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.

*1. At a restaurant jars of tomato sauce are stored in boxes in the pantry. Each box contains 8 jars of tomato sauce. A cook uses 2 jars from 1 of the boxes.
Which function shows the relationship between y, the total number of jars of tomato sauce
remaining in the pantry, and x, the number of boxes in the pantry?
A y = 8x + 6
B y = 8x
C y = 8x - 2
D y = 6x
*

**Answer: C y = 8x - 2**

We don't know how many jars of sauce are in a single box. However, we know that if one box holds *x* jars than 8 boxes holds 8x jars.

If 2 jars are taken out of one of the boxes -- not 2 boxes of jars, not 2 jars from every box -- than 2 is subtracted from the 8x, which is 8x - 2.

*2. Which expression is equivalent to -28x ^{2} + 35x?
F 7x(4x + 5)
G -7x(4x - 5)
H 7x(4x - 5)
J -7x(4x + 5)
*

**Answer: G -7x(4x - 5)**

Notice that all of the choices have a positive 4x. If you divide -28x^{2} by 4x, you will get -7x. Eliminate choice F and H.

Next, if you divide + 35x by -7x, you will get -5.

*3. Which graph best represents a system of equations that has no solution?
*

**Answer: D **

The solution to a system of equations is where the two lines meet. Choices A and C actually show the points of intersection. Eliminate them.

Next, look at B. The lines don't meet on the portion of the graph that is visible, but the lines are moving closer together. If you extend the lines, they were intersect at point just off to the right.

In graph D, the two lines are parallel. They have the same slope. That means that they will never get any closer to each other and definitely will NOT intersect. There is no solution.

*4. Which statment about the graph of y = 8(0.25) ^{x} is true?
F The coordinates of the x-intercept are (0.25, 0).
G The coordinates of the y-intercept are (0, 8).
H The equation of the asymptote is x = 0.
J The graph includes the point (2, 1).
*

**Answer: G The coordinates of the y-intercept are (0, 8).**

The graph is an exponential function which is getting smaller as x increases, but will never cross the x-axis. This means that there is NO x-intercept. Eliminate Choice F.

When x = 0, 0.25^{0} = 1, and 8 * 1 = 8. Therefore, the y-intercept is (0, 8). Choice G is the correct answer.

As stated above, the asymptote for the graph is the x-axis. The equation for the x-axis is *y = 0* NOT *x = 0*. Eliminate Choice H.

If you substitube x = 2, then y = 8(0.25)^{2} = 8(.0625) = .5, not 1. Eliminate Choice J.

*5. What is the range of y = -x ^{2} - 2x + 3?
A x < 4
B x > -4
C y < 4
D y > -4
*

**Answer: C y < 4**

The range is the

*y*values so eliminate Choices A and B.

Because the leading coefficient of the quadratic equation is negative, you know that it will have a maximum value, and the range must be less than or equal to that amount. Only Choice C has a y and less than or equal to.

You don't even need to calculate what the maximum value will be to answer the question.

More to come. Comments and questions welcome.

More STAAR problems.