Download Foundations of Math 12 Ch3 Practice Test Answer Section

Foundations of Mathematics 12
Foundations of Math 12 Ch3 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. What is the meaning of complement in set theory?
A.
B.
C.
D.
____
2. What is the meaning of disjoint in set theory?
A.
B.
C.
D.
____
a set with an infinite number of elements
a set of all the elements under consideration for a particular context
a set with a countable number of elements
a set that contains every possible element
4. Which pair of sets represents disjoint sets?
A.
B.
C.
D.
____
two or more sets having no elements in common
two or more sets that do not match
sets that are in different universal sets
sets that contain no elements
3. What is the universal set?
A.
B.
C.
D.
____
all the elements in the universal set that are not identical
a set of elements that work well with a given set
all the elements of a universal set that do not belong to a subset of it
all the elements that are the opposite of the elements in a given set
N, the set of natural numbers, and I, the set of integers
T, the set of all triangles, and C, the set of all circles
N, the set of natural numbers, and P, the set of positive integers
none of the above
5. Given the following situation:
• the universal set U = {positive integers less than 20}
• X = {4, 5, 6, 7, 8}
• P = {prime numbers of U}
• O = {odd numbers of U}
Which statement describes O?
A.
B.
C.
D.
the set of even numbers of U
the set of odd numbers of U
the set of odd, prime numbers of U
the set of even, prime numbers of U
Kim
Foundations of Mathematics 12
____
6. There are 28 students in Mr. Connelly’s Grade 12 mathematics class.
The number of students in the yearbook club and the number of students on student council are
shown in the Venn diagram. Use the diagram to answer the following questions.
How many students are in both the yearbook club and on the student council?
A.
B.
C.
D.
____
2
5
1
7
7. Consider the following Venn diagram of herbivores and carnivores:
Determine n(H  C).
A.
B.
C.
D.
____
Kim
2
9
4
3
8. Consider the following Venn diagram of foods we eat raw or cooked:
Foundations of Mathematics 12
Kim
Determine H  C.
A.
B.
C.
D.
____
{fish, spinach, apples, cucumber, lettuce, chicken, pork, rice, pasta, potatoes}
{chicken, pork, rice, pasta, potatoes}
{cucumber, lettuce}
{fish, spinach, apples}
9. A summer camp offers canoeing, rock climbing, and archery. The following Venn diagram shows
the types of activities the campers like.
Use the diagram to determine n((R  A) \ C).
A.
B.
C.
D.
____
10. What is a hypothesis?
A.
B.
C.
D.
____
an idea
a statement
a clue
an assumption
11. What is a conclusion?
A.
B.
C.
D.
____
14
5
26
8
the result of a hypothesis
an assumption
a decision
the answer to a statement
12. What is a converse?
A.
B.
C.
D.
proof that a conditional statement is false
a conditional statement in which the hypothesis and the conclusion are switched
the second part of a conditional statement
the opposite of a conditional statement
Foundations of Mathematics 12
____
13. What is a biconditional statement?
A.
B.
C.
D.
____
14. Which sentence is the converse to the conditional statement below?
“If the milk is not refrigerated, then it will spoil.”
A.
B.
C.
D.
____
a conditional statement that is only true in two cases
a statement that uses the form “if p, then q”
a conditional statement whose converse is also true
a conditional statement whose inverse is also true
Unrefrigerated milk will spoil.
The milk is spoiled because it was not put in the refrigerator.
If the milk is spoiled, then it is not refrigerated.
The milk will spoil if it is not put in the refrigerator.
15. Which statement is true?
A. If a conditional statement is true, then its contrapositive is true, and vice versa.
B. If a conditional statement is true, then its converse is true, and vice versa.
C. If the inverse of a conditional statement is true, then the contrapositive of the
statement is also true, and vice versa.
D. If the contrapositive of a conditional statement is true, then the converse of the
statement is also true, and vice versa.
____
16. What is true about the conditional statement below?
“If tomorrow is Monday, then today is Sunday.”
A.
B.
C.
D.
____
The statement and contrapositive are true but the inverse and converse are false.
The inverse and contrapositive are true but the statement and converse are false.
The converse and inverse are true but statement and contrapositive are false.
The statement, converse, inverse, and contrapositive are all true.
17. Which statement is the inverse of the conditional statement below?
“If a balloon is filled with helium, then the balloon will float upwards.”
A.
B.
C.
D.
If a balloon floats upwards, then the balloon is filled with helium.
If a balloon is not filled with helium, then the balloon will not float upwards.
If a balloon is not filled with helium, then the balloon will float downwards.
