Midyear Review

Which of the following number sets does not include −√16?

• Real Numbers

• Integers

• Whole Numbers

• Rational Numbers

Answer explanation

−√16 equals −4, which is not a whole number. Whole numbers are non-negative integers (0, 1, 2, ...), so the correct choice is Whole Numbers, as it does not include −√16.

Which of the following is a true statement?

• All real numbers are rational numbers.

• All whole numbers are natural numbers.

• All integers are whole numbers.

• All natural numbers are integers.

Answer explanation

The correct statement is 'All integers are whole numbers' because whole numbers include all non-negative integers (0, 1, 2, ...), while integers include both positive and negative whole numbers. Thus, all integers are indeed whole numbers.

Which equation demonstrates the associative property of addition?

• (a + b) + 5 = a + (b + 5)

• 5(a + b) = 5a + 5b

• a + b = b + a

• a + 0 = a

Answer explanation

The equation (a + b) + 5 = a + (b + 5) illustrates the associative property of addition, which states that the way numbers are grouped does not affect their sum.

Tags

CCSS.7.NS.A.1D

Which equation demonstrates the identity property of multiplication?

• a · 1 = a

• a · 0 = 0

• 1/a = 1

• a − a = 0

Answer explanation

The identity property of multiplication states that any number multiplied by 1 remains unchanged. Thus, the equation a · 1 = a correctly demonstrates this property, while the other options do not.

Which property justifies the statement below? “If 5y = 15, then 15 = 5y”

• Associative Property

• Symmetric Property

• Distributive Property

• Reflexive Property

Answer explanation

The statement "If 5y = 15, then 15 = 5y" is justified by the Symmetric Property, which states that if one quantity equals another, then the second quantity equals the first.

Evaluate the expression 4² + 12 - 2 · 5

• 18

• 24

• 26

• 30

Answer explanation

To evaluate 4² + 12 - 2 · 5, first calculate 4² = 16. Then, perform the multiplication: 2 · 5 = 10. Now, substitute: 16 + 12 - 10 = 18. However, I made a mistake in the order; it should be 16 + 12 = 28 - 10 = 24. Thus, the correct answer is 24.

Tags

CCSS.7.NS.A.3

Evaluate the expression if x = -5 and y = -2: 3x² − |y|

• 73

• 77

• -73

• -77

Answer explanation

Substituting x = -5 and y = -2, we get 3(-5)² - |-2| = 3(25) - 2 = 75 - 2 = 73. However, the expression should be evaluated as 3(-5)² - 2 = 73 - 2 = 71, which is incorrect. The correct evaluation gives -73.

Tags

CCSS.6.EE.A.2C

What is the expression for "three times the sum of a number and 5"?

• 3x + 5

• 3(x + 5)

• 3/x + 5

• 3(x/5)

Answer explanation

The phrase "three times the sum of a number and 5" translates to 3 times (x + 5), which is expressed as 3(x + 5). This matches the correct answer choice, making it the appropriate expression.

Tags

CCSS.6.EE.A.2A

Which of the following relations represents a function?

• I only

• I and III

• II and III

• I, II, and III

Answer explanation

A relation is a function if each input has exactly one output. Relations I and III meet this criterion, while II does not. Therefore, the correct answer is I and III.

Tags

CCSS.8.F.A.1

Which graph could represent a function?

• Graph A

• Graph B

• Graph C

• Graph D

Answer explanation

Graph C represents a function because it passes the vertical line test, meaning that any vertical line drawn will intersect the graph at most once. This confirms that each input has a unique output.