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WorksheetsCh.2 Reasoning and Proofs
Total questions: 40
Worksheet time: 52mins
Name
Class
Date
1.
What comes next in the pattern?
a)
up, down, right
b)
down, up, left
c)
up, right, down
d)
down, left, right
2.
How many blocks would be in the next picture?
a)
14
b)
9
c)
10
d)
12
3.
Find the next term in the sequence:
A, D, G, J, _____
A, D, G, J, _____
a)
L
b)
M
c)
P
d)
K
4.
Give the conjecture for the following sequence:
9,6,3,0...
9,6,3,0...
a)
To find the next term, subtract 3
b)
To find the next term, divide by 3
c)
To find the next term, divide by 3 and add 3
5.
The type of reasoning where a person makes conclusions based on observations and patterns is called...
a)
Inductive reasoning
b)
Deductive reasoning
c)
Conjecture
d)
Experiments
6.
What is a conjecture?
a)
A statement believed to be true based on observations.
b)
An example which disproves an hypothesis.
c)
the performance of tricks that are seemingly magical
7.
Complete the conjecture. Think of examples to help.
The product of any two odd numbers is _____________
The product of any two odd numbers is _____________
a)
even
b)
odd
c)
zero
d)
positive
8.
How many cubes would be in the 10th figure?
a)
18
b)
16
c)
17
d)
41
9.
What are the missing numbers in this pattern?
23, 33, ___, 53, ___, 73
23, 33, ___, 53, ___, 73
a)
32, 62
b)
42, 63
c)
43, 63
d)
42, 62
10.
Using the statements:
If it is Friday, then I will get paid.
It is Friday.
Write the conclusion.
If it is Friday, then I will get paid.
It is Friday.
Write the conclusion.
a)
It is not Friday
b)
It is Friday
c)
I will not get paid
d)
I will get paid
11.
What is the converse of the statement:
If an animal is a dog, then it does not moo.
If an animal is a dog, then it does not moo.
a)
If an animal is not a dog, then it does moo
b)
If an animal can moo, then it is not a dog
c)
If an animal does not moo, then it is a dog
d)
An animal is a dog if and only if it can moo
12.
Determine whether the stated conclusion is valid.
Given: If an animal is a dog, then they like biscuits.
Sammy is a dog.
Conclusion: Sammy likes biscuits.
Given: If an animal is a dog, then they like biscuits.
Sammy is a dog.
Conclusion: Sammy likes biscuits.
a)
Invalid
b)
Valid
c)
Sammy is a Great Dane
d)
Sammy is really a cat.
13.
Draw a conclusion from the statement.
If a whole number is even, then its square is divisible by 4.
The number I am thinking of is an even number.
If a whole number is even, then its square is divisible by 4.
The number I am thinking of is an even number.
a)
Then it's not odd.
b)
Then it's a whole number.
c)
Then its square is divisible by 4
d)
Then it's even.
14.
Draw a conclusion from the statement.
If a parasite lives in or on a host organism, then it harms its host.
A virus is a parasite.
If a parasite lives in or on a host organism, then it harms its host.
A virus is a parasite.
a)
It will harm the host.
b)
I have a cold.
c)
It lives in or on a host
d)
Invalid
15.
Draw a conclusion from the statement.
If you are at least 25 year old, then you can rent a car.
You can rent a car
If you are at least 25 year old, then you can rent a car.
You can rent a car
a)
You are at least 25 years old
b)
You can rent a car
c)
You can go on a road trip
d)
Invalid
16.
When taking the converse of a statement we_____ the hypothesis and the conclusion.
a)
negate
b)
highlight
c)
switch
d)
switch and negate
17.
If it is a triangle, then it has three sides. What is the conclusion?
a)
It is a triangle
b)
It has three sides
c)
It is a polygon
d)
It sums to 180
18.
When taking the inverse of a statement, we_______ the hypothesis and the conclusion.
a)
negate
b)
switch
c)
switch and negate
d)
keep
19.
Conditional: If it does not rain, then we will have practice.
What is "If it rains today, then we will have not practice", called
What is "If it rains today, then we will have not practice", called
a)
Inverse
b)
Converse
c)
Contrapositive
d)
Counterexample
20.
