MGF 1106Test 1 ReviewandPractice Solutions

Exam TopicsObjective Section Suggested Text Problems1) Use inductive reasoning to find the next number in a sequence. 1.1 Page 43: 3, 5, 7, 9

2) Use deductive reasoning. 1.1 Page 43: 14Answer to b: 3) Round numbers. 1.2 Page 43: 154) Work cost comparison problems. 1.3 Page 39: 355) Work coin combination problems 1.3 Page 39: 28 (answer: 12)6) Work problems involving runners in a race. 1.3 Page 39: 397) Use the symbols ∈ and ∉. 2.1 Page 109: 98) Find the cardinality of a set. 2.1 Page 109: 119) Answer True/False Questions about subsets. 2.2 Page 68: 5110) List all the subsets of a given set. 2.2 Page 68: 55, 5711) Find the number of subsets and proper subsets of a set. 2.2 Page 69: 9312) Find the complement of a set. 2.3 Page 81: 5, 713) Perform operations on two sets. 2.3 Page 109: 33, 35, 3714) Use a Venn diagram to answer questions about a set. 2.3 Page 82: 109, 11115) Place items in a Venn diagram. 2.4 Page 94: 99, 101, 10316) Work survey problems. 2.5 Page 110: 6117) Use a Venn diagram to answer questions about a survey. 2.5 Page 104: 33, 35, 37

Practice Test Solutions

1) Identify a pattern in the list of numbers. Describe the pattern. Then use this pattern to find the next number.

a) 7, 10, 13, 16, ?The difference between each number is 3.

b) 7, 14, 28, 56, ?The number doubles each time.

c) 2, 6, 12, 36, 72, 216, ?The numbers alternate between being multiplied by 3 and multiplied by 2.

2) Select a number. Multiply it by 6. Subtract 8 from the product. Divide the difference by 2. Add four to the quotient. a) Repeat this process for the numbers 1, 2, 5, 10.

b) Write a conjecture that relates the result of this process to the original number selected. The number is multiplied by 3 (tripled).c) Let represent the original number. Use deductive reasoning to prove your conjecture.

3) Round 7.899157 to the nearest:a) tenths: 7.9 b) thousandths: c) hundred – thousandths: 7.89916

4) John has a vending route. He’s paid $450 per week to service the vending machines. Kent’s company pays him $1750 per month to do the same job. In a single year, who makes more money? What is the difference between the two annual salaries? Assume 12 months in a year and 52 weeks in a year.John:Kent:

John makes more money. His annual salary exceeds Kent’s by $2400.

5) If you spend $9.74, in how many ways can you receive change from a ten-dollar bill. Use a table and show all possibilities.Quarters Dimes Nickels Pennies1 0 0 10 2 1 10 2 0 60 1 3 10 1 2 60 1 1 110 1 0 160 0 5 10 0 4 60 0 3 110 0 2 160 0 1 210 0 0 26

$

13 ways

6) Trent, Riley, Susan, Doug, and Betty competed in a race. Betty finished 11 seconds after Doug. Betty finished 24 seconds after Riley. Susan finished 8 seconds after Riley. Doug finished 18 seconds before Trent. In which order did the runners finish the race? How many seconds difference was there between first and last place? (First is on the right) 11 B D  11 13 B D R 11 5 8 B D S R    7 11 5 8 T B D S R   Order: Riley, Susan, Doug, Betty, Trent.31 seconds between first and last.

 7) Use the symbols ∈ and ∉ to make the statement true.a) 3 _____ {3, 4, 5, 6}3 __ ___ {3, 4, 5, 6}b) {7} ______ {}{7} __ ∉ ____ {}c) 9 ______ {} 9 __ ∉ ____ {}

8) Find the cardinal number for each set.a) b)

4

9) Determine if each statement is true or false.a) {1, 2} ⊆ {0, 1, 2, 3, 4, 5}True{1, 2} is a subset of {0, 1, 2, 3, 4, 5}

b) {1, 2, 3} ⊂ {}Falsec) { } ⊂ {1, 2, 3}TrueThe empty set is a proper subset of every set other than itself.

d) 1 ⊈ {1, 2, 3, 4}True1 is an element, not a subset.

