1. MGF 1106 Test 1 Review and Practice Solutions

2. Exam Topics ObjectiveSectionSuggested Text Problems 1) Use inductive reasoning to find the next number in a sequence. 1.1Page 43: 3, 5, 7, 9 2) Use deductive reasoning.1.1 3) Round numbers.1.2Page 43: 15 4) Work cost comparison problems.1.3Page 39: 35 5) Work coin combination problems1.3Page 39: 28 (answer: 12) 6) Work problems involving runners in a race.1.3Page 39: 39 7) Use the symbols ∈ and ∉.2.1Page 109: 9 8) Find the cardinality of a set.2.1Page 109: 11 9) Answer True/False Questions about subsets.2.2Page 68: 51 10) List all the subsets of a given set.2.2Page 68: 55, 57 11) Find the number of subsets and proper subsets of a set. 2.2Page 69: 93 12) Find the complement of a set.2.3Page 81: 5, 7 13) Perform operations on two sets.2.3Page 109: 33, 35, 37 14) Use a Venn diagram to answer questions about a set. 2.3Page 82: 109, 111 15) Place items in a Venn diagram.2.4Page 94: 99, 101, 103 16) Work survey problems.2.5Page 110: 61 17) Use a Venn diagram to answer questions about a survey. 2.5Page 104: 33, 35, 37

3. Practice Test Solutions

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

7. 2) Select a number. Multiply it by 6. Subtract 8 from the product. Divide the difference by 2. Add four to the quotient.

8. 3) Round 7.899157 to the nearest:

9. 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.

10. 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. QuartersDimesNickelsPennies 1001 0211 0206 0131 0126 01111 01016 0051 0046 00311 00216 00121 00026 13 ways

11. 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.

12. 7) Use the symbols ∈ and ∉ to make the statement true.

13. 8) Find the cardinal number for each set.

14. 9) Determine if each statement is true or false.

15. 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}

19. 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?

20. 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.

21. 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.

22. 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.

23. MGF 1106 Extra Practice Problems

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

26. 2) Select a number. Multiply it by 5. Subtract 15 from the product. Divide the difference by 5. Add three to the quotient.

28. 3) Round 2.71828188 to the nearest hundredth.

29. 2.72

30. 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?

32. 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.

33. 18 ways QuartersDimesNickelsPennies 1012 1007 0302 0222 0217 02012 0142 0137 012 01117 01022 0062 0057 00412 00317 00222 00127 00032

34. 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?

35. (First is on the right) 8 C B 3 5 C P B 3 5 7 C P B O Order: Ostrich, Bear, Penguin, Chicken 15 seconds between first and last.

36. 7) Use the symbols ∈ and ∉ to make the statement true.

38. 8) Find the cardinal number for the set.

40. 9) Determine if the statement is true or false.

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

43. 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}

44. 11a) How many subsets of {tea, milk, water, soda} should you have found? Proper subsets?

46. 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?

52. 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?

54. 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” ?

55. 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.

56. 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?

57. 45 like exactly one sport.

58. 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?