of the 100 Senators in the U.S. Senate, all but 43 support a new bill on environmental protection. The opposing senators start a filibuster. Is the bill likely to pass? Explain.

4. A criminal conviction (except in capital cases) in Oregon requires a guilty vote by 5/6 of the jury members. On a 12-member jury, what is the fewest number of jurors that must vote “guilty” to convict?

Unit 12A Test 1 (continued)

Name:

5. Make a preference schedule for the results of a 3-way race between candidates A, B, and C. • • • •

55 voters rank the candidates in the order (first to last choice) A, B, C. 40 voters rank the candidates in the order C, B, A 26 voters rank the candidates in the order B, C, A 18 voters rank the candidates in the order C, A, B First Second Third Number of voters

6. Find the plurality winner. Did the plurality winner also receive a majority? Explain.

7. Find the winner by a single runoff of the top two candidates.

8. Find the winner by using a point system.

9. Find the winner, if any, by the method of pairwise comparison.

Name:

Unit 12A Test 2

Date:

Suppose there are two candidates in a hypothetical U.S. Presidential election. The results are shown below. Candidate Grimes Dixon Total Popular Votes

Electoral Votes 240 298

Popular Votes 45,256,981 44,998,273 90,255,254

1. Compute each candidate’s percentage of the popular vote. Did either candidate receive a popular majority?

2. Compute each candidate’s percentage of the electoral vote. Was the electoral winner also the winner of the popular vote?

3. A proposed amendment to the U.S. Constitution has passed both the House and the Senate with the required 2/3 super majority. Each state holds a vote on the amendment and it receives a majority vote in 38 of the 50 states. Is the Constitution amended?

4. A criminal conviction (except in capital cases) in Louisiana requires a guilty vote by 5/6 of the jury members. On a 12-member jury, nine jurors vote “guilty.” Is the defendant convicted? Explain.

Unit 12A Test 2 (continued)

Name:

5. Make a preference schedule for the results of a 3-way race between candidates A, B, and C. • • • •

255 voters rank the candidates in the order (first to last choice) B, A, C 240 voters rank the candidates in the order C, A, B 126 voters rank the candidates in the order A, B, C 118 voters rank the candidates in the order B, C, A First Second Third Number of voters

6. Find the plurality winner. Did the plurality winner also receive a majority? Explain.

7. Find the winner by a single runoff of the top two candidates.

8. Find the winner by a point system.

9. Find the winner, if any, by the method of pairwise comparisons.

Name:

Unit 12A Test 3

Date:

1. Suppose there are two candidates in a hypothetical U.S. Presidential election. The results are shown below. Candidate Stark Lannister Total Popular Votes

Electoral Votes 262 276

Popular Votes 53,720,827 53,926,903 107,647,730

(a) Stark wins the popular vote and becomes President. (b) Lannister wins the popular vote and becomes President. (c) Stark wins the popular vote, but Lannister becomes President. (d) Lannister wins the popular vote, but Stark becomes President. 2. Of the 100 senators in the U.S. Senate, 54 support a new bill on environmental protection. The opposing senators start a filibuster. Is the bill likely to pass? (a) Yes

(b) No

3. A criminal conviction in Oregon requires a vote by 5/6 of the jury members. On a special 27-member jury, 23 jurors vote to convict. Will the defendant be convicted? (a) Yes

(b) No

For questions 4 – 8, refer to the following preference schedule. First

Second

Third

Fourth

Number of voters 4. Find the plurality winner. (a) A

(b) B

(d) D

5. Find the winner by a single runoff of the top two candidates. (a) A

(b) B

(d) D

6. Find the winner of a sequential runoff. (a) A

(b) B

Unit 12A Test 3 (continued)

Name:

7. Find the winner by a point system. (a) A

(b) B

(d) D

(d) None

8. Find the winner by the method of pairwise comparisons. (a) A

(b) B

Name:

Unit 12A Test 4

Date:

Choose the correct answer to each problem. 1. Suppose there are two candidates in a hypothetical U.S. Presidential election. The results are shown below. Candidate Jost Che Total Popular Votes

Electoral Votes 230 308

Popular Votes 47,825,238 47,721,962 95,547,200

(a) Jost wins the popular vote and becomes President. (b) Che wins the popular vote and becomes President. (c) Jost wins the popular vote, but Che becomes President. (d) Che wins the popular vote, but Jost becomes President. 2. A proposed amendment to the U.S. Constitution has passed both the House and the Senate with the required 2/3 super majority. Each state holds a vote on the amendment and it receives a majority vote in all but 17 of the 50 states. Is the Constitution amended? (a) Yes

(b) No

3. A criminal conviction in a Louisiana requires a vote by 5/6 of the jury members. On a special 19-member jury, 14 jurors vote to convict. Will the defendant be convicted? (a) Yes

(b) No

For questions 4 – 8, refer to the following preference schedule. First

Second

Third

Fourth

Number of voters

4. Find the plurality winner. (a) A

(b) B

(d) D

5. Find the winner by a single runoff of the top two candidates. (a) A

(b) B

(d) D

Unit 12A Test 4 (continued)

Name:

6. Find the winner of a sequential runoff. (a) A

(b) B

(d) D

(d) None

7. Find the winner by a point system. (a) A

(b) B

8. Find the winner by the method of pairwise comparisons. (a) A

(b) C

Name:

Unit 12B Test 1

Date:

For questions 1 – 3, consider the following preference schedule. First

Second

Third

Fourth

Number of voters

1. Suppose the winner is decided by plurality. Analyze whether this choice satisfies the four fairness criteria.

2. Suppose the winner is decided by the sequential runoff. Analyze whether this choice satisfies the four fairness criteria.

3. Suppose the winner is decided by the point system (Borda count). Analyze whether this choice satisfies the four fairness criteria.

4. Briefly state Arrow’s Impossibility Theorem.

Unit 12B Test 1 (continued)

Name:

5. In a 70-member parliament, a minority party has only four members. The remaining members of the parliament are divided evenly among two parties. Assume that no one ever misses a vote and that the members of any one party always vote the same way. Explain how the votes of the minority party could control the outcome of a vote.

6. Suppose that candidates A and B hold opposing political views, while candidate C is a moderate. Voter opinions about the candidates are as follows: 34% want C as their first choice, but would also approve of A. 13% want C as their first choice, and approve of neither A nor B. 14% want A as their first choice, but would also approve of C. 12% want A as their first choice, but would also approve of B. 27% want B as their first choice, but would also approve of A. a. If all voters could vote only for their first choice, which candidate would win by plurality? b. Which candidate wins by an approval vote?

The table contains the 2016 population and number of electoral votes for 4 states. State Idaho Texas Florida New York

Electoral Votes 4 38 29 29

Population 1,683,140 27,862,596 20,612,439 19,745,289

7. Compute the voting power per person for Idaho and Texas. Which state had more voting power per person?

Unit 12B Test 1 (continued)

Name:

8. Compute the voting power per person for Florida and New York. Which state had more voting power per person?

Name:

Unit 12B Test 2

Date:

For questions 1 – 3, consider the following preference schedule. First

Second

Third

Fourth

Number of voters

157

109

1. Suppose the winner is decided by plurality. Analyze whether this choice satisfies the four fairness criteria.

2. Suppose the winner is decided by the point system (Borda count). Analyze whether this choice satisfies the four fairness criteria.

3. Suppose the winner is decided by pairwise comparisons. Analyze whether this choice satisfies the four fairness criteria.

4. Briefly state Arrow’s Impossibility Theorem.

Unit 12B Test 2 (continued)

Name:

5. In a family owned company there are four shareholders. Shareholder A owns 28% of the company, Shareholder B owns 27%, Shareholder C owns 25%, and Shareholder D owns 20%. Explain what power Shareholder D does or does not have.

6. Suppose that candidates A and B have opposing political positions, while candidate C is more moderate. Voter opinions about the candidates are as follows: 15% want B as their first choice, but would also approve of C; 28% want B as their first choice, and approve of neither A nor C; 12% want C as their first choice, and approve of neither A nor B; 11% want C as their first choice, but would also approve of A; 10% want C as their first choice, but would also approve of B; 24% want A as their first choice, but would also approve of C. a. If all voters could vote only for their first choice, which candidate would win by plurality? b. Which candidate wins by an approval vote?

The table contains the 2016 population and number of electoral votes for 4 states. State Vermont Ohio Pennsylvania Illinois

Electoral Votes 3 18 20 20

Population 624,594 11,614,373 12,784,227 12,801,539

7. Compute the voting power per person for Vermont and Pennsylvania. Which state had more voting power per person?

Unit 12B Test 2 (continued)

Name:

8. Compute the voting power per person for Ohio and Illinois. Which state had more voting power per person?

Name:

Unit 12B Test 3

Date:

Choose the correct answer to each problem. 1. In 1952, Kenneth Arrow proved that it is not possible to find a voting system that satisfies all four fairness criteria. His theorem was called (a) Kenneth’s Voting System Proof (c) Kenneth’s Impossibility Theorem

(b) Arrow’s Impossibility Theorem (d) Arrow’s Voting System Proof

2. In order to have a fair voting system, how many criteria must be met? (a) 3

(b) 5

(d) 6

3. Which fairness criterion states: Suppose that candidate X is declared the winner of an election, and then a second election is held. If voters do not change their preferences, but one (or more) of the losing candidates drops out, then X should also win the second election. (a) Fairness criterion 1 (c) Fairness criterion 3

(b) Fairness criterion 2 (d) Fairness criterion 4

4. Which fairness criterion states: If a candidate receives a majority of first-place votes, that candidate should be the winner? (a) Fairness criterion 1 (c) Fairness criterion 3

(b) Fairness criterion 2 (d) Fairness criterion 4

5. In a 60-member parliament, suppose that there are 20 members of the Heart party, 16 members of the Diamond party, 14 members of the Club party, and 9 members of the Spade party. Assume that no one ever misses a vote and that the members of any one party always vote the same way. Are the members of the Spade party ever able to control the outcome of a vote? (a) Yes

(b) No

6. Suppose that candidates A and B hold similar political positions, while candidate C has opposing views. Voter opinions about the candidates are as follows: 30% want B as their first choice, but would also approve of A. 5% want B as their first choice, and approve of neither A nor C. 26% want A as their first choice, but would also approve of B. 39% want C as their first choice, and approve of neither A nor B. If an election is held using the approval voting method, which candidate wins? (a) A

(b) B

(d) There is a tie.

Unit 12B Test 3 (continued)

Name:

For questions 7 – 8, consider the following preference schedule. First

Second

Third

Number of voters

110

7. If the winner is selected by a Borda count, which of the following fairness criteria is violated? (a) Fairness criterion 2 (b) Fairness criterion 3 (c) Fairness criterion 4 (d) None of these 8. If the winner is selected by sequential runoffs, which of the fairness criteria is violated? (a) Fairness criterion 2 (b) Fairness criterion 3 (c) Fairness criterion 4 (d) None of these 9. The table contains the 2016 population and number of electoral votes for 4 states. State Massachusetts Iowa Minnesota Florida

Electoral Votes 11 6 10 29

Population 6,811,779 3,134,693 5,519,952 20,612,439

Which state had more voting power per person? (a) Massachusetts

(b) Iowa

(d) Florida

Name:

Unit 12B Test 4

Date:

Choose the correct answer to each problem. 1. How many criteria must be met in order to have a fair voting system? (a) 3

(b) 4

(d) 6

2. Which of the following statements best summarizes Arrow’s Impossibility Theorem? (a) It is impossible for one voting system to be better than another. (b) No voting system satisfies all four fairness criteria in all cases. (c) It is impossible for a voting system to fairness criterion 4. (d) The best voting system is approval voting. 3. Which fairness criterion states: If a candidate is favored over every other candidate in pairwise races, that candidate should be declared the winner? (a) Fairness criterion 1 (c) Fairness criterion 3

(b) Fairness criterion 2 (d) Fairness criterion 4

4. Which fairness criterion states: Suppose that candidate X is declared the winner of an election, and then a second election is held. If some voters rank X higher in the second election than in the first election (without changing the order of the other candidates), then X should also win the second election? (a) Fairness criterion 1 (c) Fairness criterion 3

(b) Fairness criterion 2 (d) Fairness criterion 4

5. A small company has stockholder who own 30%, 25%, 23%, and 22% of the shares. Assume votes are assigned in proportion to the number of shares each stockholder owns, and that all decisions are made by a strict majority vote. Explain the position of the person who holds 22% of the stock. (a) No effective power. Voting with any other shareholder has no effect on the outcome of the vote. (b) Little effective power. Influence on an election comes only from voting with the largest shareholder. (c) Much effective power. Voting with any other shareholder can influence the outcome of an election. (d) Much effective power. Missing a vote would have a disastrous outcome for an election. 6. Suppose that candidates A and C hold similar political views, while B holds opposing positions. Voter opinions about the candidates are as follows: 25% want C as their first choice, but would also approve of A; 30% want A as their first choice, but would also approve of C; 4% want A as their first choice, but would also approve of B; 4% want B as their first choice, but would also approve of C; 37% want B as their first choice, and approve of neither A nor C. Which candidate wins by an approval vote? (a) A

(b) B

(d) There is a tie.