If a balloon does not float upwards, then the balloon is not filled with helium.
Kim
Foundations of Mathematics 12
Kim
Short Answer
1. Tania recorded the 16 possible sums that can occur when you roll two four-sided dice.
• S = {all possible sums}
• L = {all sums less than 4}
• G = {all sums greater than 4}
• F = {all sums equal to 4}
What is n(L)?
2. What is the set notation for the set of all positive real numbers that are less than 22?
3. Grade 12 students were surveyed about their extra curricular activities.
• 58% belonged to a sports team (S)
• 63% belonged to a band or choir (B)
• 47% belonged to a school club (C)
• 24% belonged to a sports team and a band or choir
• 21% belonged to a sports team and a school club
• 36% belonged to a band or choir and a school club
• 19% engaged in all three activities
What percent of students only belong to a band or choir? Write your answer in set notation.
Problem
1. A total of 83 teens attended a performing arts camp to train in at least one of three activities:
dance, acting, or singing.
• 47 took dance, 42 took acting, and 54 took singing.
• 3 took dance and acting only.
• 16 took acting and singing only.
• 19 took dance and singing only.
How many teens trained in all three performing arts?
2. Consider this conditional statement: “If you speak French and English, then you are bilingual.”
a) What is the hypothesis? What is the conclusion?
b) Is this statement true? Explain.
c) Write the converse.
d) Is the converse true? Explain.
Foundations of Mathematics 12
3. Consider this conditional statement:
“If I live in Saskatoon, then I live in Saskatchewan.”
a) Write the converse, the inverse, and the contrapositive.
b) Verify that each statement is true, or disprove it with a counterexample.
4. Consider this conditional statement:
“If x is an odd integer, then x2 is an odd perfect square.”
a) Write the converse, the inverse, and the contrapositive.
b) Verify that each statement is true, or disprove it with a counterexample.
Kim
Foundations of Mathematics 12
Kim
Foundations of Math 12 Ch3 Practice Test
Answer Section
MULTIPLE CHOICE
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Lesson 3.1
Lesson 3.1
Lesson 3.1
Lesson 3.1
Lesson 3.1
Lesson 3.2
Lesson 3.3
Lesson 3.3
Lesson 3.4
Lesson 3.5
Lesson 3.5
Lesson 3.5
Lesson 3.5
Lesson 3.5
Lesson 3.6
Lesson 3.6
Lesson 3.6
SHORT ANSWER
1. ANS:
n(L) = 3
since
S={(1,1), (1,2) (1,3) (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3),(4,4)}
L = {(1,1), (1,2), (2,1)}
G = {(1,4), (2,3), (2,4), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}
F = {(2,2) }
n(L) = 3
2. ANS:
A = {x | 0 < x < 22, x  R}
3. ANS:
n(B \ S \ C) U n(C \ S \ B) = 31%
Foundations of Mathematics 12
Kim
PROBLEM
1. ANS:
Let x represent the number of teens trained in all three performing arts.
=> Center in the Venn Diagram
Using the principle of inclusion and exclusion for three sets:
Quick Strategy:
union of three sets (i.e. everything inside the circles)
+ full circles
- overlaps
+ center
11 teens are studying all three performing arts.
2. ANS:
a) Hypothesis: You speak French and English.
Conclusion: You are bilingual.
b) The statement is true. Being bilingual means you speak two languages.
c) If you are bilingual, you speak French and English.
d) The converse is false. Counterexample: If you are bilingual, you could speak English and
Cantonese.
3. ANS:
a) Converse: If I live is Saskatchewan, then I live in Saskatoon.
Inverse: If I do not live in Saskatoon, then I do not live in Saskatchewan.
Contrapositive: If I do not live is Saskatchewan, then I do not live in Saskatoon.
b) Converse is false. Counterexample: I could live in Moose Jaw.
Inverse is false: Counterexample: If I lived in Moose Jaw, I would live in Saskatchewan.
Contrapositive is true. Since Saskatoon is in Saskatchewan, I cannot live in Saskatoon if I do not
live in Saskatchewan.
4. ANS:
a) Converse: If x2 is an odd perfect square, then x is an odd integer.
Inverse: If x is not an odd integer, then x2 is not an odd perfect square.
Contrapositive: If x2 is not an odd perfect square, then x is not an odd integer.
b) Converse is true. If x2 is an odd integer and a perfect square, then x is an odd integer.
Inverse is true. If x is not an odd integer, then x2 cannot be an odd perfect square.
Contrapositive is true. x can only be an odd integer if its square is an odd perfect square.