Tuesday, March 02, 2021

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.

I had to put these on hold for a while. They're back now.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

More STAAR problems.

Administered May 2017

Read each question carefully. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question.

31. A student used f(x) = 5.00(1.012)x to show how the balance in a savings account will increase over time. What does the 5.00 represent?

A The interest the savings account earned for the first year
B The annual interest rate of the savings account
C The number of years the savings account has earned interest
D The starting balance of the savings account

Answer: D The starting balance of the savings account
I hope the student was using a spreadsheet and showing what happens over many, many years, because $5.00 at 1.2% interest won't accrue to much of anything. And in the real world, banking fees would eat up that money, leaving the student owing money.
But as far as the test is concerned, 5.00 is the Principal, the starting money.

32. The graph of a function is shown on the grid.

Which ordered pair best represents the location of the y-intercept?

F (1/3, 0)
G (0, -2)
H (0, 1/3)
J (-2, 0)

Answer: G (0, -2)
At the y-intercept, the value of x is 0, so Choice F and Choice J are eliminated.
It's also below the x-axis, so the value of y is negative, making G the only Choice.
(1/3, 0) is a good approximation for the x-intercept.

33. Researchers in Antarctica discovered a warm sea current under a glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate of 0.06 m per day.

Which function can be used to find the thickness of the ice shelf in meters x days since the discovery?

A t(x) = 450 - 0.06x
B t(x) = -0.06(x + 450)
C t(x) = 450 + 0.06x
D t(x) = 0.06(x + 450)

Answer: A t(x) = 450 - 0.06x
The thickness of 450 is the initial value (the y-intercept) and doesn't take a variable. The 0.06 is a daily decrease, so it gets subtracted every day for x days.
Choice C is no good because that shows the ice increasing in size, not decreasing.

34. What is the positive solution to the equation 0 = (1/3)x2 - 3?

Record your answer and fill in the bubbles on your answer document.

Answer: 3

0 = (1/3)x2 - 3
0 = x2 - 9
9 = x2
x = 3 (positive solution)

You could also have factored the Difference of Squares and continued from there, getting the same result.

35. The amount of fertilizer in a landscaping company’s warehouse decreases at a rate of 3% per week. The amount of fertilizer in the warehouse was originally 78,000 cubic yards.

Which function models the amount of fertilizer in cubic yards left after w weeks?

A f(w) = 0.97(78,000)w
B f(w) = 1.03(78,000)w
C f(w) = 78,000(0.97)w
D f(w) = 78,000(1.03)w

Answer: C f(w) = 78,000(0.97)w
Eliminate the first two immediately. The number 78,000 represents the original amount that the decay rate will be applied to. Since it is decreasing (decaying) the rate has to be less than 1.00, so Choice D is eliminated.
A 3% decrease means subtract 1.00 - 0.03 = 0.97, which is the rate in Choice C.

More to come. Comments and questions welcome.

More STAAR problems.

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