Unit 12B Test 4 (continued)

Name:

For questions 7 – 8, consider the following preference schedule. First

Second

Third

Number of voters

7. If the winner is selected by a Borda count, which of the following fairness criteria is violated? (a) Fairness criterion 2 (b) Fairness criterion 3 (c) Fairness criterion 4 (d) None of these

8. If the winner is selected by sequential runoffs, which of the fairness criteria is violated? (a) Fairness criterion 1 (b) Fairness criterion 2 (c) Fairness criterion 3 (d) Both choices (a) and (c) 9. The table contains the 2016 population and number of electoral votes for 4 states. State Pennsylvania Idaho Illinois New York

Electoral Votes 20 4 20 29

Population 6,811,779 3,134,693 12,801,539 19,745,289

Which state had more voting power per person? (a) Pennsylvania

(b) Idaho

(d) New York

Name:

Unit 12C Test 1

Date:

1. Briefly define apportionment.

2. Explain what is meant by the fractional remainder.

3. What has happened if the population paradox has occurred?

4. State the Quota Criterion.

5. What does the Balinsky and Young theorem tell us?

6. The table below gives the population of four states A, B, C, and D, among which a total of 90 seats are to be apportioned. Find the standard divisor, the standard quota, and the minimum quota. (Round the standard divisor and the standard quota to two decimal places, as necessary). State Population

Total

119,050

114,560

97,790

81,200

412,600

Standard quota Minimum quota

Unit 12C Test 1 (continued)

Name:

7. Fill in the information from the table in problem 6, then complete this table using Hamilton’s method. State Population

Total

119,050

114,560

97,790

81,200

412,600

Standard quota Minimum quota Fractional remainder Final apportionment

8. Fill in the information from the table in problem 6, then complete this table using Jefferson’s method. State Population

Total

119,050

114,560

97,790

81,200

412,600

Standard quota Minimum quota Modified quota (with divisor 4500) Minimum quota (with divisor 4500)

9. Fill in the information from the table in problem 6, then complete the table using Webster’s method. State Population

Total

119,050

114,560

97,790

81,200

412,600

Standard quota Minimum quota Modified quota (with divisor 4500) Rounded quota Comment on your results.

Unit 12C Test 1 (continued)

Name:

10. Fill in the information from the previous tables, then complete the table using the Hill-Huntington method. Round the geometric means to three decimal places. State Population

Total

119,050

114,560

97,790

81,200

412,600

Standard quota Minimum quota Modified quota (with divisor 4500) Geometric mean Rounded quota

Name:

Unit 12C Test 2

Date:

1. Explain what apportionment has to do with the U.S. House of Representatives.

2. Explain what the standard divisor is.

3. Explain the Alabama paradox.

4. What has happened if the new states paradox has occurred?

5. A school district has four elementary schools and 20 kindergarten teachers. The following table contains the kindergarten enrollment at each school for the next school year. Complete the following table using Hamilton’s method. School

Carpenter

Davis

Cary

Salem

Total

Kindergarten enrollment

150

144

107

103

504

Standard quota Minimum quota Fractional remainder Final apportionment

Unit 12C Test 2 (continued)

Name:

6. Funding may be available to hire one more kindergarten teacher. Now complete the table using Hamilton’s method, assuming there will be 21 kindergarten teachers. School

Carpenter

Davis

Cary

Salem

Total

Kindergarten enrollment

150

144

107

103

504

Standard quota Minimum quota Fractional remainder Final apportionment

7. The table contains the 2016 population and number of seats in the U.S. House of Representatives for 4 states. Find the standard quota for each state and compare it to the actual number of seats for the state. Explain whether the state is overrepresented or underrepresented in the House. Assume a U.S. population of 323.1 million, and 435 House seats. State Seats Population Idaho 4 1,683,140 Texas 38 27,862,596 Florida 29 20,612,439 New York 29 19,745,289

8. Assume that 100 representatives must be apportioned to the following sets of states with the given populations. Determine the number of representatives for each state using Hamilton’s method. Then assume that the number of representatives is increased to 101. Determine the new number of representatives for each state using Hamilton’s method. State whether the change in total number of representatives results in the Alabama paradox. A: 2540; B: 1150; C: 6560

Unit 12C Test 2 (continued)

Name:

9. Apply Jefferson’s method to the following sets of states with the given populations. Assume that 100 seats are to be apportioned. In each case, state whether the quota criterion is satisfied. A: 98; B: 689; C: 212; modified divisor 9.83

Name:

Unit 12C Test 3

Date:

1. Which of the following quantities does not vary from state to state? (a) Number of Representatives (c) Standard divisor

(b) Minimum quota (d) Standard quota

2. Which of the following varies from state to state? (a) Number of Representatives (c) Number of Senators

(b) Standard Quota (d) Both (a) and (b)

3. Which method of apportionment compares a modified quota to a geometric mean? (a) Hamilton’s method (c) Webster’s method

(b) Jefferson’s method (d) Hill-Huntington method

4. Which method of apportionment was approved by a Democratic majority in Congress and signed into law by a Democratic president because it gave the Democrats one more seat in the House at that time? (a) Hamilton’s method (c) Webster’s method

(b) Jefferson’s method (d) Hill-Huntington method

5. Which of the following best describes how the modified divisor is found? (a) Divide the state’s population by the standard divisor (b) Divide the state’s population by the standard quota (c) Divide the state’s population by the modified quota (d) Trial and error 6. The table below gives the population of four states A, B, C, and D, among which a total of 55 seats are to be apportioned. Find the standard divisor for the problem. State Population

Total

357,500

143,000

205,000

165,150

870,650

(a) 55

(b) 15,830

(d) 217,663

7. The table below gives the population of four states A, B, C, and D, among which a total of 55 seats are to be apportioned. Find the minimum quota for State A. State Population

(a) 22

Total

357,500

143,000

205,000

165,150

870,650

(b) 22.58

(d) 22.57

Unit 12C Test 3 (continued)

Name:

8. The table below gives the population of four states A, B, C, and D, among which a total of 60 seats are to be apportioned. Complete the table using Hamilton’s method. (Round answers to two decimal places, as appropriate.) How many seats does State A receive using Hamilton’s method? State Population

Total

256,500

143,000

89,000

51,500

540,000

Standard quota Minimum quota Fractional remainder Final apportionment (a) 26

(b) 27

(d) 29

9. The table below gives the population of four states A, B, C, and D, among which a total of 60 seats are to be apportioned. Complete the table using Jefferson’s method. (Round answers to two decimal places, as appropriate.) Compare the number of seats state A receives using Jefferson’s method with the number of seats state A received using Hamilton’s method. State Population

Total

256,500

143,000

89,000

51,500

540,000

Standard quota Minimum quota Modified quota (with divisor 8800)

Minimum quota (with divisor 8800)

Using Jefferson’s method, state A gets

representatives than with Hamilton’s method.

(a) 2 more

(b) 1 more

(d) 1 fewer

10. The table below gives the population of four states A, B, C, and D, among which a total of 60 seats are to be apportioned. Complete the table using Webster’s method. (Round answers to two decimal places, as appropriate.) How many seats does State D receive using Webster’s method? State Population

Total

256,500

143,000

89,000

51,500

540,000

Standard quota Minimum quota Modified quota (with divisor 9100)

Rounded quota (a) 5

(b) 6

(d) 28

Name:

Unit 12C Test 4

Date:

1. Which of the following quantities varies from state to state? (a) Number of Senators (c) Standard divisor

(b) Modified divisor (d) Standard quota

2. Which method of apportionment never leads to a violation of the Quota Criterion? (a) Hamilton’s method (c) Webster’s method

(b) Jefferson’s method (d) Hill-Huntington method

3. What is the name of the process used to divide the number of seats in the House of Representatives among states? (a) Apportionment (c) Alabama Paradox

(b) Jefferson’s method (d) Quota criterion

4. Which method of apportionment is used today? (a) Hamilton’s method (c) Webster’s method

(b) Jefferson’s method (d) Hill-Huntington method

5. What is it called when a state’s apportionment of seats is changed after new seats are added to accommodate the addition of a state? (a) Alabama paradox (c) Quota criterion

(b) Population paradox (d) New state paradox

6. What is the expectation that a states apportionment will be equal to its standard quota rounded either up or down to the nearest integer? (a) Alabama paradox (c) Quota criterion

(b) Population paradox (d) New state paradox

Unit 12C Test 4 (continued)

Name:

7. The table below gives the population of four states A, B, C, and D, among which a total of 45 seats are to be apportioned. Find the standard divisor for the problem. A

Total

357,500

143,000

205,000

165,150

870,650

State Population (a) 45

(b) 19,347.78

(d) 4555.56

8. The table below gives the population of four states A, B, C, and D, among which a total of 25 seats are to be apportioned. Complete the table using Hamilton’s method. (Round answers to two decimal places, as appropriate.) How many seats does State A receive using Hamilton’s method? State Population

Total

644,000

183,000

229,000

198,000

1,254,000

Standard quota Minimum quota Fractional remainder Final apportionment (a) 11

(b) 12

(d) 14

9. The table below gives the population of four states A, B, C, and D, among which a total of 25 seats are to be apportioned. Complete the table using Jefferson’s method. (Round answers to two decimal places, as appropriate.) Compare the number of seats state B receives using Jefferson’s method with the number of seats state B receives using Hamilton’s method. State Population

Total

644,000

183,000

229,000

198,000

1,254,000

Standard quota Minimum quota Modified quota (with divisor 46,000)

Minimum quota (with divisor 46,000)

Using Jefferson’s method, state B got (a) 2 more

(b) 1 more

representatives than with Hamilton’s method. (c) the same number of

(d) 1 fewer

Unit 12C Test 4 (continued)

Name:

10. The table below gives the population of four states A, B, C, and D, among which a total of 25 seats are to be apportioned. Complete the table using Webster’s method. (Round answers to two decimal places, as appropriate.) How many seats does State B receive using Webster’s method? State Population

Total

644,000

183,000

229,000

198,000

1,254,000

Standard quota Minimum quota Modified quota (with divisor 51,000)

Rounded quota (a) 3

(b) 4

(d) 6

Name:

Unit 12D Test 1

Date:

1. What is redistricting and how often must it be done?

2. List the two requirements that must be met in drawing district boundaries.

The table below shows the election results for the House of Representatives in Arizona.

2010 2012

Votes for Republican Candidates 900,510 1,131,663

Votes for Democratic Candidates 711,837 946,994

Republican Seats

Democratic Seats

5 4

3 5

3. Find the percentage of votes cast for Republicans and Democrats in 2010. Find the percentage of House seats won by Republicans and Democrats. Does the distribution of votes match the distribution of seats won?

4. Find the percentage of votes cast for Republicans and Democrats in 2012. Find the percentage of House seats won by Republicans and Democrats. Does the distribution of votes match the distribution of seats won? Does it appear the redistricting of 2010 affected the distribution of votes and seats? Explain.

Unit 12D Test 1 (continued)

Name:

5. Consider a state with 14 representatives and a population of 9 million. Assume everyone votes along party lines and that party affiliations are 57% Democrat and 43% Republican. If districts were drawn randomly, what would be the most likely distribution of House seats? If the districts could be drawn without restriction, what would be the maximum number of Democratic representatives who could be sent to Congress?

6. Consider a state with 32 representatives and a population of 24 million. Assume everyone votes along party lines and that party affiliations are 37.5% Democrat and 62.5% Republican. If districts were drawn randomly, what would be the most likely distribution of House seats? If the districts could be drawn without restriction, what would be the minimum number of Republican representatives who could be sent to Congress?

7. The figure below shows the distribution of voters in a state with 15 House Party voters and 10 Grey Party voters and five voters per district. Draw district boundaries (for contiguous districts) so that four House Party members and one Grey Party representative are elected.

    

House Party Grey Party

Name:

Unit 12D Test 2

Date:

1. What is gerrymandering?

2. List the two requirements that must be met in drawing district boundaries.

The table below shows the election results for the House of Representatives in Arkansas.

2010 2012

Votes for Republican Candidates 435,422 647,744

Votes for Democratic Candidates 317,975 394,770

Republican Seats

Democratic Seats

3 4

1 0

Unit 12D Test 2 (continued)

Name:

5. Consider a state with 25 representatives and a population of 18 million. Assume everyone votes along party lines and that party affiliations are 40% Democrat and 60% Republican. If districts were drawn randomly, what would be the most likely distribution of House seats? If the districts could be drawn without restriction, what would be the minimum number of Republican representatives who could be sent to Congress?

6. Consider a state with 20 representatives and a population of 13.3 million. Assume everyone votes along party lines and that party affiliations are 60% Democrat and 40% Republican. If districts were drawn randomly, what would be the most likely distribution of House seats? If the districts could be drawn without restriction, what would be the maximum number of Democratic representatives who could be sent to Congress?

7. The figure below shows the distribution of voters in a state with 15 House Party voters and 10 Grey Party voters and five voters per district. Draw district boundaries (for contiguous districts) so that two House Party members and three Grey Party representatives are elected.

