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

Tags

CCSS.7.EE.A.1

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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?

Tags

CCSS.HSA.CED.A.3

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

• 85 < 2(x + 3) < 90