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.

*21. The graph shows the linear relationship between the maximum area in square feet that can
be painted and the number of gallons of paint used.
*

Which of these best represents the rate of change of the maximum area painted with respect to the number of gallons of paint used?

A 200 ft

B 1/200 ft

C 400 ft

D 1/400 ft

Which of these best represents the rate of change of the maximum area painted with respect to the number of gallons of paint used?

A 200 ft

^{2}/galB 1/200 ft

^{2}/galC 400 ft

^{2}/galD 1/400 ft

^{2}/gal

**Answer: C 400 ft ^{2}/gal **

If you go to 1 gallon on the x-axis, that lines up with 400 ft

^{2}on the y-axis. Change in y / Change in x, it is 400 ft

^{2}/ gal.

*22. What are the solutions to (x + 7)*

F -74 and 88

G -2 and 16

H -88 and 74

J -16 and 2

^{2}= 81?F -74 and 88

G -2 and 16

H -88 and 74

J -16 and 2

**Answer: J -16 and 2**

Start with: (x + 7)^{2} = 81

Take the square root of both sides: x + 7 = __+__ 9

Split and solve: x + 7 = 9 or x + 7 = -9

x = 2 or x = -16

You could also have plugged in 2 for x and saw that it was a correct solution, while all of incorrect choices would be way off.

*23. What appears to be the domain of the part of the exponential function graphed on the grid?
*

A -1

B -1

C 5.3

D 5.3

A -1

__<__x__<__3B -1

__<__y__<__3C 5.3

__<__x__<__27D 5.3

__<__y__<__27

**Answer: A -1 < x < 3 **

This gets repeated many times, but the domain is the x values. Eliminate Choice B and D.

The leftmost point has an x coordinate of -1, so the correct choice is A.

Choice D would be the answer if your were asked about the range.

Choices B and C are just nonsense.

*24. The tables of ordered pairs represent some points on the graph of lines q and v.
*

Which system of equations is represented by lines q and v?

F 21x − y = 9 ; 5x + 6y = 40

G 3x − y − = −27 ; x + 2y = 16

H 21x −y = 9 ; 5x + 6y = 20

J 9x − y = −27 ; x + 2y = 8

Which system of equations is represented by lines q and v?

F 21x − y = 9 ; 5x + 6y = 40

G 3x − y − = −27 ; x + 2y = 16

H 21x −y = 9 ; 5x + 6y = 20

J 9x − y = −27 ; x + 2y = 8

**Answer: G 3x − y = −27 ;
x + 2y = 16**

Working backward from the answers is the quickest route. You could create the linear equations for each table, but then you would have to rewrite them in Standard form to match the choices.

My preference is to work with 0 when it is available. Looking at the table for line q, we see the point (-9, 0). Therefore x = -9 and y = 0 is a solution to one of those equations. (Note that it doesn't have to be the first of the pair. Nothing says that it is.)

21(9) - 0 =/= 9. 5(-9) + 0 =/= 40.

3(-9) - 0 = -27. (Choice G looks good so far).

21(9) - 0 =/= 0. 5(-9) + 0 =/= 20.

9(-9) - 0 =/= -27. -9 + 0 =/= 8.

Only Choice G is possible. Check the second equation for (0, 8). 0 + 2(8) = 16. Check!

*25. Which situation does NOT show causation?
A When the student population at a school increases, the number of teachers at the school increases.
B When the amount of sugar in a quart of apple juice is reduced, there are fewer calories in each serving.
C When there are more workers on a project, the project is completed in less time.
D When there is more protein in an athlete’s diet, the athlete scores more points in a game.
*

**Answer: D When there is more protein in an athlete’s diet, the athlete scores more points in a game.**

If you get more students, then you need more teachers. One causes the other.

If you reduce the sugar, you reduce the number of calories.

If you put more workers on a project, it gets completed in less time. (There's a point of diminishing returns, but that's a little beyond the level of this question. Also, there's a joke about the project being a symphony -- a bigger orchestra won't complete it sooner. But this is more about "man-hours" to finish.)

There are many factors in athletic performance. Is increasing protein one of them? It doesn't show causation. Maybe if said what the protein did, or how that affected performance, you might show causation. But this itself does not.

More to come. Comments and questions welcome.

More STAAR problems.