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Assessment: Lesson 1-4 to Lesson 1-6

Total questions: 78

Worksheet time: 2hrs 15mins

Name
Class
Date
1.
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
2.
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
3.
Complete the conjecture.  Think of examples to help.
The product of any two odd numbers is _____________
a)
even
b)
odd
c)
zero
d)
positive
4.
Find the next term in the sequence:
A, D, G, J, _____
a)
L
b)
M
c)
P
d)
K
5.
Find the seventh term in the sequence:
A, D, G, J, _____
a)
M
b)
P
c)
S
d)
V
6.
How many cubes would be in the 10th figure?
a)
18
b)
16
c)
17
d)
41
7.
What are the missing numbers in this pattern?
23, 33, ___, 53, ___, 73
a)
32, 62
b)
42, 63
c)
43, 63
d)
42, 62
8.
Where would the next red square be?
a)
bottom left
b)
top right
c)
top left
d)
bottom right
9.
a)
1
b)
15
c)
20
d)
12
10.
What are the missing numbers in this pattern?
12, 15, ___, 21, ____, 27
a)
18,23
b)
18, 24
c)
17, 25
d)
17, 24
11.
What are the next two numbers in this pattern?
12, 17, 22, 27, ___, ___
a)
32, 37
b)
30, 37
c)
30, 33
d)
32, 35
12.
What is the rule for this pattern?
1st term:32
2nd term:36
3rd term:40
a)
4x+28
b)
4x+32
c)
x+4
d)
4x
13.
How would you describe this pattern's rule?
65, 62, 59, 56, 53, 50
a)
Subtract 2
b)
Subtract 3
c)
Subtract 4
d)
Add 3
14.
What is the rule for this pattern?
32,36,40,44
a)
add 4
b)
multiply 2
c)
subtract 4
d)
divide by 2
15.
Used to prove that a conjecture is false.
a)
Counterexample
b)
Inductive Reasoning
c)
Concluding statement
d)
Conjecture
16.
Which number is a counterexample to the following statement? : 
All numbers that are divisible by 2 are divisible by 4
a)
0
b)
12
c)
28
d)
42
17.
Which is a counterexample of: The difference of two numbers is less than the greater number.
a)
(5) - (2) = 3
b)
(-5) - (4) = -9
c)
(2) - 0 = 2
d)
(3) - (3) = 0
18.
What are the missing numbers in this pattern?
12, 15, ___, 21, ____, 27
a)
18,23
b)
18, 24
c)
17, 25
d)
17, 24
19.

Given the following observation--Each day, you get to school before your friend--what conjecture can you make?

a)

You arrived at school before your friend yesterday.

b)

You will get home before your friend.

c)

You will arrive at school before your friend tomorrow.

d)

You need a new friend.

20.

Passing score of the quiz is 50 points. Linda got a score of 55.

What is the possible conclusion?

a)

Linda did not passed the quiz.

b)

Linda passed the quiz.

c)

Linda will get a grade of 95.

d)

Linda will be promoted to another grade.

21.

Which of the following is true about the conditional statement below?

If a man is 7 feet tall, then he plays basketball.

a)

Hypothesis: a man is 7 feet tall

Conclusion: he plays basketball

b)

Hypothesis: IF a man is 7 feet tall

Conclusion: THEN he plays basketball

c)

Hypothesis: THEN he plays basketball

Conclusion: IF a man is 7 feet tall

d)

Hypothesis: he plays basketball

Conclusion: a man is 7 feet tall

22.

Which of the following is the CONVERSE of the statement below?

If an object is a bird, then it can fly.

a)

If an object can fly, then it is a bird.

b)

If an object is not a bird, then it cannot fly

c)

If an object cannot fly, then it is not a bird

d)

There is no converse of the statement

23.

Which of the following is the CONVERSE of the statement below?

If you play football, then you wear

a uniform.

a)

If you wear a uniform, then you play football.

b)

If you do not play football, then you do not wear a uniform.

c)

If you do not wear a uniform, then you do not play football.

d)

There is no converse of the statement.

24.

Which of the following is the INVERSE of the statement below?

If an object is a computer, then it

has a hard drive.

a)

If an object is not a computer, then it does not have a hard drive.

b)

If an object does not have a hard drive, then it is not a computer.

c)

If an object has a hard drive, then it is a computer.

d)

There is no inverse of the statement.

25.

Which of the following is the CONTRAPOSITIVE of the statement below?

If a species walks on two feet, then

it is human.

a)

If a species is not human, then it does not walk on two feet.

b)

If a species is human, then it walks on two feet.

c)

If a species does not walk on two feet, then it is not human.

d)

There is no contrapositive of the statement.

