Name: 
 

Math 12F LG 13 Practice Unit Test #4


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
A summer camp offers canoeing, rock climbing, and archery. The following Venn diagram shows the types of activities the campers like.
mc001-1.jpg

Use the diagram to determine n((A Ç C) È (R Ç A)).
A.
16
B.
27
C.
5
D.
11
 

 2. 
A restaurant offers Chinese, Thai, and Korean food. The following Venn diagram shows the types of food the customers like.
mc002-1.jpg

Use the diagram to determine n(K) – n(C Ç T Ç K).
A.
10
B.
50
C.
27
D.
33
 

 3. 
Which sentence is written as a conditional statement?
A.
If you fall down, get right back up.
B.
Juggling is not hard if you practice.
C.
If the temperature is below freezing, it must be winter.
D.
If the sky is cloudy, then you cannot see the sun.
 

 4. 
Which truth tables apply to the conditional statement below and its converse?
“If the milk is not refrigerated, then it will spoil.”
A.                                                         C.
p
q
p Þ q
 
p
q
p Þ q
T
T
T
 
T
T
T
q
p
q Þ p
 
q
p
q Þ p
T
T
T
 
T
F
F

B.                                                          D.
p
q
p Þ q
 
p
q
p Þ q
F
F
T
 
T
F
F
q
p
q Þ p
 
q
p
q Þ p
F
F
T
 
T
F
F
A.
A.
B.
B.
C.
C.
D.
D.
 

 5. 
Which statement is the converse of the conditional statement below?
“If tomorrow is Monday, then today is Sunday.”
 
A.
If tomorrow is Sunday, then today is not Monday.
B.
If today is Sunday, then tomorrow is Monday.
C.
If tomorrow is not Monday, then today is not Sunday.
D.
If today is not Sunday, then tomorrow is not Monday.
 

 6. 
Identify the expression that is equivalent to the following:
mc006-1.jpg
A.
mc006-2.jpg
B.
mc006-3.jpg
C.
n3
D.
(n + 1)!
 

 7. 
Evaluate.
14P7
A.
17 297 280
B.
2 162 160
C.
121 080 960
D.
105 413 504
 

 8. 
Solve for r.
9Pr = 72
A.
r = 1
B.
r = 2
C.
r = 3
D.
r = 4
 

 9. 
The numbers 1 to 11 are written on identical slips of paper and put in a hat. How many ways can 4 numbers be drawn simultaneously?
A.
110
B.
220
C.
330
D.
440
 

 10. 
Which of the following is equivalent to mc010-1.jpg?
A.
mc010-2.jpg
B.
mc010-3.jpg
C.
mc010-4.jpg
D.
mc010-5.jpg
 

 11. 
Solve for n.
nC1 = 30
A.
n = 6
B.
n = 10
C.
n = 30
D.
n = 60
 

 12. 
Jake and Agnes are playing a board game. If a player rolls a sum greater than 9 or a multiple of 6, the player gets a bonus of 50 points. Determine the probability of rolling a multiple of 6.
A.
mc012-1.jpg
B.
mc012-2.jpg
C.
mc012-3.jpg
D.
mc012-4.jpg
 

 13. 
Helen is about to draw a card at random from a standard deck of 52 playing cards. Determine the probability that she will draw a black card or a spade.
A.
mc013-1.jpg
B.
mc013-2.jpg
C.
mc013-3.jpg
D.
mc013-4.jpg
 

 14. 
Select the events that are dependent.
A.
Drawing a face card from a standard deck of 52 playing cards, putting it back,
and then drawing another face card.
B.
Rolling a 4 and rolling a 3 with a pair of six-sided dice, numbered 1 to 6.
C.
Drawing a heart from a standard deck of 52 playing cards, putting it back,
and then drawing another heart.
D.
Rolling a 3 and having a sum greater than 5 with a pair of six-sided dice, numbered 1 to 6.
 

 15. 
There are 40 males and 60 females in a graduating class. Of these students, 10 males and 20 females plan to attend a certain university next year. Determine the probability that a randomly selected student plans to attend the university.
A.
0.3
B.
0.4
C.
0.5
D.
0.6
 

Short Answer
 

 1. 
Write the contrapositive  of the conditional statement below. Verify the contrapositive  or disprove it with a counterexample.
“If the height and radius of a cone and cylinder are the same, then the cone is one third the volume of the cylinder.”
 

 2. 
A combination lock opens with the correct three-letter code. Each wheel rotates through the letters A to O. How many different three-letter codes are possible?
 

 3. 
A true-false test has ten questions. How many different permutations of answers can the teacher create if at least seven answers are true?
 

Problem
 

 1. 
Lisa is looking for a book about the solar system for her younger sister, who is 11.
a) What categories and subcategories might she use to refine her search when browsing an online bookstore?
b) Draw a Venn diagram to represent a search Lisa could use to find a book for her sister.
 

 2. 
Two friends are building stacks of 12 coins. Stack 1 has 5 identical pennies, 3 identical nickels, and 4 identical quarters. Stack 2 has 3 identical pennies, 3 identical nickels, and 6 identical quarters.
Which set of coins can make more stacks of 12 coins? Show your work.
 

 3. 
From a group of eight students, four students need to be chosen for a dance committee. How many committees are possible? Show your work.
 



 
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