Given: If I have a Siberian Husky, then I have a dog
Identify the contrapositive
Identify the contrapositive
a)
If I do not have a Siberian Husky, then I do not have a dog
b)
If I do not have a dog, then I do not have a Siberian Husky.
c)
If I have a dog, then I have a Siberian Husky
d)
If I have a dog, then I don't have a Siberian Husky
21.
If two angles are supplementary, then they have a sum of 180. Is the inverse true?
a)
Yes, if two angles are not supplementary, then they do not add to 180
b)
no, if angles don't add to 180, they can still be supplementary
c)
no, Supplementary angles add to 90
d)
yes, supplementary angles add to less than 180
22.
What does this mean?
a)
Conditional
b)
Inverse
c)
Converse
d)
Contrapositive
23.
Given, "If angles are congruent, then the measures of the angles are equal." Identify the converse.
a)
If the measures of the angles are equal, then the angles are congruent.
b)
"If angles are not congruent, then the measures of the angles are not equal."
c)
If the measures of the angles are not equal, then the angles are not congruent.
d)
If the angles are not congruent, then the measure of the angles are equal.
24.
What is the if-then-form of the following statement? "It is time for dinner if it is 6 pm."
a)
If it is 6pm, then it is time for dinner.
b)
If it is time for dinner, then it is 6pm.
c)
If you want to eat dinner, then you must eat at 6pm.
d)
None of these are right
25.
Find the length of AB if AC=25
a)
7
b)
11
c)
14
d)
25
26.
Use the figure to write and solve an equation for x.
a)
5
b)
6
c)
7
d)
8
27.
Original: If Jenny buys a guitar, then she will not buy a keyboard.
What is this? If Jenny buys a keyboard, then she will not buy a guitar.
What is this? If Jenny buys a keyboard, then she will not buy a guitar.
a)
Converse
b)
Inverse
c)
Contrapositive
d)
Negation
28.
The opposite of a statement is called a ________________________.
a)
Negation
b)
Proof
c)
Contrapositive
d)
Inverse
29.
If an animal is furry, then it is a hamster. What would be an appropriate counterexample?
a)
goldfish
b)
frog
c)
elephant
d)
cat
30.
If it is a number, then it is either positive or negative. What is an appropriate counterexample?
a)
10
b)
-2
c)
0
d)
True. There is no counterexample.
31.
What phrase does a biconditional statement use?
a)
if, then
b)
if, when
c)
if and only if
d)
then, if
32.
When can a biconditional statement be written?
a)
When the inverse and the converse are both true
b)
When the original statement (conditional statement) & the contrapositive are both true.
c)
When the converse is true.
d)
When the original statement (conditional statement) and the converse are both true.
33.
Which of the following is a biconditional statement?
a)
If you do not vote, then you are not at least 18 years old.
b)
You can vote if and only if you are 18 years old.
c)
If you are 18 years old, then you can vote.
34.
Determine the conclusion for the statement and the reason:
AB + BC =AC
AB = 4
AB + BC =AC
AB = 4
a)
4+ BC =AC ; substitution
b)
AB + 4 =AC; substitution
c)
BC = 4; substitution
d)
4 +BC = AC; SAP
35.
Angle ABC is bisected by ray BD.
State the conclusion you can make and the reason
a)
angle ABD is congruent to angle DBC; def of bisect
b)
angle ABD is congruent to angle DBC; bef of Midpoint
c)
angle ABD + angle DBC = angle ABC; AAP
d)
angle ABC is congruent to angle DBC; bef of bisect
36.
Determine a valid conclusion for the statement and the reason
Given: A is the midpoint of segment XY
a)
segment XA is congruent to segment AY; def of midpoint
b)
XA is congruent to segment AY; def of bisect
c)
XA+AY+XY, SAP
d)
XA is congruent to segment AY; substitution
37.
The Transitive Property says that if AB = BC and BC = CD, then ___________
a)
AB = BC
b)
BC = CD
c)
AB = CD
d)
C is for Cookie
38.
What is the first step to solving the equation above?
a)
Use Substitution Property
b)
Use Addition Property
c)
Use Division Property
d)
Use Distribution Property
39.
What is Ms. Chiang's favorite color?
a)
pink
b)
teal
c)
black
d)
purple
40.
What is Ms. Chiang's first name?
a)
iCarly
b)
Isabella
c)
Irene
d)
Isabelle
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