Unit 2 - Reasoning and Proof

What is the next term of this sequence?

1, 3, 5, 8, 11, 15, 19, 24, ...

• 29

• 25

• 30

• 32

What is the next term of this sequence?

 $\frac{1}{2}$  ,  $\frac{2}{6}$  ,  $\frac{3}{18}$  ,  $\frac{4}{54}$  

•  $\frac{4}{162}$  

•  $\frac{5}{162}$  

•  $\frac{4}{60}$  

•  $\frac{5}{60}$  

What is the next term of this sequence?

-5, 5, -6, 6, -7, 7, -8, ...

• -8

• -9

• 9

• 8

What is the missing term in this sequence?

0.95, 0.85, 0.90, 0.80, __?__, 0.75, 0.80, ...

• 0.70

• 0.85

• 0.90

• 0.95

What is the hypothesis of the given statement?

If pigs had wings, you could fly.

• Pigs have wings.

• You can fly.

• Pigs do not have wings.

• You cannot fly.

Which statement is the converse of the given statement?

If you make an insurance claim, then your rates will go up.

• If your insurance rates do not go up, then you have not made a claim.

• If you do not make an insurance claim, then your rates will not got up.

• If you insurance rates go up, then you have made an insurance claim.

• If you make an insurance claim, then your rates will not go up.

Which statement is the contrapositive of the given statement?

If a person is a banjo player, then the person is a musician.

• If a person is not a musician, then the person is not a banjo player.

• If a person is not a banjo player, then the person is a musician.

• If a person is not a banjo player, then then person is not a musician.

• If a person is a musician, then the person is a banjo player.

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.

• Z is the contrapositive of X.

• Z is the converse of X.

• Z is the inverse of X.

• Z is the retrograde of X.

Which statement is a valid conclusion based on the argument?

If a polygon is a regular pentagon, then the polygon has exactly five congruent angles.

• Therefore, the polygon is a rectangle.

• Therefore, the polygon is a regular quadrilateral.

• Therefore, the polygon has exactly five congruent angles.

• Therefore, the polygon has congruent sides.

Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?

If it is snowing heavily, then school will be canceled.

If school is canceled, the big test will not be given today.

It is snowing heavily, therefore...

• look out for the snowplows while driving to school.

• the big test will not be given today.

• the roads will be hard to drive on.

• you should call the school to see if school is canceled.