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.
16. The water level of a river was measured each day during a two-week period. The graph
models the linear relationship between the water level of the river in feet and the number of
days the water level was measured.
Which statement best describe the y-intercept of the graph?
F The water level increased by 0.25 ft per day.
G The maximum water level was 19.5 ft.
H The initial water level was 16 ft.
J The water level was measured for 14 days.
Answer: H The initial water level was 16 ft.
The y-intercept represents the initial amount in a graph or fuction.
The other statements are all true, but have nothing to do with the y-intercept. In F, the incease in water level per day is the slope. In G, the maximum water level is a part on the graph, but not the initial point. In J, we've established the domain, 0 - 14, which concerns the x values, not the y values.
17. There are 1,024 players in a tennis tournament. In each round, half the players are
eliminated. Which function can be used to find the number of players remaining in the
tournament at the end of x rounds?
A f(x) = 1,024(1.50)x
B f(x) = 1,024(0.50)x
C f(x) = 1,024(1.05)x
D f(x) = 1,024(0.05)x
Answer: B f(x) = 1,024(0.50)x%
If half the teams are eliminated, then the rate of decay is .50, or 50%.
Choice A shows a 50% increase, meaning more players are joining the tournament. Choice C shows a 5% increase. Choice D shows a 95% decrease, with only 5% advancing to the next round.
18. Which statement about g(x) = x2 − 576 is true?
F The zeros, −288 and 288, can be found when 0 = (x + 288)(x − 288).
G The only zero, 288, can be found when 0 = (x − 288)2.
H The zeros, −24 and 24, can be found when 0 = (x + 24)(x − 24).
J The only zero, 24, can be found when 0 = (x − 24)2.
Answer: H The zeros, −24 and 24, can be found when 0 = (x + 24)(x − 24).
The Difference of Squares rule states that x2 - n2 can be factored into (x + n)(x - n). The "inner" and "outer" terms when multiplied form a zero pair and cancel out.
In this problem, 576 represents n2, so n is SQRT(576), which is 24, not 288.
19. Which graph best represents the solution set -4x < 6y - 54?
Answer: A
Two questions to ask yourself: Is it a solid or a broken line? Is (0, 0) part of the solution?
Since we want "less than or equal to" (<) and not just "less than" (<), the graph needs to have a solid line, so Choices B and C are eliminated.
Substitute (0, 0) and we get 0 < 0 - 54, which is not a true statement. Therefore, (0, 0) is not a part of the solution, and that side of the line cannot be shaded. Choice D is eliminated.
The longer method involves rewriting the problem into slope-intercept form.
6y - 54 > -4x
6y > -4x + 54
y > -4/6 x + 9
At this point, you can see that the line needs to be shaded above, not before. Also, you can see that choice A have a slope of -4/6 (or -2/3), while D has a slope of -6/4 (or -3/2).
20.Given f(x) = 1/3 (4 - x)2, what is the value of f(16)?
Record your answer and fill in the bubbles on your answer document.
Answer:
= 1/3 (-12) 2
= 1/3 (144)
= 48
More to come. Comments and questions welcome.
More STAAR problems.
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