26.
Write the following statement in if-then form.
All students at Hermitage take an English class.
a)
If you take an English class, then you are a student at Hermitage.
b)
If you are a student at Hermitage, then you take an English. class
27.

Which of the following is a valid conditional statement for the following phrase:

An acute angle has a measure less than 90°.

a)

If an angle is acute, then it has a measure less than 90°.

b)

If an angle is not acute, then it does not have a measure less than 90°.

c)

If an angle is acute, then it is acute.

d)

If an angle does not measure less than 90°, then it is not acute.

28.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

If an angle does not have a measure less than 90°, then it is not acute.

a)

Contrapositive

b)

Converse

c)

Biconditional

d)

Inverse

29.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

If an angle is not acute, then it does not have a measure less than 90°.

a)

Inverse

b)

Contrapositive

c)

Biconditional

d)

Converse

30.

Which of the following is true about the conditional statement below?

If you are flying, then you are in a

jet.

a)

Hypothesis: you are flying

Conclusion: you are in a

jet

b)

Hypothesis: IF you are flying

Conclusion: THEN you are in a

jet

c)

Hypothesis: THEN you are in a

jet

Conclusion: IF you are flying

d)

Hypothesis: you are in a

jet

Conclusion: you are flying

31.

Which of the following is true about the conditional statement below?

If you are in Alaska, then you are

cold.

a)

Hypothesis: you are in Alaska

Conclusion: you are

cold

b)

Hypothesis: IF you are in Alaska

Conclusion: THEN you are

cold

c)

Hypothesis: THEN you are

cold

Conclusion: IF you are in Alaska

d)

Hypothesis: you are

cold

Conclusion: you are in Alaska

32.
Given, "If I have a Siberian Husky, then I have a dog." Identify the hypothesis.
a)
If I have a Siberian Husky.
b)
I have a Siberian Husky.
c)
Then I have a dog.
d)
I have a dog.
33.
Given, "If I have a Siberian Husky, then I have a dog." Identify the conclusion.
a)
If I have a Siberian Husky.
b)
I have a Siberian Husky.
c)
Then I have a dog.
d)
I have a dog.
34.
Given, "If angles are congruent, then the measures of the angles are equal." Identify the hypothesis.
a)
If angles are congruent.
b)
Angles are congruent.
c)
Then the measures of the angles are equal.
d)
The measures of the angles are equal.
35.
Given, "If angles are congruent, then the measures of the angles are equal." Identify the conclusion.
a)
If the angles are congruent.
b)
The angles are congruent.
c)
Then the measures of the angles are equal.
d)
The measures of the angles are equal.
36.
Conditional: If it does not rain today, then we will have practice.
What is this statement called: If it rains today, then we will not have practice.
a)
Converse
b)
Inverse
c)
Contrapositive
d)
Negation
37.
Conditional: If Maria gets married, then the reception will be at the country club.
What is this statement: If the reception is at the country club, then Maria will be getting married.
a)
Converse
b)
Inverse
c)
Contrapositive
d)
Negation
38.
Original: If Emily is not late to class, then she will not be marked tardy.
What is this? If Emily is late to class, then she will be marked tardy.
a)
Converse
b)
Inverse
c)
Contrapositive
d)
Negation
39.
What is the hypothesis of the given Conditional Statement?
a)
Jimmy will go to Orlando
b)
Jimmy goes on vacation
c)
Jimmy will go to Orlando
d)
Who is Jimmy?
40.

Which type of if/then statement is this?

a)

Conditional Statement

b)

Converse

c)

Inverse

d)

Contrapositive

41.

Which type of if/then statement is this?

a)

Conditional Statement

b)

Inverse Statement

c)

Converse Statement

d)

Contrapositive Statement

42.

Which type of if/then statement is this?

a)

Conditional Statement

b)

Inverse

c)

Converse

d)

THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!

43.

Match the following

a)

∼p→∼q\sim p\rightarrow\sim q  

1.

Inverse

b)

q→pq\rightarrow p  

2.

Converse

c)

p→qp\rightarrow q  

3.

Original Conditional

d)

∼q→∼p\sim q\rightarrow\sim p  

4.

Contrapositive

44.

What is the converse ( q→pq\rightarrow p  ) of the statement:

If you are 13, then you are a teenager.

a)

If you are not 13, then you are a teenager.

b)

If you are 13, then you are not a teenager.

c)

If you are a teenager, then you are 13.

d)

If you are not a teenager, then you are not 13.

45.

