STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2018, cont.

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

More STAAR problems.

Administered May 2018

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.





6. Which expression is equivalent to (144k²r¹⁴)^(1/2) for all positive values of k and r?

F 12kr⁷
G 72k²r¹⁴
H 144kr⁷
J 12k²r¹⁴

Answer: F 12kr⁷
The 1/2 exponent gets applied to each of the factors in the parentheses. When a variable with an exponent is raised to another exponent, you multiply the exponents. So k²r¹⁴ becomes k¹r⁷. (We don't need to write the 1.)

The 144 also gets the 1/2 exponent, and 144^(1/2) is the square root of 144, which is 12.



2. The graph shows the height in feet of an object above the ground t seconds after it was launched from the ground.

Which function is best represented by the graph of this situation?

A h(t) = -16t² - 64t
B h(t) = -16t² + 128t - 256
C h(t) = -16t² + 64t
D h(t) = -16t² - 128t - 256

Answer: C h(t) = -16t² + 64t
Notice that the y-intercept is 0, so Choices B and D can be eliminated.

If you substitute t = 2 into Choice A, you will get -16(2)² - 64(2), which you can see is a negative number before you put it into your calculator. (It's -192.)

If you substitute t = 2 into Choice C, you will get -16(2)² + 64(2), which is 64.

8. What value of n makes the equation 4(0.5n − 3) = n − 0.25(12 − 8n) true?

F 3
G -9
H 0
J -15

Answer: G -9
Solve the equation for n:

4(0.5n − 3) = n − 0.25(12 − 8n)
2n - 12 = n - 3 + 2n
-12 = n - 3
-9 = n

Check:
4(0.5(-9) - 3) = -9 - 0.25(12 - 8(-9))
4(-4.5 - 3) = -9 - 0.25(12 + 72)
4(-7.5) = -9 - 0.25(84)
-30 = -9 - 21
-30 = -30 (check!)



9. In a sequence of numbers, a₃ = 0, a₄ = 6, a₅ = 12, a₆ = 18, and a₇ = 24. Based on this information, which equation can be used to find the nth term in the sequence, a_n?

A a_n = 6n + 18
B a_n = -18n + 6
C a_n = 6n - 18
D a_n = 18n - 6

Answer: C a_n = 6n - 18
The Common Difference in this arithmetic is 6 - 0 = 6, 12 - 6 = 6, 18 - 12 = 6, etc. So the coefficient of the variable is 6. Eliminate choices B and D.

At this point, we would need to work backward to find the y-intercept (a₀), but it isn't necessary. The choices are -18 and +18. However, a₆ is 18 and the numbers are getting larger as the sequence continues. So it has to be -18, which is Choice C.

Working backward: a₃ = 0, so a₂ = 0 - 6 = -6, then a₁ = -6 - 6 = -12, and a₀ = -12 - 6 = -18.



10. The value of y varies directly with x. If x = 3, then y = 21. What is the value of x when y = 105??

F 3/5
G 1 2/3
H 7
J 15

Answer: J 15
It the value of y varies directly with x, then the slope of the line is simply the ratio y/x. (The y-intercept of the line is 0.)
This means that a proportion can be set up:

y / x = y / x
21 / 3 = 105 / x
21x = 315
x = 15

Or you might have noticed that 21/3 = 7, so the ratio is 7/1. Divide 105 by 7, and you get 15, which is J.

You might also have divided 105 / 21 = 5 and then multiplied 3 x 5 = 15.

Honestly, I've surprised that 735 was not one of the incorrect choices. Someone was likely to find the ratio 7 and then multiply instead of divide.

More to come. Comments and questions welcome.

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