More STAAR problems.
Administered May 2019
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.
21. Which graph best represents y = -x2 + 6x - 1?
[SEE IMAGE]
Answer: A
Since the coeffiicient of x2 is negative, the parabola opens downward. So choices B and C are eliminated.
When x = 0, y = -1. The point (0, -1) is on the line in graph A but not graph D. So choice D is eliminated. This leaves B as the answer.
You can check by trying any other point, such as the vertex. The zeroes aren't a good choice in this example because they are not integers.
22.Which graph best represents the solution set of y > 3x − 4?
F 77
G 137
H 83
J 105
Answer: H 83
I put all the data into a table in the graphing calculator and did a linear regression to find the line of best fit.
My results were y=5.5392709845975 + 0.051934923490403x (You don't need that many decimals.)
To get a prediction for 1500, substitute 1500 for x.
Then 5.54 + 0.052(1500) = 83.54, which is closest to H. (If you used more decimal places, you would get even closer.)
23. The graph of a linear function is shown in the grid.
Which equation is best represented by this graph?
A y + 2 = 7/5 (x + 7)
B y - 2 = 7/5 (x - 7)
C y + 2 = 5/7 (x + 7)
D y - 2 = 5/7 (x - 7)
Answer: D y - 2 = 5/7 (x - 7)
The choices are given in Point-Slope form, which is written in the form:
Let's look at the slope first.
There appears to be a point at (0, -3). It looks like there's a point at (4, 0), which would give a slope of 3/4. However, that isn't a choice, so I'm deducing that (4, 0) isn't really a point on the line, but is so close to the line that it is hard to tell.
There also appears to be a point at (7, 2). The choices are all full of 7s and 2s, so this looks good. The slope of a line from (0, -3) to (7, 2) would be found as follows:
There is a slope of 5/7 in choices C and D.
Next, notice that the form has minus signs in it. For y + 2 and x + 7 to be in the equation, then the point (-7. -2) would have to be on the line. However, it is not.
On the other hand, we know that the point (7, 2) is on the line. So Choice D is the answer.
24. Which expression is equivalent to (xy-6)2 for all values of x and y where the expression is defined?
F xy-36
G xy36
H x2y-12
J x2y12
Answer: H x2y-12
The rule for exponents is that the exponent goes only with the constant or the variable right next to it on its left. If there is a parenthesis there, then the exponent is a applied to everything within the parentheses.
So the x, which doesn't show an exponent, gets an exponent of 2. Because the y already has an exponent of -6, it gets multiplied by 2, which makes it -12.
Another way to look at it is this:
25. A college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses.
How many courses worth 3 credits did the student complete?
A 13
B 5
C 20
D 39
Answer:
You can set up a system of equations that says
x + y = 18
Multiply the second equation by -4 so we can eliminate the y terms
4x + 4y = 72
3x + 4y = 59
x = 13
The student took 13 three-credit course (which means the student took 5 four-credit courses).
Choices C and D are actually the number of the 59 credits earned from four- and three-credit courses.
More to come. Comments and questions welcome.
More STAAR problems.
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