House Party Grey Party

Name:

Unit 12D Test 3

Date:

Choose the correct answer to each problem. 1. What is meant by redistricting for the House of Representatives? (a) The decision on how to divide the number of representatives among the 50 states. (b) The decision on how to draw the boundaries for each district within each state. (c) The time when the total number of seats for the House of Representatives is determined. (d) The time when the number of seats in the House of Representatives for each state is determined. 2. Suppose you decide the redistricting for a state that has a pretty equal number of Republicans and Democrats. If you are not concerned with ethics, how should you draw the boundaries to maximize the number of Democrats elected? (a) Draw boundaries that concentrate very large majorities of Democrats in a few districts. (b) Draw boundaries that concentrate very large majorities of Republicans in a few districts. (c) Draw boundaries that spread the Republicans out across the most districts. (d) It is not possible to determine how that can be done ahead of time. 3. The term gerrymandering originated (a) when President Gerald Ford was elected with the help of oddly shaped districts. (b) in 1812 and came from the name of a governor and the salamander shaped district he created. (c) when Representative Gerry was elected with the help of oddly shaped districts. (d) with the name of a wagon wheel—synonymous with the idea of “running” for office. The table below shows the election results for the House of Representatives in Minnesota.

2010 2012

Votes for Republican Candidates 435,422 647,744

Votes for Democratic Candidates 317,975 394,770

Republican Seats

Democratic Seats

3 4

1 0

4. Find the percentage of votes cast for Republicans and the percentage of House seats won by Republicans in 2010. Does the distribution of votes match the distribution of seats won? (a) Yes, the percentage of votes cast is very close to the number of seats won. (b) Yes, although the percentages are not close, that is due to the small number of seats available. (c) No, the percentage of votes cast imply the seats won should have been split more evenly. (d) No, the percentage of votes cast imply the number of seats won should have been reversed. 5. Find the percentage of votes cast for Republicans and the percentage of House seats won by Republicans in 2012. Does the distribution of votes match the distribution of seats won? (a) Yes, the percentage of votes cast is very close to the number of seats won. (b) Yes, although the percentages are not close, that is due to the small number of seats available. (c) No, the percentage of votes cast imply the Democrats should have won at least one seat. (d) No, the percentage of votes cast imply the number of seats won should have been reversed.

Unit 12D Test 3 (continued)

Name:

6. What do the results above say about the effects of the redistricting done in 2010? (a) Redistricting kept or increased favor for the Republicans. (b) Redistricting decidedly decreased favor for the Republicans. (c) Redistricting increased favor for the Democrats. (d) Redistricting was necessary to accommodate an additional seat. 7.

Consider a state with 25 representatives and a population of 16 million. Assume everyone votes along party lines and that party affiliations are 92% Democrat and 8% Republican. If districts were drawn randomly, what would be the most likely distribution of House seats? If the districts could be drawn without restriction, what would be the maximum and minimum number of Democratic representatives who could be sent to Congress? (a) 15 Democrats and 10 Republicans; maximum is 24; minimum is 22 (b) 24 Democrats and 1 Republican; maximum is 25; minimum is 22 (c) 23 Democrats and 2 Republicans; maximum is 24, minimum is 22 (d) 23 Democrats and 2 Republicans; maximum is 25; minimum is 22

8. Which of the following is not an idea for reforming the redistricting process? (a) Derive a mathematical algorithm to draw the boundaries without human input (b) Turn redistricting over to a nonpartisan, independent panel (c) Have each state’s legislature draw the boundaries (d) Allowing a computer to perform the process

Name:

Unit 12D Test 4

Date:

Choose the correct answer to each problem. 1. How often is the process for redistricting for the House of Representatives performed? (a) After each presidential election (b) Only when new states are added to the Union (c) Every time the party in power changes (d) Every 10 years, after the census data is computed 2. Suppose you decide the redistricting for a state that has a large number of Democrats and few Republicans. If you are not concerned with ethics, how should you draw the boundaries to maximize the number of Republicans elected? (a) Draw boundaries that concentrate very large majorities of Republicans in a few districts. (b) Draw boundaries that spread the Democrats out across the most districts, maintaining majorities. (c) Draw boundaries that spread the Republicans out across the most districts, maintaining majorities. (d) It is not possible to determine how that can be done ahead of time. The table below shows the election results for the House of Representatives in Minnesota.

2010 2012

Votes for Republican Candidates 435,422 647,744

Votes for Democratic Candidates 317,975 394,770

Republican Seats

Democratic Seats

3 4

1 0

3. Find the percentage of votes cast for Democrats and the percentage of House seats won by Democrats in 2010. Does the distribution of votes match the distribution of seats won? (a) Yes, the percentage of votes cast is very close to the number of seats won. (b) Yes, although the percentages are not close, that is due to the small number of seats available. (c) No, the percentage of votes cast imply the seats won should have been split more evenly. (d) No, the percentage of votes cast imply the number of seats won should have been reversed. 4. Find the percentage of votes cast for Democrats and the percentage of House seats won by Democrats in 2012. Does the distribution of votes match the distribution of seats won? (a) Yes, the percentage of votes cast is very close to the number of seats won. (b) Yes, although the percentages are not close, that is due to the small number of seats available. (c) No, the percentage of votes cast imply the Democrats should have won at least one seat. (d) No, the percentage of votes cast imply the number of seats won should have been reversed.

Unit 12D Test 4 (continued)

Name:

5. What do the results above say about the effects of the redistricting done in 2010? (a) Redistricting kept or increased favor for the Republicans. (b) Redistricting decidedly decreased favor for the Republicans. (c) Redistricting increased favor for the Democrats. (d) Redistricting was necessary to accommodate an additional seat. 6. Consider a state with 24 House seats and a fairly equal number of Republican and Democratic voters. Assuming everyone votes along party lines, which of the following outcomes is not possible? (a) 12 Republicans and 12 Democrats (b) 8 Republicans and 16 Democrats (c) 22 Republicans and 2 Democrats (d) 16 Republicans and 8 Democrats 7. In 2008, Republicans in New York received 31% of the statewide vote, and won 3 of New York’s 29 House seats. This implies that (a) the district boundaries fairly represent the preferences of the New York voters. (b) the district boundaries were drawn to favor Republicans. (c) the district boundaries were drawn to favor Democrats. (d) not everyone votes party lines. 8. Which of the following is not a criterion for redistricting? (a) Each district should maintain a ratio of voting parties similar to the ratio found across the state. (b) Each district must be contiguous (connected). (c) Each district should have a nearly equal population. (d) Both a and c. 9.

Consider a state with 15 representatives and a population of 9.6 million. Assume everyone votes along party lines and that party affiliations are 80% Republican and 20% Democrat. If districts were drawn randomly, what would be the most likely distribution of House seats? If the districts could be drawn without restriction, what would be the maximum and minimum number of Republican representatives who could be sent to Congress? (a) 8 Republicans and 7 Democrats; maximum is 14; minimum is 3 (b) 12 Republicans and 3 Democrats; maximum is 15; minimum is 9 (c) 11 Republicans and 4 Democrats; maximum is 14; minimum is 3 (d) 12 Republicans and 3 Democrats; maximum is 15; minimum is 10

Chapter 1 Answers Unit 1A Test 1 1. Premises and conclusion 2. Possible answer: An argument based on the idea that since a person may not be ethical or reliable, all of that person’s beliefs must be untrue. 3. Possible answer: An argument in which event “A” occurred before event “B”, therefore “A” caused “B”. 4. Possible answer: Mayor Brown opposes a tax increase to build new schools. A critic states, “Mayor Brown is not concerned with improving the quality of education for our children.” 5. Premise: The dogs are barking. Conclusion: Someone is outside. 6. Premise: People love puppies. Conclusion: There won’t be any puppies at the shelter. 7. Possible answer: This argument is based on two isolated examples 8. Possible answer: This argument asserts that what “most people do” is proof of superiority. 9. Possible answer: Appeal to Ignorance: no proof means assertion is false. 10. The need to evaluate whether a source is clear and credible on the issue and whether it has any potential bias.

5. Premise: Not many people saw the movie version of “IT” when I did. Conclusion: People around here do not like horror movies. 6. Premise: Fashion choices indicate poor judgement. Conclusion: The one who made that choice should not be mayor. 7. Pictures of puppies and kitten are there to evoke an emotional response. 8. Absence of proof means the argument is false. 9. Possible answer: Straw man: the arguments regarding academics and sports may be related, but one does not negate the other. 10. Possible answer: Find whether the information is past, present, repeating, or on-going.

Unit 1A Test 3 1. (c) 2. (a) 3. (c) 4. (b) 5. (c) 6. (c) 7. (c) 8. (c)

Unit 1A Test 2 1. Possible answer: A deceptive argument in which the conclusion is not supported by the premises. 2. Possible answer: An argument in which the premise and conclusion say essentially the same thing.

9. (d) 10. (d)

Unit 1A Test 4 1. (b) 2. (d)

3. Possible answer: An argument which asserts that no evidence automatically means not true.

3. (b)

5. (a)

Possible answer: I’ve heard 3 cases on “Judge Judy” where pit bulls attacked other dogs. Pit bulls are a violent breed.

4. (a) 6. (c) 7. (c)

Chapter 1 Answers (continued) Unit 1A Test 4 (continued) 9. (b)

p T T F F

q T F T F

p T T F

q T F T

10. (c)

Unit 1B Test 1 1. Possible answer: A complete sentence that makes a distinct assertion or denial. 2. No, it is a complete sentence but does not make an assertion. 3. Yes, Stephen saw spoilers. 4. You must study 5. p: all varieties of apples are fruit, true; q: Taylor Swift is a rap artist, false. The proposition p and q is false. 6. Exclusive; most people would not do both in one night 7.

Unit 1B Test 3 1. (c)

not p F F T T

if not p, then q T T T F

2. (c)

p T T F F

q T F T F

not p F F T T

(not p) and q F F T F

6. (b)

9. p: sparrows can swim, false; q: fish can fly, false. The proposition p or q is false.

10. (d)

Unit 1B Test 2

3. (d) 4. (d) 5. (d) 7. (d) 8. (b) 9. (c)

Unit 1B Test 4 1. (d) 2. (c)

1. Possible answer: The opposite of a proposition.

3. (d)

2. Yes, it is a complete sentence that makes an assertion.

5. (b)

4. (b)

3. No

6. (a)

4. You need to order now

7. (d)

5. p: Apple makes iPads, true; q: bananas are fruit, true. The proposition p and q is true.

8. (b)

6. Inclusive: the policy will cover both

p and (not q) F T F

10. If a lion is male, it has a mane.

q T F T F

10. If it is a Siamese, it is a cat.

not q F T F

9. p: cows have calves, true; q: chickens lay eggs, true. The proposition p or q is true.

p T T F F

p and q T F F F

9. (b) 10. (b)

Chapter 1 Answers (continued) 8. 6 of the people surveyed are left-handed girls

Unit 1C Test 1 1. {21, 23, 25, 27, 29}

2. Possible answer: A = men B = surgeons

Musicians Piano 13

Guitar 18

3. Possible answer: A = women B = kings B

10.

4. a) A = roses = subject set B = red roses = predicate set b) A

History

Science

Total

Men

Women

Total

Unit 1C Test 2 B

c) Yes 5. a) A = cows = subject set B = plants = predicate set b)

1. {Minnesota, Mississippi, Montana, Missouri, Maine, Massachusetts, Maryland, Michigan} 2. Possible answer: A = snakes B = rocks

A B

c) No 6. a) A = Labradoodles = subject set

3. Possible answer: A = celebrities B = politicians

B = dogs = predicate set b) B

4. Possible answer: a) A = fish = subject set B = things that live in water = predicate set

b) c) No

c) Yes 7. 22 of the students surveyed are righthanded and girls

Chapter 1 Answers (continued) Unit 1C Test 2 (continued)

Unit 1C Test 3 1. (a)

5. Possible answer: a) A = cheese = subject set B = things made from goat milk = predicate set

2. (a) 3. (d) 4. (d)

5. (c)

c) Yes B

6. (d) 7. (a) 8. (b) 9. (c)

6. Possible answer: a) A = salamanders = subject set B = mammals = predicate set

10. (b)

Unit 1C Test 4

1. (c)

c) No

2. (a)

3. (a) 4. (d)

7. X = athletes that play basketball and not volleyball

5. (b)

8. Y = athletes that play neither basketball nor volleyball

7. (d)

6. (c) 8. (d)

Pets

9. (a) 10. (a) Dogs 5

Cats 3

Unit 1D Test 1

1. Possible answer: An argument whose conclusion follows directly from its premises.

2. Possible answer: Makes a general conclusion from specific premises.

10. Math

History

Total

Men

Women

Total

3. Possible answer: Premise: All dogs bark. Premise: Zoe is a dog. Conclusion: Zoe barks. 4. True; true; false 5. Denying the hypothesis. Not valid. 6. If Amy studies for the test, she has a good chance of passing the course.

Chapter 1 Answers (continued) Unit 1D Test 1 (continued) 7. 8.

Girls

People who like to color

speeders X

law breakers

The argument is valid. Answer: The argument is invalid.

9. 6 × 3 = 18; 6 × 4 = 24; 6 × 5 = 30; 6 × 6 = 36; inductive.

animal X

coldblooded

10. Let a= 2, b=3, and c=4.

Answer: The argument is invalid. 9. Possible Answer: 1 + 3 = 4; 9 + 5 = 14; 7 + 3 = 10; 11 + 7 = 18; inductive.

