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.
6. The area of a rectangle is 54x9y8 square yards. If the length of the rectangle is 6x3y4
which expression represents the width of the rectangle in yards?
F 9x3y2
G 48x6y4
H 9x6y4
J 60x12y12
Answer: H 9x6y4
Divide 54x9y8 by 6x3y4
54 divided by 6 is 9.
x9 divided by x3 is x6, because 9 - 3 = 6
y8 divided by y4 is y4 becayse 8 - 4 = 4
7. The total number of seats in an auditorium is modeled by f(x) = 2x2 - 6x, where x represents the number of rows of seats. How many rows are there in the auditorium if it has a total of 416 seats?
A 32
B 13
C 20
D 16
Answer: D 16
When does 2x2 - 6x = 416? Set the equation equal to 0 and factor.
x2 - 3x - 208 = 0
What are two factors of -208 that add up to -3? They must be close together.
Knowing that 142 is 196, I might guess 13, which goes into 208 16 times. Good guess. Yeah, me!
-208 factors into -16 and 13
(x - 16)(x + 13) = 0
x = 16 or x = -13
We discard -13 because the number of rows must be positive.
8. The graph of an exponential function is shown on the grid.
F Line q
G Line r
H Line s
J Line t
Answer: H Line s
In an exponential graph, the asymptote is the horizontal line that the function draws nearer and nearer to, without ever intersecting, even if it's own by a millionth of a unit.
9. Which situation best represents causation?
A When the number of bus stops increases, the number of car sales decreases.
B When fewer firefighters report to a house fire, the damage caused by the fire decreases.
C When ice cream sales increase, incidents of sunburn increase.
D When it rains several inches, the water level of a lake increases.
Answer: D When it rains several inches, the water level of a lake increases.
If it rains, water levels will rise. One causes the other.
Increasing bus stops doesn't necessaily affect car sales. People aren't suddenly going abandon their cars in favor of taking the bus.
If there are fewer firefighters, fire damage would likely increase since for lack of people to put out the fire.
Ice cream sales will spike in the summer at the same time that sunburn incidents increase. But these are both caused by the heat of the Sun. One doesn't cause the other.
Which function is best represented by this graph?
10. The graph of a quadratic function is shown on the grid.
F f(x) = x2 + 3x - 4
G f(x) = -x2 - 3x + 4
H f(x) = x2 - 3x - 4
J f(x) = -x2 + 3x + 4
Answer: J f(x) = -x2 + 3x + 4
The parabola opens downward, so the a value must be negative. Eliminate Choices F and H.
You could graph the other two. Or you could find the zeroes. Or rewrite them into vertex form, etc. You could also substitute -4 and 1 for x and see if you get 0.
Choice G has -3x for the b term and J has +3x. If you look for the Axis of Symmetry, then x = -b/2a.
Either x = -(-3)/(2(-1)) = 1.5 or x = -(3)/(2(-1)) = -1.5
From the graph, the Axis of Symmetry is x = -1.5, so we need the b term to be +3, which is Choice J.
More to come. Comments and questions welcome.
More STAAR problems.
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