10) List the subsets of {cake, pie, cookie}No elements: { }One element: {cake}, {pie}, {cookie}Two elements: {cake, pie}, {cake, cookie}, {pie, cookie}

Three elements: {cake, pie, cookie}

11) Suppose S is the set How many subsets does S have? How many proper subsets does S have?

12) Suppose Find A’.Find B’.

13) Suppose .Find the following.a)

b) c) d)

14) Jacob was preparing to pack for college. He called his future roommate Marcus to ask if he had purchased certain items. He put the outcome of that phone conversation in the Venn diagram below. What is the set of items that Jacob purchased but not Marcus?

{𝑡𝑜𝑎𝑠𝑡𝑒𝑟 , 𝑓𝑢𝑡𝑜𝑛 , 𝑡𝑒𝑛𝑡 }

15) Suppose A represents the set of letters in the word “canned”. Set B represents the set of letters in the word “processed”. Set C represents the set of letters in the word “organic”. In what region would you place the letter “e” ?

The letter “e” is in sets A and B but not in set C.The region that contains A and B but not C is II.

16) A survey of 180 high school students was taken to determine participation in various college activities. 43 were in a service club. 52 were in the band. 35 were on an athletic team. 13 were in a service club and the band. 14 were in the band and on an athletic team. 12 were in a service club and an athletic team. Five students participated in all three activities.

17) Pete’s Pet Shop surveyed dog owners to find out if they gave their pets canned dog food or pet treats. The results of the survey are summarized in the Venn diagram below.How many dog owners gave their pets canned dog food and pet treats?

The answer is the intersection of the two sets: 7.

MGF 1106Extra Practice Problems

1) Identify a pattern in the list of numbers. Describe the pattern. Then use this pattern to find the next number.

1) Identify a pattern in the list of numbers. Describe the pattern. Then use this pattern to find the next number.

2) Select a number. Multiply it by 5. Subtract 15 from the product. Divide the difference by 5. Add three to the quotient. a) Repeat this process for the numbers 1, 2, 5, 10.

b) Write a conjecture that relates the result of this process to the original number selected. c) Let represent the original number. Use deductive reasoning to prove your conjecture.

2) Select a number. Multiply it by 5. Subtract 15 from the product. Divide the difference by 5. Add three to the quotient. a) Repeat this process for the numbers 1, 2, 5, 10.

b) Write a conjecture that relates the result of this process to the original number selected. The result is the original number.c) Let represent the original number. Use deductive reasoning to prove your conjecture.

3) Round 2.71828188 to the nearest hundredth.

3) Round 2.71828188 to the nearest hundredth.2.72

4) Rayna works as a math tutor and earns $2,495 each month. Her sister Jeanine gives private piano lessons and charges $45 per hour. If Jeanine gave piano lessons for 57 hours last month, who made more money? How much more?

4) Rayna works as a math tutor and earns $2,495 each month. Her sister Jeanine gives private piano lessons and charges $45 per hour. If Jeanine gave piano lessons for 57 hours last month, who made more money? How much more?Rayna:Jeanine

Jeanine made more money. She earned 70 more dollars.

5) If you spend $9.68, in how many ways can you receive change from a ten-dollar bill? Use a table and show all possibilities.

5) If you spend $9.68, in how many ways can you receive change from a ten-dollar bill? Use a table and show all possibilities.$

18 ways

Quarters Dimes Nickels Pennies1 0 1 21 0 0 70 3 0 20 2 2 20 2 1 70 2 0 120 1 4 20 1 3 70 1 2 120 1 1 170 1 0 220 0 6 20 0 5 70 0 4 120 0 3 170 0 2 220 0 1 270 0 0 32

6) Four mascots competed in a race at a baseball game. The dancing bear finished eight seconds ahead of the chicken. The chicken finished 3 seconds behind the penguin. The ostrich finished 12 seconds ahead of the penguin. Who finished first? What was the difference between first place and last?

