Keystone Algebra 2023 Sampler Module 1

Which monomial is the greatest common factor (GCF) of x⁴y⁸ and x⁶y⁴ ?

• x²y⁴

• x⁴y⁴

• x⁶y⁸

• x¹²y⁸

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 d fruit drinks and pays $36.53. Which value could be the number of fruit drinks Jon buys?

• 6

• 9

• 12

• 19

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

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

• additive property of equality

• associative property of addition

• commutative property of addition

• identity property of addition

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.

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.

• 85 < x < 90

• 85 < 2(x + 3) < 90

• 85 < 2x + 3 < 90

• 85 < 3x + 2 < 90

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