Algebra Keystone Items and Scoring Sampler

Landry is working with the expression 2√18x. Determine an integer value of x less than 10 for which 2√18x is a rational number.

Mathematical Equivalence

ON

Write an expression that is equivalent to 2√18x and is in the form a√bx, where a and b are positive integers and a ≠ 2.

Mathematical Equivalence

ON

What is the largest integer value of x for which 2√18x < 36 is true?

Mathematical Equivalence

ON

Landry is working with the three expressions shown below. Determine all the integer values of x for which 2√18x is greater than x^2 and 2√18x is also greater than 18/x.

• 1

• 0

• 4

• 2

• 3

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

• additive property of equality

• associative property of addition

• commutative property of addition

• identity property of addition

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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?

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 < 2(x + 3) < 90