2023-2024 Algebra Keystone Item Sampler (Module 1)

Which monomial is the greatest common factor (GCF) of the two given monomials?

• x^2y^4

• x^4y^4

• x^6y^8

• x^12y^8

Wyatt incorrectly simplified the given expression. His work is shown below.

What error did Wyatt make when he attempted to simplify the expression?

• Going from the given expression to line 1, Wyatt divided the exponents in the numerator by 2 instead of by 3.

• Going from the given expression to line 1, Wyatt divided all the exponents by 2 but should have subtracted 3 from the exponents in the numerator and subtracted 2 from the exponents in the denominator.

• Going from line 2 to line 3, Wyatt subtracted the exponents when he should have added the exponents.

• Going from line 2 to line 3, Wyatt put the y-term in the numerator when it should have been in the denominator and he put the x-term in the denominator when it should have been in the numerator.

A local store sells different types of fruit drinks for $2 to $4 each. Jon buys 𝑥 fruit drinks and pays $36.53. Which value could be the number of fruit drinks Jon buys?

• 6

• 9

• 12

• 19

Tags

CCSS.6.EE.B.8

A polynomial expression is shown. (7x²y – 5x + 8y²) – (3x²y + 2x – 6y²) Which expression is equivalent to the polynomial expression?

• 4x²y – 3x + 2y²

• 4x²y – 7x + 14y²

• 10x²y – 7x + 14y²

• 10x²y – 3x + 2y²

Tags

CCSS.HSA.APR.A.1

Kaden wants to have exactly $600 in his bank account by the end of the next 12 months. His bank account currently has $84 in it. The bank account does not earn interest. He decides to deposit the same amount each month for the next 12 months. Which equation can be used to find the amount of money (x), in dollars, he must deposit each month to reach his goal?

• 12x + 84 = 600

• 12x - 84 = 600

• 12x + 84 = 684

• 12x - 84 = 684

Tags

CCSS.HSA.CED.A.3

Franklin is solving an equation. His first step is shown below. 4x + 7 - 3x + 10 = 12 4x - 3x + 7 + 10 = 12 Which property justifies Franklin’s first step?

• additive property of equality

• associative property of addition

• commutative property of addition

• identity property of addition

Tags

CCSS.HSA.REI.A.1

Fernando works at a clothing store . Each week, he earns $120 plus a 25% commission on any clothing he sells . The equation shown below can be used to determine the total amount (y), in dollars, Fernando earns in a week during which he sells x dollars’ worth of clothing .

y = 0 .25x + 120

The ordered pair (225, 176.25) is a solution of the equation. What does this solution represent in the context of the situation?

• In a week during which Fernando sells $176.25 worth of clothing, he earns a total of $225.

• In a week during which Fernando sells $176.25 worth of clothing, he earns $225 in commission.

• In a week during which Fernando sells $225 worth of clothing, he earns a total of $176.25.

• In a week during which Fernando sells $225 worth of clothing, he earns $176.25 in commission.

Tags

CCSS.HSF.LE.B.5

Nikki and Emily are buying tickets to a school play for their families. Nikki buys 3 adult tickets and 1 student ticket for $15. Emily buys 2 adult tickets and 2 student tickets for $14. The coordinate plane shown below displays a graph that models this situation, but the labels for the two axes are missing. What does the point of intersection on the coordinate plane represent?

• Nikki pays $3 for each ticket, and Emily pays $4 for each ticket.

• Nikki pays $4 for each ticket, and Emily pays $3 for each ticket.

• The price of each adult ticket is $3, and the price of each student ticket is $4.

• The price of each adult ticket is $4, and the price of each student ticket is $3.

Tags

CCSS.8.EE.C.8C

Ingrid collects autographs:

• -She started her collection with x autographs.

• -Then, she doubled the number of autographs in her collection.

• -Later, she received 3 additional autographs in the mail.

• -She now has between 85 and 90 autographs in her collection.

• Which inequality can be used to determine the number of autographs with which Ingrid started her collection?

• 85 < x < 90

• 85 < 2(x + 3) < 90

• 85 < 2x + 3 < 90

• 85 < 3x + 2 < 90

Rajeev unpacks 1 box that has 8 books in it. He has 4 other boxes that each have x books in them. He knows he has at least 80 books. The inequality shown below represents this situation. 4x + 8 ≥ 80 Which graph best models all the possible numbers of books in each of Rajeev’s 4 other boxes?

• A

• B

• C

• D

Tags

CCSS.7.EE.B.4B