Friday, December 11, 2020

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

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.





1. Which expression is equivalent to SQRT(147)?

A 3 SQRT(7)
B 7 SQRT(3)
C 21 SQRT(7)
D 49 SQRT(3)

Answer: 7 SQRT(3)
Factor the number in the square root, and pair the like factors up.

SQRT(147) = SQRT(3 * 7 * 7) = 7 SQRT(3)

The square root of 49 is 7, and 49 is a factor of 149, so it can be separated and rooted.



2. A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote. They wrote a total of 46 songs.

Which system of equations models this situation if the drummer wrote d songs and the guitarist wrote g songs?

F g = 2d - 8 ; g + d = 46
G g = 8 - 2d ; g = 46 - d
H d = 2g - 8 ; d = 46 - g
J d = 8 - 2g ; d + g = 46

Answer: F g = 2d - 8 ; g + d = 46
Please understand why Choices F and H can be eliminated immediately. The first equation in both choices would work if there were a total of 8 songs written. Think of the difference of having $20 less than you had originally, and originally having $20 and spending some amount of money.

Translate guitarist wrote 8 fewer than twice the drummer into
g equals subtract 8 from two times d, or g = 2d - 8

The total output of the two writers is 46 is g + d = 46. That being said, the other ways it is written -- g = 46 - d and d = 46 - g -- are not incorrect.





3. Which graph best represents the solution set of y ≤ -4x?



Answer: C
The ≤ symbol tells us that we will be shading underneath a solid line. The -4 cofficient of x tells us that it is a steep slope down and to the right.

That is Choice C. Choices A and D have the line y = -4, not y = -4x. Choice B has a broken line and is graphed above.



4. The graph of f(x) = x2 was transformed to create the graph of g(x) = (x - 7.5)2. Which of these describes this transformation?

F A horizontal shift to the right 7.5 units
G A horizontal shift to the left 7.5 units
H A vertical shift down 56.25 units
J A vertical shift up 56.25 units

Answer: F A horizontal shift to the right 7.5 units
This is pretty much a definition question, but you could graph them both in your calcultor and see the shift.

The vertex of a parabola is at the point (h, k) in the formula

y = a(x - h)2 + k
The vertex of f(x) = (0, 0) and the vertex of g(x) = (7.5, 0). That means a shift 7.5 units to the right.

Had the 7.5 been the k instead of the h, the graph would have shifted up or down, but only by 7.5 spaces.



5. A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f(x) = 20x + 4.

What is the range of the function for this situation?

A {0, 1, 2, 3, 4, 5, 6}
B {4, 24, 44, 64, 84, 104, 124}
C {0, 2, 4, 6}
D {4, 44, 84, 124}

Answer: C
The range is the output, the dependent variable, the f(x) values, y. All that.

If the valid inputs are 0, 1, 2, 3, 4, 5, 6 because you can you that many pairs of weights, then the outputs are 4, 24, 44, 64, 84, 104, 124.

Choice A is the Domain. Choice C is the domain if you misread the question concerning the pairs of weights. Choice D is the range if you misread the question regarding pairs of weights.





More to come. Comments and questions welcome.

More STAAR problems.

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