What is the Inverse ( ∼p→∼q\sim p\rightarrow\sim q )  of the statement: If I go to the cafeteria, then I get lunch.

a)

If I get lunch, then I go to the cafeteria.

b)

If I do not get lunch, then I do not go to the cafeteria.

c)

If I do not go to the cafeteria, then I do not get lunch.

d)

If I do not get lunch, then I do not go to the cafeteria.

46.

What is the contrapositive ( ∼q→∼p\sim q\rightarrow\sim p  ) of the statement:

If you play the guitar, then you are a musician.

a)

If you are a musician, then you play the guitar.

b)

If you are not a musician, then you do not play the guitar.

c)

If you do not play the guitar, then you are not a musician.

d)

If you play the guitar, then you are a musician.

47.

What is the inverse ( ∼p→∼q\sim p\rightarrow\sim q  ) of the statement:

If you play the guitar, then you are a musician.

a)

If you are a musician, then you play the guitar.

b)

If you are not a musician, then you do not play the guitar.

c)

If you do not play the guitar, then you are not a musician.

d)

If you play the guitar, then you are a musician.

48.

Match the following

a)

∼p\sim p  

1.

Negation of the hypothesis

b)

∼q\sim q  

2.

Negation of the conclusion

c)

pp  

3.

Hypothesis

d)

qq  

4.

Conclusion

49.

A counterexample is an example that proves a conjecture to be true.

a)

True

b)

False

50.

To fully disprove a conjecture, one needs to find only ONE counterexample.

a)

True

b)

False

51.
If an animal is furry, then it is a hamster. What would be an appropriate counterexample?
a)
goldfish
b)
frog
c)
elephant
d)
cat
52.
If it is a fraction, then it is a number between zero and one. What is an appropriate counterexample?
a)
2/3
b)
4/5
c)
1/2
d)
3/2
53.
Which is a counterexample of: If a four sided shape has two sides the same length, then it must be a rectangle.
a)
quadrilateral
b)
rectangle
c)
square
d)
triangle
54.

________, also known as logical reasoning, is the process of reasoning logically from given statements or facts to a conclusion.

a)

Inductive Reasoning

b)

Deductive Reasoning

c)

Biconditional Statements

d)

Contrapositive statements

55.
(1) If a figure is a square, then it is a polygon.
(2) Figure A is a polygon.
(3)  ???????
What belongs in line 3?
a)
Figure A is a polygon.
b)
Figure A is a circle.
c)
Figure A is a square.
d)
invalid; nothing belongs in line 3
56.

If an angle measures 40⁰, then the angle is acute.
m∠A=40m\angle A=40  
What is the logical conclusion?

a)

∠A is complementary to ∠B

b)

∠A is acute.

c)

∠A is obtuse.

d)

∠A is 40⁰

57.

Make a conclusion.

1. If a number is divisible by 10, then it is divisible by 2.

2. If a number is divisible by 2, then it is even.

a)

If a number is divisible by 10, then it is even,

b)

If a number is even, then it is divisible by 10.

c)

If a number is divisible by 2, then it is even.

d)

If a number is even, then it is divisible by 2.

58.

Make a conclusion.

  1. If the perimeter of a square is 20 ft, then the length of a side is 5 ft.
  2. If the length of a side of a square is 5 ft, then the area is 25 ft2.
a)

If the side of a square is 5 ft, then the perimeter is 20 ft.

b)

If the perimeter of a square is 20 ft, then the area is 25 ft2

c)

If the area of a square is 25 ft2, then the side length is 5 ft.

d)

If the are of a square is 25 ft2, then the perimeter is 20 ft.

59.

Write the conditional statement that follows from the pair of true statements.


If the sun is shining, then it is a beautiful day.

If it is a beautiful day, then we will have a picnic.

a)

If the sun is shining, then it is a beautiful day.

b)

If it is a beautiful day, then the sun is shining.

c)

If the sun is shining, then we will go on a picnic.

d)

If we go on a picnic, then the sun is shining.

60.
What can be concluded from the following statements?
If Tom goes fishing then he brings a pole.
If Tom brings his pole then he catches a fish.
a)
If Tom goes fishing then he catches a fish.
b)
If Tom brings his pole then he goes fishing
c)
 If Tom catches a fish then he brought his pole.
d)
If Tom brings his pole then he catches a fish.
61.

Determine if the conjecture is valid.


Given: If you are in California, then you are in the west coast. If you are Los Angeles, then you are in California.

Conjecture: If you are in Los Angeles, then you are in the west coast.

a)

No, the conjecture is not valid.

b)

Yes, the conjecture is valid.