6) Four mascots competed in a race at a baseball game. The dancing bear finished eight seconds ahead of the chicken. The chicken finished 3 seconds behind the penguin. The ostrich finished 12 seconds ahead of the penguin. Who finished first? What was the difference between first place and last? (First is on the right) 8 C B  3 5 C P B 3 5 7 C P B O     Order: Ostrich, Bear, Penguin, Chicken15 seconds between first and last.

 7) Use the symbols ∈ and ∉ to make the statement true. c _____ {}

 7) Use the symbols ∈ and ∉ to make the statement true. c ___ ∈ _ {}

8) Find the cardinal number for the set.{}

8) Find the cardinal number for the set.{}

9) Determine if the statement is true or false. ⊂{}

9) Determine if the statement is true or false. ⊂{}True

10) List the subsets of {tea, milk, water, soda}

10) List the subsets of {tea, milk, water, soda}No elements: { }One element: {tea}, {milk}, {water}, {soda}Two elements: {tea, milk}, {tea, water}, {tea, soda}, {milk, water}, {milk, soda}, {water, soda}

Three elements: {tea, milk, water}, {tea, milk, soda}, {tea, water, soda}, {milk, water, soda}Four elements:{tea, milk, water, soda}

11a) How many subsets of {tea, milk, water, soda} should you have found? Proper subsets?

11a) How many subsets of {tea, milk, water, soda} should you have found? Proper subsets?

11b) Jacob is going on vacation. He is thinking about bringing some of his textbooks on the trip. He has five textbooks and will bring some, all, or none of the textbooks. How many different options does he have?

11b) Jacob is going on vacation. He is thinking about bringing some of his textbooks on the trip. He has five textbooks and will bring some, all, or none of the textbooks. How many different options does he have?

The number of options is the number of subsets of the set of his five textbooks.

12) Find A’:

12) Find A’:

𝐴′={𝑝𝑙𝑎𝑛𝑒 , 𝑓𝑒𝑒𝑡 ,𝑏𝑎𝑙𝑙𝑜𝑜𝑛}

13) Find ,

13) Find ,

14) Jacob was preparing to pack for college. He called his future roommate Marcus to ask if he had purchased certain items. He put the outcome of that phone conversation in the Venn diagram below. What is the set of items they both purchased?

14) Jacob was preparing to pack for college. He called his future roommate Marcus to ask if he had purchased certain items. He put the outcome of that phone conversation in the Venn diagram below. What is the set of items they both purchased?

{𝑔𝑢𝑖𝑡𝑎𝑟 ,𝑚𝑖𝑐𝑟𝑜𝑤𝑎𝑣𝑒 ,𝑡𝑒𝑙𝑒𝑣𝑖𝑠𝑖𝑜𝑛 }

15) Suppose A represents the set of letters in the word “canned”. Set B represents the set of letters in the word “processed”. Set C represents the set of letters in the word “organic”. In what region would you place the letter “g” ?

15) Suppose A represents the set of letters in the word “canned”. Set B represents the set of letters in the word “processed”. Set C represents the set of letters in the word “organic”. In what region would you place the letter “g” ?

The letter “g” is in set C but not in A or B.The region that contains C but not A or B is VI.

16) 100 people were surveyed about what sport they like they like. 35 people like basketball. 31 people like baseball. 59 people like football. 16 people like basketball and baseball. 25 like basketball and football. 20 like baseball and football. 14 like all three sports. How many like exactly one sport?

16) 100 people were surveyed about what sport they like they like. 35 people like basketball. 31 people like baseball. 59 people like football. 16 people like basketball and baseball. 25 like basketball and football. 20 like baseball and football. 14 like all three sports. How many like exactly one sport?

45 like exactly one sport.

17) Pete’s Pet Shop surveyed dog owners to find out if they gave their pets canned dog food or pet treats. The results of the survey are summarized in the Venn diagram below.How many dog owners were surveyed?

17) Pete’s Pet Shop surveyed dog owners to find out if they gave their pets canned dog food or pet treats. The results of the survey are summarized in the Venn diagram below.How many dog owners were surveyed?

Answer: