Tuesday, November 17, 2020

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2019, cont.

Continuing with the State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2019.

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:

y - y1 = m(x - x1)

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:
m = (y2 - y1) / (x2 - x1) = (2 - -3) / (7 - 0) = 5 /7

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:

(xy-6)2 = (xy-6)(xy-6) = x x y-6 y-6 = x2 y-12




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

3x + 4y = 59
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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