62.

IF All even numbers are divisible by 2

AND 28 is even

THEN

a)

2 is an even number

b)

28 is divisible by 2

c)

All numbers are divisible by 2

d)

All numbers are even numbers

63.

IF an apple a day keeps the doctor away.

AND Joe ate an apple every day.

THEN

a)

He will get a stomach ache

b)

This makes no sense, what do apples have to do with doctors?

c)

Joe will be spending lots of time at the dentists office

d)

The doctor will stay away

64.
How are the two statements given below related to each other?
X: If you run for 10 minutes, then you will raise your heart rate.
Z: If you do not run for 10 minutes, then you will not raise your heart rate.
a)
Z is the contrapositive of X.
b)
Z is the converse of X.
c)
Z is the inverse of X.
d)
no idea
65.
What is a valid counterexample for the following statement? "If an animal is a panther, then it lives in the forest."
a)
It lives in a zoo.
b)
No counterexample, this is true.
c)
It lives in an aquarium.
d)
It is a monkey
66.
Using the Law of Detachment, what can you conclude?
If you earn more than $14, then you can buy a new CD.
You earn $15.
a)
you can buy a new CD
b)
you cannot buy a new CD
c)
no conclusion can be made
d)
you earn more than $14
67.
Draw a conclusion from the statement.
Given: If you are at least 25 year old, then you can rent a car.
Clay can rent a car.
Conclusion: ?
a)
Clay is at least 25 years old
b)
Clay can rent a car
c)
Clay can go on a road trip
d)
Invalid
68.
Draw a conclusion from the statement.
Given: If you live in Orlando, then you live in Florida.
Roger lives in Orlando.
Conclusion: ?
a)
Roger lives in Disney Land
b)
Roger is an old person.
c)
Roger lives in Florida
d)
Roger lives in Orlando
69.

If a figure is a square, then it is a rectangle. If a figure is a rectangle, then it has 4 right angles.


What can you conclude?

a)

If a figure has 4 right angles, then it is a square.

b)

If a figure is a square, then it has 4 right angles.

c)

Nothing

d)

If a figure is a rectangle, then it is a square with 4 right angles.

70.

How would you describe the Law of Detachment symbolically?

a)

if p -> q is true and q is true; then p is true

b)

if p -> q is true and p is true; then q is true

c)

if p -> q and q -> r, then p -> r

71.

Use the Law of Detachment to determine what you can conclude from the given information, if possible.


If you passed the final, then you pass the class. You passed the final.

a)

You passed the class.

b)

You didn't pass the class

c)

Not possible

72.

Use the Law of Detachment to determine what you can conclude from the given information, if possible.


If your parents let you borrow the car, then you will go to the movies with your friend. You will go to the movies with your friend.

a)

Your parents let you borrow the car.

b)

Your parents didn't let you borrow the car.

c)

Not possible

73.

How would you describe the Law of Syllogism symbolically?

a)

if p -> q is true and q is true, then p is true.

b)

if p -> q is true and p is true, then q is true.

c)

if p -> q is true and q -> r is true, then p -> r is true

74.

Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements, if possible.

If x < -2, then |x| > 2. If x > 2, then |x| > 2.

a)

If x < -2, then x > 2.

b)

If |x| > 2, then x > 2.

c)

Not possible

75.

Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements, if possible.


If a figure is a rhombus, then the figure is a parallelogram. If a figure is a parallelogram, then the figure is a quadrilateral.

a)

If a figure is a rhombus, then the figure is a quadrilateral.

b)

If a figure is a quadrilateral, then the figure is a rhombus.

c)

Not possible

76.

Which law of logic is illustrated by these statements?


If you miss practice the day before a game, then you will not be a starting player in the game.

You miss practice on Tuesday. You will not start the game Wednesday.

a)

Law of Detachment

b)

Law of Syllogism

c)

Speed Limit

d)

None of the above

77.

Which law of logic is illustrated by the following statements?


If <1 and <2 are vertical angles, then <1 is congruent to <2. If <1 is congruent to <2, then m<1 = m<2.

If <1 and <2 are vertical angles, then m<1 = m<2.

a)

Law of Detachment

b)

Law of Syllogism

c)

5th Amendment

d)

Not possible

78.

If the school cafeteria sells pizza today, Greg is going to eat four pieces. Pizza is on sale for school lunch today.


Using deductive reasoning, what statement can you make based on this information?

a)

Lots of people will buy pizza.

b)

The school cafeteria sells pizza.

c)

Greg will eat four pieces of pizza.

d)

Greg needs to go on a diet.

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