2(3 + 4) ≠ 2 × 3 + 4 2× 7 ≠ 6 + 4 14 ≠ 10

Unit 1D Test 3 1. (a)

10. −2 − (−5) = 3

2. (b)

Unit 1D Test 2 1. Possible answer: A valid argument that has true premises. 2. Possible answer: An argument that makes a case for a specific conclusion from more general premises. 3. Possible answer: 6 + 3 = 9; 2 + 5 = 7; 8 + 7 = 15; An even number plus an odd number equals an odd number. 4. Possible answer: True; true; false.

3. (d) 4. (b) 5. (d) 6. (d) 7. (a) 8. (b) 9. (a) 10. (d)

5. Affirming the conclusion. This is an invalid argument.

Unit 1D Test 4 1. (c)

6. If Aaron goes to bed early, he should not be late for his appointment.

2. (d)

4. (a) Green

3. (c) 5. (d)

Horses

6. (b)

7. (a) 8. (b)

The argument is valid.

Chapter 1 Answers (continued) 4. This does make sense. Andy paid $27 total on-line. He would have had to pay $32 total at the gate.

Unit 1D Test 4 (continued) 10. (b)

Unit 1E Test 1 1. No, I do not have cable. 2. I want to find the best airfare to Phoenix. 3. Possible answers: My old mower takes me more time to mow than a new mower would. My old mower is costing more in maintenance and repairs than a new mower would. 4. This does make sense. Andy paid $15 for the two tickets on-line. He would have had to pay $16 at the gate for the two tickets. 5. 24 × 3 + 15 per month × 9 months = $207. 6. Possible answer: Late bills will result in bad credit. 7. Possible answer: Plan A will cost $1900 if you go and $0 if you do not. Plan B will cost $1000 if you go and $250 if you do not. If you go, Plan A costs $900 more. If you cancel, Plan B only costs $250 more. Plan B seems like the better choice.

5. The 48-load bottle is a better deal at $0.135 per load. The 64-load bottle costs $0.242 per load. 6. Possible answer: A good cardiovascular system is important to your health. 7. Possible answer: Plan A will cost $2100 if you go and $0 if you do not. Plan B will cost $1600 if you go and $250 if you do not. If you go, Plan A costs $500 more. If you cancel, Plan B only costs $250 more. Plan B seems like the better choice. 8. No, (i) unearned income was less than $950, (ii) earned income was less than $5950, and (iii) gross income was less than earned income plus $300. 9. No, (i) unearned income was less than $950, (ii) earned income was less than $5950, and (iii) gross income was less than earned income plus $300. 10. Yes, condition (ii), $7500 is greater than $5950

Unit 1E Test 3

8. Yes, under condition (iii), $3050 is more than $2700.

1. (c)

9. No, (i) unearned income was less than $950, (ii) earned income was less than $5950, and (iii) gross income was less than earned income plus $300.

3. (c)

10. Yes, under condition (ii), $7560 is more than $5950.

6. (c)

Unit 1E Test 2 1. A no vote means that you believe the state legislature should have the authority to restrict religious expression. 2. The stores at the mall should stay open later this month. 3. Possible answer: The dictator knows that an unarmed populace is easier to keep in submission.

2. (b) 4. (c) 5. (c) 7. (a) 8. (a) 9. (b) 10. (c)

Unit 1E Test 4 1. (b) 2. (d) 3. (c) 4. (c)

Chapter 1 Answers (continued) Unit 1E Test 4 (continued) 5. (d) 6. (c) 7. (c) 8. (b) 9. (b) 10. (b)

Chapter 2 Answers 2. (d)

Unit 2A Test 1 1. 400 miles per hour

3. (d)

2. 14.25 gallons

4. (b)

3. $69.83

5. (b)

4. 2184 feet3

6. (c)

5. 93.75 feet3

7. (c)

6. 16,200 seconds

8. (b)

7. 84 inches

9. (b)

8. 1215 feet2

10. (c)

9. $29.62

Unit 2B Test 1 1. 96-oz bottle = 29 cents per ounce; 28-oz bottle = 28 cents per ounce; 28-ounce bottle is the better deal

10. $65.91

Unit 2A Test 2 1. 450 miles per hour

2. 361.7 miles

2. 60 gallons

3. 2.1 quarts

3. $127.80

4. 24.6 meters per second 5. 140° F

4. $1047 3

5. 697.5 feet

6. 33.33° C

6. 9000 seconds

7. 313.15° K

7. 102 inches 8. 432 feet2 9. $9.15 10. $34.18

8. approximately 189 people per square mile 9. 5.625 cents

Unit 2B Test 2

1. (b)

1. 48-oz bottle = 15.6 cents per ounce; 10-oz bottle = 17.9 cents per ounce; 48-ounce bottle is the better deal

2. (b)

2. 381.5 miles

3. (b)

3. 18.9 liters

4. (c)

4. 35.5 miles per hour

5. (b)

5. −6.67° C

6. (c)

6. 122° F

7. (b)

7. 298.15° K

Unit 2A Test 3

8. (b) 9. (d) 10. (c)

Unit 2A Test 4 1. (c)

8. approximately 11 people per square mile 9. 19.2 cents

Chapter 2 Answers (continued) set of seven into two sets of three, and one by itself. Now weigh the two sets of three coins. If they balance, the single coin is the lightweight coin, and you are done in two weighings; otherwise, separate the lightweight triad, and weigh two of the coins. Either one of them is the lightweight coin or the one not weighed is.

Unit 2B Test 3 (continued) 3. (d) 4. (d) 5. (a) 6. (b) 7. (c)

8. Half girls and half boys

8. (b)

Unit 2C Test 2

9. (b)

1. (a)

1. Possible answers are: 2 cars and 13 light trucks; 5 cars and 11 light trucks; 8 cars and 9 light trucks; 11 cars and 7 light trucks; 14 cars and 5 light trucks; 17 cars and 3 light trucks; 20 cars and 1 light truck

2. (b)

2. Karen

3. (c)

3. 57.6 mi

4. (c)

4. 12 socks

5. (b) 6. (c)

5. The number of green marbles in the black bucket is greater.

7. (c)

6. 182.8 in.

8. (b)

7. Possible answer: Separate the coins into two sets of nine coins. Weigh the two sets. The lightweight coin is in the lighter of the two sets. Divide the light set into three set of three coins. Now weigh two of the triads of coins. Either the lightweight coin is in the lighter of the two triads, or, if the two pairs balance, it is in the third triad. Finally, weigh two of the lightweight triads to find the lightweight coin.

10. (b)

Unit 2B Test 4

9. (d) 10. (a)

Unit 2C Test 1 1. Possible answers are: 1 car and 13 light trucks; 4 cars and 11 light trucks; 7 cars and 9 light trucks; 10 cars and 7 light trucks; 13 cars and 5 light trucks; 16 cars and 3 light trucks; 19 cars and 1 light truck

8. Half girls and half boys

2. Silas

Unit 2C Test 3

3. 42 mi

1. (c)

4. 7 socks

2. (a)

5. The number of yellow marbles in the red bucket is greater.

3. (c)

6. 250.2 in. 7. Possible answer: Separate the coins into two sets of seven coins and a single coin. Weigh two of the sets. If the two sets balance, the single coin is the lightweight coin and you are done in one weighing. Otherwise, the lightweight coin is in the lighter of the two sets. Separate the lighter

4. (a) 5. (b) 6. (d) 7. (b) 8. (a)

Chapter 2 Answers (continued) Unit 2C Test 4 1. (b) 2. (b) 3. (b) 4. (d) 5. (b) 6. (d) 7. (c) 8. (b)

Chapter 3 Answers Unit 3A Test 1

9. (a)

1. 28%

10. (c)

2. Absolute change = 13,000; Relative change = 76.5% 3. Absolute change = -167 injuries Relative change = -60.5%

Unit 3A Test 4 1. (c) 2. (a) 3. (d)

4. -78.6%

4. (d)

5. 0.86

5. (b)

6. 46.4% 7. Absolute change = -0.5 percentage points Relative change = -20.8%

6. (a) 7. (a)

8. $24,990

8. (d)

9. 3

9. (c)

10. No, it is 3.02% increase.

10. (d)

Unit 3A Test 2

Unit 3B Test 1

1. 27%

1. 0.036

2. Absolute change = -$0.32; Relative change = -11.6%

2. 5.6 ×109

3. Absolute change = 47,480; Relative change = 192% 4. Relative change = 200%

3. 9.7862 ×105 4. 1.4 ×1016 5. 2 ×107

5. 1.24

6. 150 candy bars

6. 53.3% 7. Absolute change = 4.4 percentage points; Relative change = 29.5%

7. 1 to 3,168,000 8. About 4.6 days

8. $89.99

9. About 61 years

9. 700%

10. 2.0 ×109 seconds

10. No, it is 10.24%

Unit 3B Test 2

Unit 3A Test 3

1. 590,000,000

1. (b)

2. 7.8 ×10−7

2. (a)

3. 9.7 ×10−6

3. (b) 4. (c) 5. (c) 6. (c)

4. 1×1012 5. 4 ×107 6. About 1923 years

7. (d)

7. 1.05 ×105

8. (b)

Chapter 3 Answers (continued) 9. 1 to 7,603,200

7. 680.67

Unit 3B Test 2 (continued)

8. 95,100

10. 3.5 ×106 years

9. $35 10. 24

Unit 3B Test 3

Unit 3C Test 2

1. (a)

1. 3 significant digits. Precise to the nearest hundred thousandth.

2. (c) 3. (b)

2. 2 significant digits. Precise to the nearest thousand

4. (d) 5. (b)

3. Absolute error: 85 years; Relative error: 16.2%

6. (c)

4. Evelyn was more accurate, and Priscilla was more precise.

7. (c) 8. (d)

5. getting misaligned with key on one test

9. (a)

6. Absolute error: -$5.68; Relative error: -37.3%

10. (d)

Unit 3B Test 4

7. 16,730

1. (b)

8. 4105.82

2. (b)

9. $22

3. (d)

10. 39 miles

4. (b)

Unit 3C Test 3

5. (c)

1. (a)

6. (c)

2. (a)

7. (c)

3. (d)

8. (c)

4. (c)

9. (b)

5. (a)

10. (c)

6. (c)

Unit 3C Test 1

7. (c)

1. 4 significant digits. Precise to the nearest hundredth of a liter.

8. (b)

2. 3 significant digits. Precise to the nearest hundred.

10. (b)

3. Absolute error: –7 years; Relative error: –6.7%

Unit 3C Test 4 1. (d)

4. Carolyn was more accurate, and Bobby was more precise. 5. Incorrect answer on an answer key 6. Absolute error: $7.32; Relative error: 59.9%

9. (a)

2. (b) 3. (a) 4. (d) 5. (a)

Chapter 3 Answers (continued) 6. (c)

9. $40.34 10. $54,405.07

Unit 3C Test 4 (continued) 7. (b)

Unit 3D Test 3

8. (c)

1. (a)

9. (b)

2. (d)

10. (a)

3. (d)

Unit 3D Test 1

4. (c)

1. Arizona - $53,558

5. (a)

2. 126.5

6. (b)

3. $55,513.04

7. (a)

4. Alabama: 68.3; Alaska: 112.8; Arizona: 79.1; Arkansas: 65.4

8. (b)

5. monthly

10. (b)

6. 6.64%

Unit 3D Test 4

7. -0.37%

9. (d)

1. (b)

8. $1.12

2. (b)

9. $79.54

3. (c)

10. $50,349.65

4. (c)

Unit 3D Test 2

5. (a)

1. An index number provides a simple way to compare measurements made at different times or in different places.

6. (b)

2. Regular Grade Gasoline Prices

8. (d)

7. (d) 9. (a)

Date

Price

Price Index

2013

$3.505

144.3

2014

$3.358

138.2

2015

$2.429

100.0

2. About 41.5%

2016

$2.143

88.2

3. 5%; 6%

10. (b)

Unit 3E Test 1 1. About 60.8%; 31.9%

4. About 7.3%; about 6.25% 3. 99.4 4. U.S. Bureau of Labor Statistics 5. -0.37% 6. 1.27% 7. 50 cents 8. $19,808.98

5. Possible answer: Non-coffee drinkers have the higher rate of violence in both categories. This data certainly does not support the theory that coffee drinkers are more violent. On the other hand, within each category the rates of violence for coffee drinkers and non-coffee drinkers are so close that the data does not support a conclusion

Chapter 3 Answers (continued) that non-coffee drinkers are more violent either.

Unit 3E Test 1 (continued) 6. Possible answer: The group of coffee drinkers is comprised of 150 felons and 100 non-felons, while the group of non-coffee drinkers is comprised of 16 felons and 100 non-felons. The greater number of felons, among whom we would expect more violence, virtually guaranteed that the combined rate for the coffee drinkers would be higher. 7. Possible answer: Though the actual number of homicides per year may be increasing, the population of the city is increasing at a higher rate so that the percentage of the population murdered each year is down.

breast cancer, virtually guaranteed that the combined rate for the group who had abortions would be lower. 8. 9% 9. 6.8% 10. 98.1%

Unit 3E Test 3 1. (a) 2. (b) 3. (c) 4. (b) 5. (d) 6. (c)

8. About 1.3%

7. (a)

9. About 2.8%

8. (b)

10. 26%

9. (a)

Unit 3E Test 2

10. (b)

1. 62%; about 29.9%

Unit 3E Test 4

2. 38%; about 89.4%

1. (c)

3. Possible answer: Though the actual number of jobs in the city decreased, a large number of the unemployed moved away from the city to find jobs elsewhere so that the percentage of the population that is unemployed decreased.

