## Friday, February 26, 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.

More STAAR problems.

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.

21. The population of Center City is modeled by exponential function f, where x is the number of years after the year 2015. The graph of f is shown on the grid.

Which inequality best represents the range of f in this situation?
A x ≥ 0
B y ≥ 250,000
C 0 ≤ x ≤ 110
D 250,000 ≤ y ≤ 1,000,000

The range is composed of all the possible y values. This eliminates choices A and C.
The line starts halfway between 200,000 and 300,000. Both choices use 250,000. However the arrow at the end of the line indicates that the function continues upward, above the 1,000,000 line at the top of the graph. So the answer is B.

22. A sequence can be generated by using an = 4a(n - 1), where a1 = 6 and n is a whole number greater than 1. What are the first four terms in the sequence?

F 6, 24, 96, 384
G 6, 10, 14, 18
H 6, 20, 100, 500
J 6, 20, 76, 300

Answer: F 6, 24, 96, 384
Each term in the sequence is FOUR TIMES larger than the previous one, with the first tern being 6. That means 6 X 4 = 24, 24 X 4 = 96, and 96 X 4 = 384, which is choice F.
Choice G would work if the sequence was an = 4 + a(n - 1), adding FOUR MORE than the previous term.
Choice H and J assume you made a blunder with the (n - 1) expression. Choice H multiplies by 5 X 4, instead of 6, but then multiplies by 5 after that for some reason. Choice J subtracts one from a(n - 1> and then multiplies by 4.

23. What is the equation in slope-intercept form of the line that passes through the points (-4, 47) and (2, -16)?

A y = (-21/2)x + 979/21
B y = (-2/21)x + 979/21
C y = (-21/2)x + 5
D y = (-2/21)x + 5

Answer: C y = (-21/2)x + 5
The slope of the line is (y2 - y1) / (x2 - x1), which is (47 - -16) / (-4 - 2), so m = 63/-6 = - 21/2. This elimates B and D, which were done upside down.
Picking one of the points, you plug in what we know:

y = m x + b
-16 = (-21/2)(2) + b
-16 = -21 + b
5 = b

So the equation is y = (-21/2)x + 5, which is Choice C.

24. The graph of f(x) = x2 is transformed to create the graph of h(x) = 2f(x). Which graph best represents f and h?

If h(x) = 2f(x), then h(x) = 2x2, which is a parabola with a vertex of zero that will climb the graph more quickly than f(x) would. This is a dilation, not a translation.
Choice F is incorrect because it shifts (translates) the parabola two spaces up, instead of doubling the y-coordinate.
Choice H is incorrect because it shifts the parabola two spaces to the right.
Choice G looks correct, but it reverses functions f and h.
Choice J is correct.

25. A student is ordering a flower arrangement. She can choose any combination of roses and carnations for her flower arrangement, and she does not want to spend more than \$30. If roses cost \$3 each and carnations cost \$2 each, which inequality represents all possible combinations of x roses and y carnations?

A 3x + 2y < 30
B 3x + 2y ≤ 30
C 2x + 3y > 30
D 2x + 3y ≤ 30

Answer: D 2x + 3y ≤ 30
This entire question boils down to knowing that "not ... more than \$30" means "less than or equal to \$30", with is Choice D.

More to come. Comments and questions welcome.

More STAAR problems.