MGF 1106Test 1 ReviewandPractice Solutions

• You will need to have your own calculator for the test. • You may not share calculators or use any type of communication device in place of a calculator. • Tests may not be made up for any reason other than a mandatory school – sponsored activity for which you must miss class. • If you miss one test for any other reason, your final exam score will be substituted for that test. A second missed test is a zero. No homework bonuses are awarded on a test when the final exam is substituted or you receive a zero on a missed test.

Be sure to complete each assignment with a score of at least 80% to receive the 10 point bonus.

Exam TopicsObjective Section Suggested Text Problems1) Use inductive reasoning to find the next number in a sequence. 1.1 Page 38: 3, 5, 7, 9

2) Round numbers. 1.2 Page 38: 153) Work cost comparison problems. 1.3 Page 40: 354) Work coin combination problems 1.3 Page 41: 38 (answer: 6)5) Work problems involving runners in a race. 1.3 Page 35: 396) Express a set using the roster method. 2.1 Page 54: 277) Use the symbols ∈ and ∉. 2.1 Page 99: 98) Find the cardinality of a set. 2.1 Page 99: 119) Answer True/False Questions about subsets. 2.2 Page 100: 25, 27, 2910) List all the subsets of a given set. 2.2 Page 63: 55, 5711) Find the number of subsets and proper subsets of a set. 2.2 Page 100: 3112) Find the complement of a set. 2.3 Page 74: 5, 713) Perform operations on two sets. 2.3 Page 100: 33, 35, 3714) Perform operations on three sets. 2.4 Page 100: 4715) Use a Venn diagram to answer questions about a set. 2.4 Page 100: 49, 51, 5316) Work survey problems. 2.5 Page 101: 6117) Negate statements 3.1 Page 18) Negate quantified statements. 3.1 Page 190: 13, 1519) Translate a compound statement to symbolic form. 3.2 Page 189: 7, 920) Translate symbolic form to a compound statement. 3.2 Page 189: 3

Practice Test Solutions

1) Find the next number in the sequence.a) 7, 10, 13, 16, ?

b) 7, 14, 28, 56, ?

c) 2, 6, 12, 36, 72, 216, ?

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

3) 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.

4) 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 1 211 0 0 26

$

13 ways

5) 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.

6) Express the following set using the roster method:

 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) Suppose Find the following.a)b)

c)

15) Use the Venn diagram below to list the members of each set.

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) Negate each statement.a) Hayley is going to see the sequel.Hayley is not going to see the sequel.b) Grant does not like apples.Grant likes apples.

18) Negate each statement.a) All whales are mammals. Some whales are not mammals. b) No blue clouds are in the sky. Some blue clouds are in the sky. c) Some pianists are not proficient.All pianists are proficient. d) Some children like video games.No children like video games.

19) Let p, q, and r represent the following statements. p: Jim likes oranges q: Mike likes strawberries r: Katie likes mangoesTranslate each statement to symbolic form.a) Jim likes oranges and Katie does not like mangoes. p ∧ ~r b) Katie likes mangoes if and only if Mike likes strawberries. r ↔ qc) If Jim does not like oranges, then Mike likes strawberries or Katie does not like mangoes. ~p→(q ∨ ~r)

20) Let p, q, and r represent the statements in question 19.p: Jim likes oranges q: Mike likes strawberries r: Katie likes mangoesTranslate each symbolic form to English.a) p ∨ q Jim likes oranges or Mike likes strawberries. b) q ∧ (~p →~r) Mike likes strawberries, and if Jim does not like oranges then Katie does not like mangoes.

MGF 1106Extra Practice Problems

1) Find the next number in the sequence.

1) Find the next number in the sequence.

Each number is the sum of the two previous.

2) Round 2.71828188 to the nearest hundredth.

2) Round 2.71828188 to the nearest hundredth.2.72

3) 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?

3) 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.

4) 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.

4) 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

5) 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?

5) 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.

6) Express the following set using the roster method:

6) Express the following set using the roster method:

 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}

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

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

12) Find A’:

12) Find A’:

𝐴′={𝑝𝑙𝑎𝑛𝑒 , 𝑓𝑒𝑒𝑡 ,𝑏𝑎𝑙𝑙𝑜𝑜𝑛}

13) Find ,

13) Find ,

14) Suppose Find

14) Suppose Find

15) Use the Venn diagram below to list the members of the set.

(𝐴⋂𝐶′ )⋃ (𝐴⋂𝐵)

15) Use the Venn diagram below to list the members of the set.

(𝐴⋂𝐶′ )⋃ (𝐴⋂𝐵)

{1, 3, 4, 9}

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) Negate the statement.Valerie does not like yogurt.

17) Negate the statement.Valerie does not like yogurt.

Valerie likes yogurt.

18) Negate each statement.a) All squirrels can climb.  b) Some people like the NFL.  c) Some tests are not graded on a curve. d) No roller coasters are scary.

18) Negate each statement.a) All squirrels can climb. Some squirrels cannot climb. b) Some people like the NFL. No people like the NFL. c) Some tests are not graded on a curve.All tests are graded on a curve. d) No roller coasters are scary.Some roller coasters are scary.

19) Let p, q, and r represent the following statements. p: Jim likes oranges q: Mike likes strawberries r: Katie likes mangoesTranslate the statement to symbolic form.If Mike doesn’t like strawberries or Jim doesn’t like oranges, then Katie doesn’t like mangoes and Jim likes oranges.

19) Let p, q, and r represent the following statements. p: Jim likes oranges q: Mike likes strawberries r: Katie likes mangoesTranslate the statement to symbolic form.If Mike doesn’t like strawberries or Jim doesn’t like oranges, then Katie doesn’t like mangoes and Jim likes oranges.(~q ∨ ~p )→(~r ∧ p)

20) Let p, q, and r represent the statements in question 19.p: Jim likes oranges q: Mike likes strawberries r: Katie likes mangoesTranslate the symbolic form to English.  (p ∧ q) ↔ ~r

20) Let p, q, and r represent the statements in question 19.p: Jim likes oranges q: Mike likes strawberries r: Katie likes mangoesTranslate the symbolic form to English.  (p ∧ q) ↔ ~r

Jim likes oranges and Mike likes strawberries, if and only if Katie does not like mangoes.