2. (c)

4. 4%; 3%

3. (c) 4. (b) 5. (c) 6. (d) 7. (a)

5. About 98.9%; 1% 6. Possible answer: Women who have had abortions have the higher rate of breast cancer in both age groups. However, the differences are so small that it is impossible to make a conclusion about the correlation between abortion and breast cancer.

8. (b) 9. (a) 10. (c)

7. Possible answer: The 225 women who had abortions were unequally divided among the two age groups, 175 in the younger group and 50 in the older group, while the 200 women who did not have abortions were equally divided into the two age groups. Over representing abortions amongst a greater number of younger women, among whom we would expect fewer incidence of Copyright © 2023 Pearson Education, Inc. - 400 -

Chapter 4 Answers 7. (c)

Unit 4A Test 1

8. (a)

1. $936; $1800; 52% 2. $219.60

Unit 4B Test 1

3. $55.83

1. $2268

4. $1239.17

2. $6344.18

5. $1793.33

3. $1927.72

6. Allison spends 6.9% of her income on entertainment, more than the 5% average

4. $15,389.81

7. $19.26

5. 2.84% 6. $1443.86

8. $3200.00

7. 3.98%

Unit 4A Test 2

8. $5516.05

1. 40.8%

9. $13,356.77

2. $262.50

Unit 4B Test 2

3. $82.67

1. $1310.40

4. $235.50

2. $15,271.64

5. $1565

3. $3481.31

6. Tom spends 36% of his income on housing, more than the 35% average 7. $11.20 8. $4300

Unit 4A Test 3 1. (c) 2. (d) 3. (a) 4. (c) 5. (a) 6. (b) 7. (d) 8. (c)

Unit 4A Test 4 1. (d) 2. (a) 3. (b) 4. (d) 5. (a) 6. (a)

4. $6426.35 5. 1.82% 6. $4012.89 7. 7.12% 8. $5299.91 9. $2080.81

Unit 4B Test 3 1. (b) 2. (a) 3. (c) 4. (a) 5. (d) 6. (d) 7. (b) 8. (c) 9. (b)

Chapter 4 Answers (continued) Unit 4B Test 4 (continued)

6. (d)

3. (b)

7. (d)

4. (b)

8. (a)

5. (b)

9. (b)

6. (b)

Unit 4C Test 4

7. (a)

1. (a)

8. (c)

2. (d)

9. (a)

3. (b)

Unit 4C Test 1

4. (d)

1. $40,429.89

5. (d)

2. $12,981.36; $9000

6. (d)

3. $594.72

7. (b)

4. $158.50

8. (b)

5. $1651.16

9. (c)

6. Total Return = 42.86%; Annual Return = 9.33% 7. $5.75 8. 8.70%

Unit 4C Test 2

Unit 4D Test 1 1. a) $445.48; b) $53,457.60; c) 78.6%; d) 21.4% 2. monthly payment: $1222.54; total: $440,114.40

1. $320,717.92

3. monthly payment: $2263.59; total: $407,446.20

2. $153,137.01; $51,840

4. $440.90

3. $447.20

5. $366.20; $460.21; $21,381.60

4. $265.97

6. $1721.12

5. $2194.76

7. Choice 1: monthly payment = $757.15 and $1500 closing cost; Choice 2: monthly payment = $712.91 and $4260 closing cost. Answers may vary: payment $44.24 less with Choice 2, but closing costs are $2760 more. It would take 5.2 years of monthly payments to make up the closing costs.

6. Total Return = -26.67%; Annual Return = -7.46% 7. $25.50 8. Liquidity, risk, and return 9. $175

Unit 4C Test 3 1. (a) 2. (c) 3. (a) 4. (a) 5. (a)

Unit 4D Test 2 1. a) $236.55; b) $22,708.39; c) 79.3%; d) 20.7% 2. monthly payment: $850.89; total: $306,320.36 3. monthly payment: $1403.33; total: $252,599.40 4. $332.01 Copyright © 2023 Pearson Education, Inc. - 402 -

Chapter 4 Answers (continued) Unit 4D Test 2 (continued) 5. $1681.30; $1983.22; $129,295.20 6. $357.32 7.

6. FICA = $4016.25; marginal = $4595; total = $8611.25; overall tax rate = 16.4% 7. $19,200

Unit 4E Test 2

Monthly Payments

Total Payoff

$126.91

$6091.68

2. $24,211

$238.96

$25,807.68

3. $5356; 11.4%

$121.92

$10,241.28

4. They both have a final bill of -$700; Penny receives $0 as her credit was nonrefundable. Irving receives $700 refund.

8. $545.35; $39,265.20; $2875.44 less

Unit 4D Test 3

1. Gross income: $32,500; adjusted gross income: $30,900; taxable income: $18,350

5. $1356 net monthly cost to buy. Cost to rent is greater.

1. (a)

6. $3675

2. (a)

7. Decreased by $684

3. (c)

Unit 4E Test 3

4. (b)

1. (c)

5. (c)

2. (a)

6. (c)

3. (c)

7. (b)

4. (d)

Unit 4D Test 4

5. (d)

1. (d)

6. (b)

2. (c)

7. (d)

3. (c)

8. (a)

4. (a)

Unit 4E Test 4

5. (c)

1. (a)

6. (c)

2. (c)

7. (d)

3. (b)

Unit 4E Test 1

4. (b)

1. Gross income: $54,700; adjusted gross income: $51,100; taxable income: $33,100

5. (c)

2. $11,286 in itemized deductions, so should take the standard deduction which is $25,100

7. (c)

3. $6440.50 4. $29,658; 14.9% 5. $960

6. (a) 8. (b)

Chapter 4 Answers (continued) Unit 4F Test 1 (continued)

2. (b)

2. $10,900 surplus

3. (d)

3. $40,969

4. (a)

4. $1135 (thousand)

5. (a)

5. -$210 (thousand); -$983 (thousand)

6. (b)

6. Answers may vary: education, transportation, housing, defense, nondefense, etc.

7. (d)

7. 61.6%; 100.1%; 124.5%; rates rising, now over 100% 8. $765 billion

Unit 4F Test 2 1. Answers may vary: the total value of goods produced and services provided by a country in a year 2. $56,000 3. $1150 (thousand) 4. -$155 (thousand); -$928 (thousand) 5. 1. Mandatory expenses, which include interest on the debt and entitlements 2. Discretionary spending, including spending for national defense and education. 6. The government borrows money from the public by selling Treasury bills, notes, and bonds to investors. 7. $1.9 trillion more 8. collected $1.584 trillion; spent $1.196 trillion; $388 billion more received

Unit 4F Test 3 1. (c) 2. (b) 3. (d) 4. (c) 5. (a) 6. (a) 7. (a)

Chapter 5 Answers 3. (c)

Unit 5A Test 1 1. New York City residents.

4. (c)

2. The 1200 New York City residents who were surveyed.

5. (b)

3. The average number of vehicles per household in rural VA.

7. (c)

4. The average number of 2.7 vehicles per household in the sample taken from rural VA.

9. (c)

5. An observational study makes no attempt to change the behavior of the participants.

6. (d) 8. (b) 10. (b)

Unit 5A Test 4 1. (b)

6. Systematic sampling

2. (d)

7. Convenience 8. Observational study, not retrospective

3. (c)

9. Single-blind experiment; treatment group: those diners in a darkened room; control group: diners in regularly lit room

4. (c)

10. 40% to 50%

8. (b)

1. All dentists.

9. (a)

2. The 164 dentists surveyed. 3. The average number of pets per household in Alaska. 4. The average of 1.2 pets per household in the Alaskan households surveyed. 5. Bias favors one outcome over another. Bias can come from poor sampling methods or poor design in the study. 6. Simple Random Sample 7. Stratified sampling 8. Experiment; treatment group: football players who take ballet classes; control group; football players without ballet classes. 9. Observational retrospective; Cases: infants in the back seat; Controls: infants in the front seat.

Unit 5A Test 3 1. (c)

6. (a) 7. (d)

Unit 5A Test 2

10. 62% to 68%

5. (b)

10. (c)

Unit 5B Test 1 1. Answers may vary: Participation bias occurs when participation in a study is voluntary because people who feel strongly are more likely to volunteer. 2. Answers may vary: The study may be biased in favor of those who are carrying it out. 3. Answers may vary: A survey question that asks whether your favorite cola is Coke or Pepsi has an availability error because someone may have answered Shasta if given an open ended question. Additionally, if Coke is mentioned first, then the answer “Coke” may be favored. 4. Answers may vary: A magazine calling all of its subscribers to ask if they are satisfied with their articles has a selection bias because subscribers are more likely to be satisfied with the content of the magazine. 5. Answers may vary: Since the Dairy Council paid for the study, the scientists might be

Chapter 5 Answers (continued) team than it would be to measure which member of the team is the best looking.

Unit 5B Test 1 (continued) more likely to find results in favor of consuming dairy. 6. Answers may vary: The variables of interest are not well-defined. What does “twice as violent” mean? How did the researchers define “behavior problem”? 7. Possible sample: A phone poll of registered voters throughout the state. 8. Answers may vary: It can be difficult to define a quantity of interest when it is a part of the population that is difficult to reach. For example, it would be difficult to estimate how many people were not counted in the last census.

Unit 5B Test 3 1. (c) 2. (a) 3. (c) 4. (d) 5. (a) 6. (b) 7. (d) 8. (c) 9. (d)

Unit 5B Test 4

Unit 5B Test 2 1. Answers may vary: Selection bias occurs when researchers select a sample that is unlikely to represent the population. 2. Answers may vary: Availability error is the tendency to make judgments based on what is available in the mind. This can depend on what choices are mentioned or the order that choices are mentioned. 3. Answers may vary: A comment box in a grocery store has a participation bias, because people with negative comments tend to participate more than those with positive comments. 4. Answers may vary: A political party would be an inappropriate source for an election poll.

1. (c) 2. (c) 3. (a) 4. (c) 5. (b) 6. (d) 7. (d) 8. (a) 9. (b)

Unit 5C Test 1 1. Qualitative 2.

Grade

Frequency

5. Answers may vary: The wording of the question is confusing, therefore the results of the study may not reflect the true opinions of the students.

6. Answers may vary: The study compared two sugary foods. Either of the sugary foods could have caused the acne or possibly there is another source.

7. Possible sample: A telephone survey. Call a sample of county residents from a list of those who filed tax returns last year.

3. 20%; 32%; 28%; 12%; 8%

8. Answers may vary: A variable of interest can be difficult to measure if it is not countable. For example, it is easier to measure the average height of a basketball Copyright © 2023 Pearson Education, Inc. - 406 -

Chapter 5 Answers (continued) 10.

Unit 5C Test 1 (continued) 4.

Number of Students

Math Test

4/5

4/15

4/25

5/5

Price

$4.50

$5.00

$3.00

$3.50

Value

$225

$250

$150

$175

Unit 5C Test 2

1. Qualitative 2.

0 A

Grade

Frequency

Grades

5. Quantitative 6. Grade

Frequency

30 – 39

40 – 49

50 – 59

60 – 69

70 – 79

80 – 89

90 – 99

3. 24%; 20%; 20%; 16%; 20%. 4.

Number of Students

Math Test

8 6 4 2 0 A

Grades

Frequency

Quiz Grades 10 5 0

5. Quantitative 6.

Grade

Frequency

30 – 39

40 – 49

50 – 59

8. 9.1%; 4.5%; 4.5%; 9.1%; 18.2%; 27.3%; 27.3%

60 – 69

70 – 79

9. 2; 3; 4; 6; 10; 16; 22

80 – 89

90 – 99

30 - 40 - 50 - 60 - 70 - 80 - 90 39 49 59 69 79 89 99 Quiz Score

Chapter 5 Answers (continued) Unit 5C Test 2 (continued)

7. (a)

8. (b)

Unit 5D Test 1

Frequency

Quiz Grades

1. 39.0% 2. 25.5%

3. Finland, Hong Kong

4. 11.1%; while the percent difference is 11% the difference on graph appears to be double

0 30 - 40 - 50 - 60 - 70 - 80 - 90 39 49 59 69 79 89 99 Quiz Scores

8. 9.1%; 4.5%; 9.1%; 9.1%; 22.7%; 18.2%; 27.3% 9. 2; 3; 5; 7; 12; 16; 22 10. 6/5

6/15

6/25

7/5

Price

$7.50

$8.00

$6.50

Value

$300

$320

$260

5. Answers may vary: Lines closer together define terrain that is steeper than the terrain defined by lines further apart. 6. Answers may vary: An exponential scale is used to display data that is growing or shrinking very rapidly, such as bacteria growth. 7. Answers may vary: I might start the vertical scale at a higher number than 0 so that it appears more dramatic. I could also minimize the sizes of the horizontal scales to make the increases or decreases seem more dramatic.

