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.
Which statement is the best interpretation of one of the values in this function?
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.
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.
For one day of work, what is the range of the function for this situation?
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.
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
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.
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