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.





46. Scientists are studying a bacteria sample. The function f(x) = 245(1.12)^x gives the number of bacteria in the sample at the end of x days.

Which statement is the best interpretation of one of the values in this function?

F The initial number of bacteria is 12.
G The initial number of bacteria decreases at a rate of 88% each day.
H The number of bacteria increases at a rate of 12% each day.
J The number of bacteria at the end of one day is 245.

Answer: H The number of bacteria increases at a rate of 12% each day.
Taking apart the function: 245 is the initial number, and 1.12 indicates a 12% increase.

The initial number is not 12. The bacteria are increasing, not decreasing. The starting value is 245, not the amount after 1 day.



47. The daily cost of hiring a plumber, y, to work x hours on a repair project can be modeled using a linear function. The plumber charges a fixed cost of $80 plus an additional cost of $45 per hour. The plumber works a maximum of 8 hours per day.

For one day of work, what is the range of the function for this situation?

A 0 ≤ x ≤ 8
B 80 ≤ y ≤ 440
C 0 ≤ x ≤ 10
D 45 ≤ y ≤ 685

Answer: B 80 ≤ y ≤ 440
The plumber charges $80 before any hours of work have been done. This will be the minimum charge. Only one choice, B, has this as the minimum.

Choice A refers to the amount of hours he might work. Choice C doesn't seem to make any sense. Choice D has the equation backward with a fixed $45 and $80 per hour.

48. The graph of g(x) = x² was transformed to create the graph of h(x) = -(x/4)². Which of these describes the transformation from the graph of g to the graph of h?

F A reflection over the x-axis and a horizontal stretch
G A reflection over the y-axis and a horizontal stretch
H A reflection over the x-axis and a vertical stretch
J A reflection over the y-axis and a vertical stretch

Answer: F A reflection over the x-axis and a horizontal stretch
You can put both of these in your graphing calculator and just look at them.

The negative coefficient means that the parabola means that it will be flipped upside down, reflected across the x-axis. The 1/4 (which will become 1/16 when it's squared) will flatten out the curve, which is to say that is will be stretched out horizontally.



49. Which expression is equivalent to

(10q²w⁷) / (2w³) X (4(q⁶)²) / (w^-5)
for all values of q and w where the expression is defined?

A (32q⁷) / w
B 20q¹⁷w⁹
C 32q⁷w⁹
D 20qw

Answer: B 20q¹⁷w⁹

In the first fraction, simplify 10/2 to get 5. Simplify w⁷ / w³ to get w⁴.

In the second fraction, (q⁶)² becomes q¹². Also, w^-5 in the denominator becomes w⁵ in the numerator.

At this point, there is nothing left in the denominator.

In the numerator, there is (5)(4) = 20, w⁴ * w⁵ = w⁹, q⁵ * q¹² = q¹⁷.



50. A graph of a quadratic function is shown on the grid.

Which coordinates best represent the vertex of the graph?

F (2.4, 0)
G (0, −1)
H (−0.4, 0)
J (1, −2)

Answer: J (1, −2)
The vertex is that minimum point at the bottom of the curve. The x-coordinate is 1, and the y-coordinate is -2. (1, -2).

Choices F and H appear to be the zeroes (roots) of the function. Choice G is the y-intercept, which is rarely important with quadratic functions (in my own opinion).

More to come. Comments and questions welcome.

More STAAR problems.