Unit 5D Test 2 1. 42.0%

Unit 5C Test 3

2. 20.5%

1. (d)

3. Japan

2. (d)

4. 7.6%; while the percent difference is 7.6% the difference on graph appears to be triple

3. (c) 4. (d) 5. (a) 6. (d) 7. (d) 8. (d)

Unit 5C Test 4 1. (c) 2. (c) 3. (d) 4. (c) 5. (b)

5. Answers may vary: On a contour map, quantities are represented by curves. A quantity represented by a curve has the same value along the entire curve. On a geographical map, the boundaries of the map are used and the measurements within the boundaries are computed. 6. Answers may vary: A three-dimensional graph requires three axes to display three related quantities for each data point. A common misuse is to display twodimensional data on three-dimensional axes. 7. Answers may vary: Infographics present multiple interrelated sets of information and data, often combining words, data and graphs

Chapter 5 Answers (continued) Unit 5D Test 2 (continued)

18-Nov-17 Diesel Prices

8. Answers may vary: Negative fluctuations in a relative frequency graph indicate increases that are not as large as previous increases. 9. Answers may vary: I could manipulate the scale of the vertical axis. The larger the scale, the more differences would be minimized.

4 3.9 3.8 3.7 2.8

Unit 5D Test 3

3.2

3.4

3.6

Gasoline Prices

1. (b) 2. (a)

8. Strong, positive linear correlation

3. (d)

9. The result of some common underlying cause, most likely the cost of oil.

4. (c)

Unit 5E Test 2

5. (d) 6. (b)

1. Strong positive linear correlation

7. (b)

2. Common underlying cause

Unit 5D Test 4

3. Positive correlation; Answers may vary: since pay equals hours times the hourly wage, pay would go up as the number of hours worked goes up.

1. (b) 2. (d)

4. No correlation; Answers may vary: a high concentration of those with a Ph.D might be found in a university town surrounded by many cows or a university and high tech area with not a single cow in the county.

3. (b) 4. (d) 5. (d) 6. (b)

5. Direct Cause

7. (a)

6. Coincidence

Unit 5E Test 1 1. Strong negative linear correlation

Students

2. Direct cause

4. Positive correlation; Answers may vary: as the size of a development increases so would the amount of mowing, edging, and trimming that needs to be done. 5. Common underlying cause 6. Direct Cause 7.

GPA

3. Negative correlation; Answers may vary: those who have spent more time spent in jail will most likely have a lower level of education

4 2 0 60

Height 8. Strong positive linear correlation 9. Coincidence

Chapter 5 Answers (continued) Unit 5E Test 3 1. (b) 2. (b) 3. (d) 4. (c) 5. (c) 6. (d) 7. (a) 8. (d) 9. (a)

Unit 5E Test 4 1. (d) 2. (c) 3. (b) 4. (b) 5. (b) 6. (b) 7. (b) 8. (b) 9. (c)

Chapter 6 Answers any less than that, and many ages greater but with lessening frequencies.

Unit 6A Test 1 1. 10.2

7. Mean = C, median = B, mode = A

2. 8 3. 8 4. Answers may vary: If there are outliers present, the median is a better measure of center than the mean. 5. Answers may vary: An outlier is a data item that is much larger or much smaller than the majority of the data. 6. Right skewed; Answers may vary: most ages would be between 18 and 25, with few if any less than that, and many ages greater but with lessening frequencies. 7. Mean = B, median = B, mode = B 8. Answers may vary: The student is finding the mean class size of only two classes, one lecture of 100 students and one lab of 20 students, while the chairperson is finding the mean class size of 18 classes, 3 lectures and 15 labs. The greater number of labs with smaller enrollment in the chairperson’s calculation produces a smaller mean. 9. Answers may vary: Since the mean price is greater than the median price, the distribution is likely to be right-skewed. There may also be outliers, such as a home price of $1,000,000, that would drastically increase the mean price but have little effect on the median price. 10. Two peaks; Answers may vary: males and females would likely have different most common weights.

8. Answers may vary: The owner is using the median salary as the average, while the employee is using the mean salary as the average. 9. Answers may vary: Since the mean score is less than the median score, the distribution is likely to be left-skewed. There may also be outliers, such as a score of 0, that would drastically reduce the mean score but have little effect on the median score. 10. No peaks; Answers may vary: A fair die should not have any one roll or group of rolls that out-number the rest significantly. Every roll should occur approximately the same number of times.

Unit 6A Test 3 1. (c) 2. (c) 3. (a) 4. (a) 5. (c) 6. (d) 7. (c) 8. (a) 9. (b) 10. (b)

Unit 6A Test 4

Unit 6A Test 2

1. (c)

1. 73.3

2. (d)

2. 14

3. (a)

3. 1

4. (a)

4. Answers may vary: A distribution of standardized test scores can be expected to be symmetric.

5. (c) 6. (d)

5. Answers may vary: A uniform distribution has no peaks.

7. (c)

6. Right skewed; Answers may vary: most ages would be between 18 and 25, with few if

9. (a)

8. (b) 10. (d)

Chapter 6 Answers (continued) 3.

Unit 6B Test 1 1. Men: mean = 1136.7, median = 1111.5; Women: mean = 1165.3, median = 1218.5 2. Men: 923, 1040, 1111.5, 1290, 1328; Women: 841, 1053, 1218.5, 1300, 1393 3.

4. Women had the highest median. Men performed more consistently. 5. Men: range = 17, standard deviation = 5.8; Women: range = 23, standard deviation = 8.0

4. Women had the highest median. Men performed more consistently. 5. Men: range = 405, standard deviation = 133.8; Women: range = 552, standard deviation = 166.1 6. Men: 101.25; Women: 138; Answers may vary: Neither was that close to the actual values. The estimate for the men was closer. The women had scores that were much more spread out than the men’s scores. 7. Answers may vary: The median score for the women was greater than the median score for the men, but the women’s scored varied much more than the men.

Unit 6B Test 2 1. Men: mean = 24.9, median = 24; Women: mean = 25.8, median = 26 2. Men: 17, 20, 24, 30, 34; Women: 12, 22, 26, 33, 35

6. Men: 4.25; Women: 5.75; Answers may vary: Neither was that close to the actual values. The estimate for the men was closer. The women had scores that were much more spread out than the men’s scores. 7. Answers may vary: The median score for the women was greater than the median score for the men, but the women’s scored varied much more than the men.

Unit 6B Test 3 1. (d) 2. (c) 3. (c) 4. (a) 5. (c) 6. (c) 7. (b) 8. (a)

Unit 6B Test 4 1. (c) 2. (b) 3. (d) 4. (b) 5. (b) 6. (a) 7. (c)

Chapter 6 Answers (continued) 10. (b)

Unit 6B Test 4 (continued) 8. (b)

Unit 6C Test 4

Unit 6C Test 1

1. (b)

1. 95%

2. (b)

2. 50%

3. (c)

3. 68%

4. (b)

4. 2.5%

5. (a)

5. 1.75

6. (a)

6. 1.5; 93rd percentile (93.32)

7. (b)

7. 0.4; 65th percentile (65.54)

8. (d)

8. 0.8 below

9. (a)

9. 2nd percentile (2.28)

10. (c)

10. 79% of those who took the same test scored lower than Bob.

Unit 6C Test 2 1. 68%

Unit 6D Test 1 1. Answers may vary: The probability of an observed difference occurring by chance is 1% or less.

3. 95%

2. Answers may vary: A sampling distribution is a distribution consisting of proportions from many individual samples.

4. 2.5%

3. 0.02

5. 0.6

4. 3.7% to 14.3%

6. -0.4; 34th percentile (34.46)

5. Answers may vary: No, the difference is likely due to chance.

2. 97.5%

7. -0.7; 24th percentile (24.20) 8. 0.5 above 9. –1; 15th percentile (15.87) 10. 34% of the students who took the test received scores lower than Carol’s score.

Unit 6C Test 3 1. (a) 2. (b) 3. (c) 4. (a) 5. (d) 6. (c) 7. (c) 8. (b) 9. (a)

6. Answers may vary: Null hypothesis: 30% of the customers are university students. Alternate hypothesis: The percentage of University customers at the restaurant is not 30%. 7. Answers may vary: If the null hypothesis is true, 30% of the customers at the restaurant come from the university. 8. Answers may vary: If the null hypothesis is not true, then the alternate hypothesis is true and the percentage of restaurant customers from the university is not 30. 9. Answers may vary: Null hypothesis: The average number of student absences for the local school system is 5.6. Alternate hypothesis: The average number of student absences is less than 5.6. 10. The sample provides evidence to reject the null hypothesis.

Chapter 6 Answers (continued) 2. (b)

Unit 6D Test 2 1. Answers may vary: The probability of an observed difference occurring by chance is 5% or less. 2. The population proportion 3. Answers may vary: 0.38, or the true population proportion

3. (a) 4. (a) 5. (c) 6. (d) 7. (a)

4. 0.0158

8. (b)

5. Answers may vary: You are 95% confident that the true population parameter lies within the interval.

9. (a) 10. (a)

6. 0.022 7. Answers may vary: Null hypothesis: The number of manatee deaths has remained the same. Alternative hypothesis: The number of manatee deaths has been reduced. 8. Answers may vary: Either is it shown that the manatee deaths have been reduced by the campaign, or the study will fail to show any change in the number of manatee deaths. 9. Answers may vary: Null hypothesis: The average number of student absences for the local school system is 5.6. Alternate hypothesis: The average number of student absences is less than 5.6. 10. The sample does not provide evidence to reject the null hypothesis.

Unit 6D Test 3 1. (c) 2. (c) 3. (b) 4. (b) 5. (c) 6. (a) 7. (b) 8. (b) 9. (a) 10. (d)

Chapter 7 Answers Unit 7A Test 1

1. 4080 2. Answers may vary: probability quoted from experience or intuition 3. 1 or 0.5 2

11 or 0.917 12

9. odds for: 1 to 3; odds against: 3 to 1 10. odds for: 2 to 7; odds against 7 to 2

Unit 7A Test 3 1. (b)

4. 1 or 0.0769 13

2. (c)

5. 1 or 0.5; assumption: boy and girl are 2 equally likely outcomes

3. (b) 4. (b) 5. (a)

6. 27 or 0.771 35

6. (b)

1 or 0.00274 7. 365

8. (b)

7. (a) 9. (b)

10 8. or 0.769 13

10. (b)

9. odds for: 1 to 35; odds against: 35 to 1 10. odds for: 1 to 12; odds against: 12 to 1

3. (b)

1. 1716 2. Answers may vary: Repeat a process a number of times, recording the observations. Compute the probability of some event A by dividing the number of times A occurs by the total number of observations. 3

5. (a) 6. (b) 7. (a) 9. (d)

1 or 0.0769 13

10. (b)

7 or 0.583; assumption: rain and not rain 12 events will remain consistently proportional

6. Theoretical 7. Number of Tails 0 1 2 3

4. (b)

8. (c)

3. 1 or 0.333

1. (b) 2. (a)

Unit 7A Test 2

Unit 7A Test 4

Probability 0.125 0.375 0.375 0.125

Unit 7B Test 1 1. Answers may vary: The probability of one event occurring is influenced by the probability of another event occurring. 2. Answers may vary: Choosing a king from a standard deck and choosing a queen. 3.

1 ; these are independent events 16

4. 0.00035; these are independent events 5. 0.375; these are dependent events

Chapter 7 Answers (continued) 7. (b)

Unit 7B Test 1 (continued) 6. 1 or 0.5; these are non-overlapping events 2

8. (c)

2 or 0.154; these are non-overlapping 13 events

10. (d)

4 or 0.308; these are overlapping events 13

9. (d)

Unit 7B Test 4 1. (a) 2. (d)

9. 0.306

3. (a)

10. 0.096

4. (b)

Unit 7B Test 2

5. (c)

1. Answers may vary: drawing a king from a standard deck and drawing a queen without replacing the first card. 2. Answers may vary: events that cannot occur at the same time 3.

1 or 0.083; these events are independent 12

1 4. or 0.00592; these events are 169 independent 5. 0.0637; these events are dependent 6. 7.

4 or 0.308; these are overlapping events 13 2 or 0.154; these are non-overlapping 13 events

77 8. or 0.95 81 9. 0.912 10. 0.251

Unit 7B Test 3 1. (b) 2. (d) 3. (c) 4. (a) 5. (a) 6. (b)

6. (c) 7. (b) 8. (c) 9. (c) 10. (c)

Unit 7C Test 1 1. $64,000 2. 18 3. innocent: 5175; minor: 180; serious: 45 4. Answers may vary: the idea that an event is more or less likely because of previous outcomes. 5. $32,100 6. $598,400 7. 21.3 minutes 8. $5.20 per warranty sold 9. 8 cents per dollar 10. about 7.69 cents per dollar

Unit 7C Test 2 1. 20,010 2. 50 3. not repay: 5700; with difficulty: 9500; without incident: 22,800 4. The gambler’s fallacy. 5. $3640 6. $2,088,000

Chapter 7 Answers (continued) answers may vary: the number of fatalities per billion miles has decreased dramatically until the number reached zero.

