Math 1332 Review 1



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Name:___________________________ Math 1332 Test 1(Due no later than 10PM, Sep. 18)

1. Identify a pattern in the given list of numbers, and use inductive reasoning to find the next two numbers in the list:

a) [pic] b) [pic]

2. Consider the following procedure: Select a number. Multiply the number by 6. Add six to the product. Divide the sum by three. Subtract two from the quotient.

a) Perform these operations on the given numbers in the table, and write in your results:

|The original number |The result of the operations |

|2 | |

|3 | |

|4 | |

|5 | |

b) Using inductive reasoning, write a conjecture that relates the result of the operations to the original number.

c) Use deductive reasoning to prove your conjecture in part b).

3. Notice that [pic], [pic],[pic],

[pic].

a) Use inductive reasoning to find a formula for [pic].

b) Use the pattern or your formula in part a) to find the value of [pic].

Show work/calculation!

Bonus #1: Prove the formula using deductive reasoning by completing the following argument:

[pic]

Bonus #2: What is the tens digit of [pic]?

4. Fill in the blank with either [pic] or [pic]to make each statement true.

a) [pic] b) [pic]

5. Fill in the blank with either [pic] or [pic] to make each statement true.

a) [pic]

b) [pic] c) [pic]

6. Determine whether [pic] or [pic] , both, or neither can be placed in each blank to make the statement true.

a) [pic]

b) [pic]

7. Determine if the pair of sets are equal, equivalent, both, or neither.

a) [pic]

[pic]

b) [pic]

[pic]

8. Find the number of subsets and the number of proper subsets of the set [pic].

|# of Subsets |# of Proper Subsets |

| | |

| | |

Bonus #3: How many of the subsets of [pic] don’t have a as an element?

9. Set A contains 24 elements, set B contains 18 elements, and [pic] contains 40 elements.

a) How many elements are in [pic]? b) How many elements are in [pic]?

c) How many elements are in [pic]?

Hint: You may use the following Venn Diagram:

Bonus #4: If a set E has 8 elements, a set F has 10 elements, and the universe has 13 elements, what is the fewest number of elements of the universe that could be in[pic]?

10. Let [pic], [pic], [pic], and [pic].

List the elements in the following sets:

a) [pic] b) [pic]

c) [pic] d) [pic]

e) [pic] f) [pic]

g) [pic] h) [pic]

11. A survey of 200 students at a nonresidential college revealed the following results:

Of those surveyed 112 used cars, 100 used public transportation, and 68 used bikes. Forty-eight students used cars and public transportation, 36 used cars and bikes, and 24 used public transportation and bikes. Twenty students used all three modes of transportation.

a) Complete the Venn Diagram:

b) How many used only bikes? Also, shade the corresponding region in the Venn Diagram.

c) How many used cars and bikes, but not public transportation? Also, shade the corresponding region in the Venn Diagram.

d) How many used cars or bikes, but not public transportation? Also, shade the corresponding region in the Venn Diagram.

e) How many used exactly two of these modes of transportation? Also, shade the corresponding region in the Venn Diagram.

f) How many used two or more of these modes of transportation? Also, shade the corresponding region in the Venn Diagram.

12. A popular brand of pen comes in red, blue, black, or purple ink. The writing tip can be chosen from extra-bold, bold, regular, fine, or micro. How many different choices of pens do you have with this brand?

| | | |

| | |= |

|Ink color |Tip | |

13. Eight acts [pic]are scheduled to perform in a variety show.

a) How many different ways are there to schedule their appearances?

| | | | | | |

| | | | | | |

|President |Vice-president |Secretary |Treasurer |Sergeant at arms | |

15. How many different rearrangements are there of the letters in the word mississippi?

Show work/calculation!

16. A political discussion group consists of 6 Republicans and 8 Democrats. If a committee of four people is to be selected, how many different committees consisting of the following are possible?

a) all four are Republicans

Indicate the calculation!

b) two are Democrats and two are Republicans.

Indicate the calculation!

Bonus #5: How many of the possible committees in problem #16 have at least 1 Democrat?

Bonus #6: Let [pic]and [pic]. Write the set [pic].

-----------------------

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

Car

Bike

Public transportation

20

U

Car

Bike

Public transportation

U

Car

Bike

Public transportation

U

Car

Bike

Public transportation

U

Car

Bike

Public transportation

U

Car

Bike

Public transportation

U

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