Quiz 1-1 Review

Properties

100

Identify the property shown below:

(x + 2) + 5 = (2 + x) + 5

commutative: order doesn't matter

200

Identify the property shown below:

3(1/3) = 1

Inverse of multiplication: using the opposite to cancel

300

Identify the property shown below:

If a=b, and b=c, then a=c

Transitive

400

Identify the property shown below:

2=x, x=2

symmetric

500

Provide a numerical example of the transitive property.

If 3-4 = -1, and (-1)³ = -1, then 3-4 = (-1)³

PEMDAS

100

5(6 - 2) + 3²

29

200

2[3(4 + 2) - 5]

26

300

|5 - 12| + 2⁴

23

400

3{2³ + [4(6 - 9) + 5²]}

63

500

2{[3² - (8 - 12)] + |-4|}

34

Evaluating

100

2x + 3y   when x = 4 and y = -2

2

200

(x - y)² + z    when z = 3, y = 7, z = -5

11

300

2(|x - y| + z²)   when x = -3, y = 5, z = -2

24

400

[(x - y)² / z] + |y|    when x = 8, y = -6, z = 2

104

500

[(2x² + |y|) / z] - (x - y)   when x = 4, y = -6, z = 2

9

Closure

100

Is the set of fractions closed under multiplication? If not, provide a counterexample.

No, because (2/3)(3/2) = 1 which is not a fraction.

200

Is the set of rational numbers closed under division? If not, provide a counterexample.

Yes

300

Is the set of natural numbers closed under multiplication? If not, provide a counterexample.

Yes

400

Is the set of perfect squares closed under subtraction? If not, provide a counterexample.

No, because 16 - 9 = 8 which is not a perfect square.

500

Is the set of irrational numbers closed under multiplication? If not, provide a counterexample.

No, because (sqrt 2)(sqrt 2) = 2 which is not irrational.

Classifying

100

7

R, Q, Z, W, N

200

-1.5555555555...

R, Q

300

sqrt 10

R, I

400

sqrt 15 - sqrt 15

R, Q, Z, W

500

-14/2

R, Q, Z