Unit 7C Test 2 (continued) 7. 260 years 8. $105,000

3. 0.000419

9. 4 cents per dollar

4. about 1.69 times

10. about 3.70 cents per dollar

5. about 1365

Unit 7C Test 3

6. 3.47 per 100,000; 0.0000347

1. (c)

7. 0.0000609

2. (b)

8. 0.0000975

3. (a)

Unit 7D Test 2

4. (c)

1. 2000: 6.90 accidents per billion miles; 2005: 4.36 accidents per billion miles; 2010: 3.84 accidents per billion miles; 2015: 3.55 accidents per billion miles; answers may vary: the number of accidents per billion miles has decreased every period

5. (c) 6. (d) 7. (c) 8. (b)

2. 2000: 5.33 fatalities per million hours; 2005: 1.18 fatalities per million hours; 2010: 0 fatalities per million hours; 2015: 0 fatalities per million hours; answers may vary: the number of fatalities per million miles decreased dramatically until the number reached zero.

9. (b) 10. (c)

Unit 7C Test 4 1. (a) 2. (b)

3. 0.000453

3. (b)

4. about 4.62 times

4. (d)

5. about 35

5. (a)

6. 0.189 per 100,000; about 0.00000189

6. (b)

7. 0.0000347

7. (d)

8. 0.0000975

8. (c)

Unit 7D Test 3

9. (c)

1. (d)

10. (d)

2. (c)

Unit 7D Test 1

3. (a)

1. 2000: 2.93 accidents per million hours; 2005: 1.82 accidents per million hours; 2010: 1.63 accidents per million hours; 2015: 1.55 accidents per million hours; answers may vary: the number of accidents per million miles has decreased every period 2. 2000: 12.5 fatalities per billion miles; 2005: 2.82 fatalities per billion miles; 2010: 0 fatalities per billion miles; 2015: 0 fatalities per billion miles;

4. (c) 5. (b) 6. (d) 7. (c) 8. (c)

Unit 7D Test 4 1. (c)

Chapter 7 Answers (continued) Unit 7D Test 4 (continued)

5. (b)

2. (b)

6. (a)

3. (a)

7. (c)

4. (b)

8. (c)

5. (d)

9. (d)

6. (a)

10. (a)

7. (b)

Unit 7E Test 4

8. (d)

1. (b)

Unit 7E Test 1

2. (c)

1. 32,760

3. (c)

2. 3360

4. (a)

3. 1056

5. (b)

4. 468,000

6. (b)

5. 1,757,600,000

7. (c)

6. 24

8. (b)

7. 4845

9. (a)

8. 311,875,200

10. (a)

9. 56 10. 495

Unit 7E Test 2 1. 13,366,080 2. 21 3. 168 4. 78,624,000 5. 1,188,137,600 6. 5,200,300 7. 2730 8. 6,497,400 9. 455 10. 7315

Unit 7E Test 3 1. (b) 2. (a) 3. (b) 4. (c)

Chapter 8 Answers Unit 8A Test 1

Unit 8A Test 4

1. Linear; there is an absolute rate of change

1. (a)

2. Exponential; there is a relative rate of change

2. (b)

3. $106.29

4. (b)

4. 6000

5. (b)

5. $9758.28

6. (d)

6. 906

7. (b)

7. 262,143; about 37.45pounds 8. $10,485.76 9. 2

10. (a)

10. 2,368,000 people

Unit 8B Test 1

Unit 8A Test 2

1. 16

1. Exponential; there is a relative rate of change 2. Linear; there is an absolute rate of change 3. $120.31

3. $15,119.05 4. 219,226 6. 366

5. $958.30

7. 75.8 milligrams

6. 685 7. 65,535; about 9.36 pounds

10. 768,000

2. 174 years

5. $45.76

4. 4500

1 9. 64

8. (d) 9. (c)

8. $2621.44

3. (d)

8. 173.7 9. 57 10. 48; answers may vary: estimate is within 20% of the exact answer

Unit 8B Test 2 1. 64

Unit 8A Test 3

2. 75 years

1. (c)

3. $29,627.99

2. (d)

4. 645,080

3. (b)

5. $1884.26

4. (a)

6. 547

5. (d)

7. 189.5 milligrams

6. (b)

8. 206.7

7. (a)

9. 38,954,449

8. (d)

10. 11,208,188; answers may vary: estimate is over 3 times the actual answer

9. (b) 10. (c)

Chapter 8 Answers (continued) Unit 8B Test 3

Unit 8C Test 2

1. (b)

1. Answers may vary: A model of population growth based on the assumption that the rate of growth is nearly exponential when the population is small, then decreases smoothly, and becomes zero when the carrying capacity is reached.

2. (c) 3. (a) 4. (d) 5. (c)

2. 54; 12.9 billion

6. (c)

3. The birth rate has been decreasing.

7. (b)

4. The death rate was decreasing, then steady

8. (b)

5. 0.38%; 0.38%; 0.21%

9. (a)

1. (c)

6. Answers may vary: The population is likely to level off. This prediction may not be reliable because influence of pandemic is uncertain and because the effects of immigration have not been considered.

2. (c)

7. 4.23%; 3.08%

10. (b)

Unit 8B Test 4

3. (b)

Unit 8C Test 3

4. (b)

1. (c)

5. (c)

2. (b)

6. (c)

3. (b)

7. (a)

4. (c)

8. (a)

5. (b)

9. (a)

6. (b)

10. (d)

7. (a)

Unit 8C Test 1

Unit 8C Test 4

1. Answers may vary: The number of people (or other organisms) that an environment can support over a long period of time. 2. 78 years; 11.0 billion 3. The birth rate is decreasing. 4. The death rate is increasing. 5. 0.69%; -0.02%; -0.39% 6. Answers may vary: The population is decreasing. This prediction may not be reliable because influence of pandemic is uncertain and because the effects of immigration have not been considered. 7. 2.45%; 1.64%

1. (b) 2. (c) 3. (b) 4. (d) 5. (b) 6. (c) 7. (d)

Unit 8D Test 1 1. 7.9 ×1011 joules 2. 103 3. softest audible sound 4. 41.8 dB

Chapter 8 Answers (continued) Unit 8D Test 1 (continued)

5. (c)

5. 100,000 times

6. (d)

6. 16

7. (b)

7. 3.16 meters

8. (a)

8. Any kind of citrus juice

9. (c)

9. 10-5.5 mole per liter

10. (c)

10. 11

Unit 8D Test 2 1. 2.5 ×1013 joules 2. 103 3. inaudible sound 4. 33.8 dB 5. 100,000 times more intense 6. 100 7. 10 meters closer, or 20 meters away from the siren. 8. Answers may vary: baking soda, ammonia, antacid tablets. 9. 10-8.7 mole per liter 10. 2

Unit 8D Test 3 1. (c) 2. (a) 3. (b) 4. (c) 5. (b) 6. (b) 7. (a) 8. (a) 9. (c) 10. (a)

Unit 8D Test 4 1. (d) 2. (a) 3. (d) 4. (c)

Chapter 9 Answers 3. (c)

Unit 9A Test 1 1. Data table, graph, and equation

4. (c)

2. Altitude and time

5. (b)

3. (time in seconds, altitude in feet)

6. (b)

4. 10 meters

7. (c)

5. (Depth, Atmospheres)

8. (a)

6. Domain: 0 – 91; Range: 1 – 10

Unit 9B Test 1

7. (year, price in cents)

1. 3 ppm

8. Domain: 2001 – 2013; Range: 34 cents – 46 cents

2. −

Unit 9A Test 2

1 ppm per day 3

3. 6 ppm

1. Answers may vary: A mathematical model represents something real and helps us understand that real thing.

4. 2 ppm 5. c = 6 –

2. Temperature and time

1 t 3

3. One possible answer is: (time in seconds, temperature in Fahrenheit)

6. 1 ppm

4. $4317

8. V = 2350 – 425t; $862.50

5. (cost of car, repair cost)

9. V = 10,200 – 712.5t; $5925

6. Domain: $8164 - $18,910; Range: $2114 - $4327

10. C = 3200 + 400t; $5200

7. (maintenance cost, repair cost) 8. Domain: $2525 – $2800; Range: $550 – $700

Unit 9A Test 3 1. (c) 2. (c) 3. (b) 4. (b) 5. (d) 6. (c) 7. (a) 8. (b)

Unit 9A Test 4 1. (a) 2. (b)

7. E = 135 + 26t; 213

Unit 9B Test 2 1. 4.5 ppm 2.

1 ppm per day 6

3. 3 ppm 4. 1 ppm 5. c = 3 +

1 t 6

6. 6 ppm 7. C = 3.17 + 2.7(m – 0.1); $47.45 8. W = 162 – 0.8t; 145.2 pounds 9. V = 12,200 – 675t; $8150 10. C = 4100 + 300t; $5900

Unit 9B Test 3 1. (b) 2. (c) 3. (a)

Chapter 9 Answers (continued) 3.

Unit 9B Test 3 (continued)

Price (in thousands of $)

4. (b) 5. (a) 6. (c) 7. (d) 8. (c) 9. (d)

100 80 60 40 20 0 0

10. (b)

Year

Unit 9B Test 4 1. (b) 3. (a)

4. Q = 52(1.09)t, where Q is the enrollment (in hundreds of students) and t is the number of years after 2015.

4. (d)

2. (b)

5. (c)

Year

6. (a)

0 1 2 3 4 5 6 7 8 9 10

7. (d) 8. (b) 9. (b) 10. (a)

Unit 9C Test 1 1. Q = 86(0.96)t, where Q is the average home price (in thousands of dollars) and t is the number of years after 2015. 2.

Enrollment (in hundreds of students) 52 56.7 61.8 67.3 73.4 80.0 87.2 95.1 103.6 112.9 123.1

0 1 2 3 4 5 6 7 8 9 10

Price (in thousands of $) 86 82.6 79.3 76.1 73.0 70.1 67.3 64.6 62 59.6 57.2

Enrollment (in hundreds of students)

Year

150 100 50 0 0

Year

7. 4.3% 8. 7.2 hours 9. 27 years

Chapter 9 Answers (continued) Unit 9C Test 2 6. Enrollment (in hundreds of students)

1. Q = 74(0.92)t, where Q is the average home price (in thousands of dollars) and t is the number of years after 2016. 2.

Price (in thousands of $) 74 68.1 62.6 57.6 53.0 48.8 44.9 41.3 38.0 34.9 32.1

Year 0 1 2 3 4 5 6 7 8 9 10

120 100 80 60 40 20 0 0

7. 6.2% 8. 16.6 hours 9. 51 years

Unit 9C Test 3 Price (in thousands of $)

1. (c) 80

2. (b)

3. (d)

4. (b)

5. (c)

0 5

Year

6. (b) 7. (b) 8. (a) 9. (a)

4. Q = 58(1.07) , where Q is the enrollment (in hundreds of students) and t is the number of years after 2015.

10. (b)

Unit 9C Test 4 1. (b)

Year 0 1 2 3 4 5 6 7 8 9 10

Enrollment (in hundreds of students) 58 62.1 66.4 71.1 76.0 81.3 87.0 93.1 99.7 106.6 114.1

Year

2. (d) 3. (c) 4. (b) 5. (b) 6. (d) 7. (b) 8. (b) 9. (d) 10. (d)

Chapter 10 Answers 3. (a)

Unit 10A Test 1 1. Perimeter = 360 yards; Area = 8100 yards

4. (d)

2. Perimeter = 26 feet; Area = 42 feet2

5. (a)

3. Perimeter = 30 inches; Area = 30 inches2

6. (d)

4. Perimeter = 26 cm; Area = 38.5 cm

7. (a)

5. 9600 m2

8. (c)

Unit 10B Test 1

6. 321.6 inches3 7. Volume = 942.5 m3; Surface area = 377 m2

1. 163° 10′ 48′′

8. 3000 yards3; 1420 yards2

2. 9.465°

9. 50 times

3. 3.82°

10. 2500 times

4. road = 0.12; sidewalk = 0.167; sidewalk steeper

Unit 10A Test 2 1. Perimeter = 240 yards; Area = 3600 yards2

5. 0.75; 15 feet

2. 158 m2

6. 7.2 miles

3. Perimeter = 240 mm; Area = 1596 mm2

7. 2.1 acres

4. 3500 m2

8. x = 3; y = 5.3

5. Volume = 523.6 inches3; Surface area = 314.2 inches2

9. 27 feet; yes

6. 21,237 feet3 7. 64 inches3; 96 inches2

10. square = 2025 m2; circular = 2578.7 m2; more area in circular enclosure

Unit 10B Test 2

8. 40 times

1. 142° 31′ 12′′

9. 1600 times

2. 12.115°

10. 64,000 times

3. 3.44°

Unit 10A Test 3 1. (a)

4. road = 0.07; sidewalk = 0.125; sidewalk steeper

2. (a)

5. 0.67; 12 feet

3. (c)

6. 8.6 miles

4. (b)

7. 0.61 acres

5. (c)

8. x = 1.5; y = 2.7

6. (b)

9. 26.4 feet; yes

7. (c)

10. square = 900 m2; circular = 1145.9 m2; more area in circular enclosure

8. (d)

Unit 10A Test 4 1. (b) 2. (a)

Unit 10B Test 3 1. (c) 2. (d) 3. (a)

Chapter 10 Answers (continued) 5. (c)

3. Answers may vary: The object has properties like area (two dimensions) and other properties that are more like volume (three dimensions).

6. (c)

4. Answers may vary:

Unit 10B Test 3 (continued) 4. (a)

7. (b) 8. (d) 9. (b)

5. 1.893; fractal

Unit 10B Test 4

6. 3; ordinary

1. (c)

Unit 10C Test 3

2. (a)

1. (a)

3. (a)

2. (a)

4. (b)

3. (b)

5. (c)

4. (c)

6. (c)

5. (a)

7. (c)

6. (c)

8. (a)

7. (c)

Unit 10C Test 1 1. Answers may vary: Coastline, leaves, etc. 2. Answers may vary: The countries can use two different ruler lengths to measure. 3. Answers may vary: An island can be surrounded by an imaginary rectangle, and the area of the rectangle is larger than the area of the island—this can be an upper limit to the area of the island. As we use smaller units to measure the island’s coastline, we will continue to find a larger coastline.

Unit 10C Test 4 1. (b) 2. (a) 3. (a) 4. (b) 5. (a) 6. (b) 7. (b)

4. Answers may vary: The object has a property like length (one dimension) and another property that is more like area (two dimensions). 5. 3; ordinary 6. 3.321; fractal

Unit 10C Test 2 1. Answers may vary: Iteration is repeating a rule over and over. 2. Answers may vary: A fractal is self-similar if it looks similar to itself when examined at different scales.

Chapter 11 Answers Unit 11A Test 1

Unit 11B Test 1

1. Answers may vary: Sound is produced by any vibrating object. 2. Answers may vary: The rate at which the string moves up and down. 3. Answers may vary: The ratios of frequencies in a 12-tone scale are not exactly ratios of whole numbers. 4. The frequency is multiplied by eight.

1. Possible answers: F, G, J, K, P, Q, R 2. Perspective, symmetry, and proportion. 3. Answers may vary: faces, bodies, open books, etc. 4. Answers may vary: Aperiodic tiling does not have a pattern that is repeated throughout the tiling. 5. Possible drawing

5. 195 cps

•

6. 378 cps

Unit 11A Test 2 1. Answers may vary: It is the lowest possible frequency for a particular string. 2. Answers may vary: The higher the frequency, the higher the pitch. 3. Answers may vary: Harmonics have frequencies that are integer multiples of the fundamental frequency

6. Possible answer; no

4. The frequency is multiplied by four. 5. 300 cps 6. 491 cps

Unit 11A Test 3 1. (a) 2. (d) 3. (c)

7. 4; 4

4. (b)

8. Answers may vary: Tiling with other regular polygons leave gaps between the polygons.

5. (d)

9. Possible answer:

6. (b) 7. (b)

Unit 11A Test 4

10. Possible answer:

1. (a) 2. (c) 3. (c)

Unit 11B Test 2

4. (b)

1. Possible answers: A, H, I, M, O, T, U, V, W, X, Y

5. (d)

2. Possible answers: B, C, D, E, H, I, K, O, X

6. (c)

3. Possible answers:

Chapter 11 Answers (continued) 7. (b)

Unit 11B Test 2 (continued)

8. (a)

4. Answers may vary: Copies of the same shape are placed on a surface so that they cover the surface with no gaps or overlaps.

Unit 11B Test 4

5. Answers may vary: To translate an object means to move it in one direction, without rotating it.

2. (c)

6. Answers may vary: A property of an object that remains unchanged under certain operations.

1. (b) 3. (c) 4. (a) 5. (b) 6. (d)

7. Possible answer:

•

7. (a) 8. (c) 9. (c)

Unit 11C Test 1

8. Possible answer; no

1. Answers may vary: Describe how a line segment can be divided into two pieces with the most visual appeal. 2. 38.8 cm 3. 15.7 m 4. No. The only way a rectangle can be a golden rectangle is if the ratio of the long side to the short side is the golden ratio. 5. 6.5 inches 6. 6.8 meters 7. Answers may vary: the ratio of successive terms appear to approach the golden ratio.

Unit 11C Test 2 1. Answers may vary: How can a line segment be divided in two pieces with the most visual appeal? 2. 47.1 cm

Unit 11B Test 3

3. 19.4 inches

3. (a)

4. Answers may vary: Yes. The size of the rectangle does not affect the golden ratio, only the ratio of the lengths of the sides. An infinite number of lengths can fit the ratio

4. (d)

5. 17.8 m

5. (b)

6. 2.5 feet

6. (c)

7. Answers may vary: sunflowers, pine cones, etc.

1. (b) 2. (a)

Chapter 11 Answers (continued) Unit 11C Test 3 1. (b) 2. (a) 3. (d) 4. (c) 5. (b) 6. (b) 7. (d)

Unit 11C Test 4 1. (c) 2. (b) 3. (d) 4. (b) 5. (c) 6. (b) 7. (b) 8. (a)

Chapter 12 Answers Unit 12A Test 1

Unit 12A Test 3

1. Rizzoli = 49.5%; Isles = 50.5%; Isles has popular vote majority. 2. Rizzoli = 52.6%; Isles = 47.4%; No, Rizzoli is the electoral winner but not the winner of the popular vote.

1. (b) 2. (b) 3. (a) 4. (d)

3. No

5. (d)

4. 10

6. (d)

7. (d)

First

Second

Third

Number of voters

8. (c)

Unit 12A Test 4 1. (c) 2. (b)

6. C; No, because 70 votes are needed for a majority and C only has 58. 7. C

6. (a)

9. no winner—Condorcet paradox

7. (c)

Unit 12A Test 2

8. (b)

1. Grimes = 50.1%; Dixon = 49.9%; Grimes has the popular vote majority. 2. Grimes = 44.6%; Dixon = 55.4%; No, Dixon is the electoral winner, but not the winner of the popular vote. 3. Yes 4. No 5. First

Second

Third

Number of voters

255

240

126

118

6. B; with more than 370 votes, B is also the majority winner 8. B 9. B

4. (a) 5. (a)

8. B

7. B

3. (b)

Unit 12B Test 1 1. Fairness criterion 1 does not apply. Fairness criterion 2 is satisfied. Fairness criterion 3 is satisfied. Fairness criterion 4 is not satisfied. 2. Fairness criterion 1 does not apply. Fairness criterion 2 is satisfied. Fairness criterion 3 is satisfied. Fairness criterion 4 is satisfied. 3. Fairness criterion 1 does not apply. Fairness criterion 2 is satisfied. Fairness criterion 3 is satisfied. Fairness criterion 4 is satisfied. 4. Answers may vary: It is impossible to create a voting system that always satisfies all four fairness criteria. 5. Answers may vary: Since the minority party plus either major party forms a majority, the votes of the minor party will determine the outcome of a vote whenever the major party factions disagree. 6. a. C; b. A

Chapter 12 Answers (continued) 2. (b)

Unit 12B Test 1 (continued) 7. Idaho = 420,785; Texas = 733,226; Idaho

3. (b)

8. Florida = 710,774; New York = 680,872; New York

4. (c)

Unit 12B Test 2

6. (d)

1. Fairness criterion 1 does not apply. Fairness criterion 2 is not satisfied. Fairness criterion 3 is satisfied. Fairness criterion 4 is not satisfied.

7. (c)

2. Fairness criterion 1 does not apply. Fairness criterion 2 is satisfied. Fairness criterion 3 is satisfied. Fairness criterion 4 is satisfied.

Unit 12C Test 1

3. Fairness criterion 1 does not apply. Fairness criterion 2 is satisfied. Fairness criterion 3 is satisfied. Fairness criterion 4 is satisfied. 4. It is impossible to create a voting system that always satisfies all four fairness criteria. 5. Answers may vary: Shareholder D holds no real power. Any of the other two shareholders together make a majority. Shareholder D would need two others to get a majority and those two would have a majority anyway without him. 6. a. B; b. C 7. Vermont = 208,198; Pennslyvania = 639,211; Vermont

5. (b)

8. (c) 9. (a)

1. Answers may vary: Apportionment is a process used to divide a set of people or objects among various individuals or groups. 2. Answers may vary: The fractional remainder is the fraction that remains in the standard quota after subtracting the minimum quota. 3. Answers may vary: A slow-growing state gained a seat at the expense of a fastergrowing state. 4. Answers may vary: In a fair apportionment, the number of seats assigned to each state should be its standard quota rounded either up or down to the nearest integer. 5. Answers may vary: The Balinsky and Young theorem tells us that we cannot choose between apportionment procedures on the basis of fairness alone. A 119,050 25.97 25

8. Ohio = 645,243; Illinois = 640,077; Illinois

Unit 12B Test 3

B 114,560 24.99 24

C 97,790 21.33 21

D 81,200 17.71 17

1. (b)

6. The standard divisor is 4584.44.

2. (c)

3. (d) 4. (a) 5. (b) 6. (b) 7. (d) 8. (d) 9. (b)

Unit 12B Test 4

Total 412,600 87

A 119,050 25.97 25 0.96 26

B 114,560 24.99 24 0.99 25

C 97,790 21.33 21 0.33 21

D 81,200 17.71 17 0.71 18

Total 412,600

A 119,050 25.97 25 26.46 26

B 114,560 24.99 24 25.46 25

C 97,790 21.33 21 21.73 21

D 81,200 17.71 17 18.04 18

Total 412,600

87 90

1. (b)

87 90

Chapter 12 Answers (continued) Unit 12C Test 1 (continued) 9. A 119,050 25.97 25 26.46 26

B 114,560 24.99 24 25.46 25

C 97,790 21.33 21 21.73 22

D 81,200 17.71 17 18.04 18

Total 412,600 87 91

This divisor gives too many seats. You must choose another one for this method to work. 10.

7. Idaho: standard quota = 2.27; 4 seats; overrepresented Texas: standard quota = 37.51; 38 seats; fairly represented Florida: standard quota = 27.75; 29 seats; slightly overrepresented New York: standard quota = 26.58; 29 seats; over-represented 8. No, A gets 25 each way; B gets 11 each way; C goes from 64 seats to 65. 9. A: yes; B: no; C: yes

A 119,050 25.97 25 26.46 26.495 26

B 114,560 24.99 24 25.46 25.495 25

C 97,790 21.33 21 21.73 21.494 21

D 81,200 17.71 17 18.04 18.493 18

Total 412,600 87

Unit 12C Test 3 1. (c) 2. (d) 3. (d) 4. (d)

Unit 12C Test 2

5. (d)

1. Answers may vary: It is the process used to divide the available seats in the House of Representatives among the 50 states.

6. (b)

2. Answers may vary: The standard divisor is the average number of people per seat in the House of Representatives for the entire U.S. population.

7. (b) 8. (c) 9. (b) 10. (b)

3. Answers may vary: This occurs when the total number of available seats in the House of Representatives increases, yet one state (or more) loses a seat as a result.

Unit 12C Test 4

4. Answers may vary: The addition of seats for a new state changed the apportionment for existing states.

3. (a)

5. Carpenter 150 5.95 5 0.95 6

Davis 144 5.71 5 0.71 6

Cary 107 4.25 4 0.25 4

Salem 103 4.09 4 0.09 4

Total 504 20 18 2 20

1. (d) 2. (a) 4. (d) 5. (d) 6. (c) 7. (b) 8. (c) 9. (d) 10. (b)

Unit 12D Test 1 Carpenter 150 6.25 6 0.25 6

Davis 144 6 6 0.00 6

Cary 107 4.46 4 0.46 5

Salem 103 4.29 4 0.29 4

Total 504 21 20 1 21

1. Answers may vary: Redistricting is the process of redrawing the district boundaries for the House of Representatives in each state. This occurs every ten years.

Chapter 12 Answers (continued) Unit 12D Test 1 (continued) 2. Answers may vary: All districts must have nearly equal populations and each district must be contiguous. 3. Votes: Republican = 55.9%; Democrat = 44.1%; Seats: Republican = 62.5%; Democrat = 37.5%; Republicans overrepresented by 6.6% and Democrats underrepresented by 6.6%. 4. Votes: Republican = 54.4%; Democrat = 45.6%; Seats: Republican = 44.4%; Democrat = 55.6%; does not match— Republicans cast more votes but won fewer seats than the Democrats. It appears that the redistricting favored the Democrats.

4. Votes: Republican = 62.1%; Democrat = 37.9%; Seats: Republican = 100%; Democrat = 0%; does not match— Democrats cast over 1/3 of the votes so you would expect them to have won at least one seat. It appears that the redistricting has further favored the Republicans. 5. 10 Democrats and 15 Republicans; the minimum number of Republicans is 6 6. 12 Democrats and 8 Republicans; the maximum number of Democrats is 20 7. Possible answer:  

5. 8 Democrats and 6 Republicans; the maximum number of Democrats is 14



6. 12 Democrats and 20 Republicans; the minimum number of Republicans is 9



7. Possible answer:  

Unit 12D Test 3    

1. (b) 2. (b) 3. (b) 4. (c) 5. (c) 6. (a) 7. (d)

Unit 12D Test 2 1. Answers may vary Gerrymandering is the practice of drawing district boundaries for political advantage. 2. Answers may vary: All districts must have nearly equal populations and each district must be contiguous. 3. Votes: Republican = 57.8%; Democrat = 42.2%; Seats: Republican = 75%; Democrat = 25%; does not match well— would expect the seats to be divided more evenly.

8. (c)

Unit 12D Test 4 1. (d) 2. (c) 3. (c) 4. (c) 5. (a) 6. (a) 7. (c)

Chapter 12 Answers (continued) Unit 12D Test 4 (continued) 8. (a) 9. (d)