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

And now for something completely different.

While I'm waiting for new Regents exams to come along, I looked to other states for standardized tests that have been made public.

It's nice to say how other states live, right?

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.


6. What is the equation in slope-intercept form of the line that passes through the points(-4, 2)and (12, 6)?

F y = 0.25x + 3
G y = 0.25x - 4.5
H y = 4x + 18
J y = 4x - 42

Answer: F y = 0.25x + 3
First step is to find the slope, which will eliminate two choices immediately.
After that, you have two methods to choose from: you can use slope-intercept form and solve for the y-intercept; or, you can use point-slope form, and rewrite the equation in slope-intercept form.

m = (y2 - y1) / (x2 - x1) = (6 - 2) / (12 - (-4)) = 4 / 16 = 1 / 4 = 0.25. Eliminate choices H and J.
Point-slope form: y - 6 = .25(x - 12) or y = .25(x - 12) + 6 (I prefer the latter because it looks like a transformation.)
y = .25x - 3 + 6
y = .25x + 3, which is choice F.

2. Which graph best represents -5y = -6x + 15?

[SEE IMAGE FOR CHOICES]

Answer: C [SEE IMAGE]
Rewrite in slope-intercept form by dividing the equation by -5: y = 6/5 x - 3
Choices A and B have negative slopes and can be eliminated.
Choice C goes through (0, -3), which is what we want. Choice D goes through (0, 3), which is incorrect.



8. A baker determined the annual profit in dollars from selling pies using p(n) = 52n − 0.05n², where n is the number of pies sold. What is the annual profit if the baker sells 400 pies?

F $20,780
G $12,800
H $28,800
J $20,760

Answer: G $12,800
As I would see on a New York test, this question seems very silly. It would imply that there will come a point where the baker will start to lose money making more pies. Then again, maybe this takes into account that he can only sell so many, and after that the go into the dumpster.

To solve the problem, substitute 400 for n and evaluate the expression.
52(400) - 0.05(400)² = 12,8000

9.An exponential function is graphed on the grid.

Answer: A
The graph is positive, so the rate can't have a negative sign in front of it: C and D are eliminated.
The graph is showing decay, so A is correct. B would show growth.
Of course, you could just put each of these equations into a calculator and look.



10. What is the equation in slope-intercept form of the line that crosses the x-axis at 36 and is perpendicular to the line represented by y = −4/9 x + 5 ?

F y = 4/9 x + 16
G y = 4/9 x - 16
H y = 9/4x + 81
J y = 9/4 x - 81

Answer: J y = 9/4 x - 81
A slope that it perpendicular to a slope of -4/9 would be its negative multiplicative inverse -- that is, the inverse reciprocal.
Flip the fraction and switch the sign and -4/9 becomes +9/4.
Two slopes are perpendicular if their product is -1, and (-4/9)(9/4) = -1.

We've eliminated F and G.
To finish the problem, check H and J for the point (36, 0)

y = 9/4 (36) + 81 = 9 (9) + 81 = 162 =/= 0
y = 9/4 (36) - 81 = 9 (9) - 81 = 0
Hopefully, it was obvious that it you were adding two positive numbers, you could get a sum of 0 in choice H.



More to come. Comments and questions welcome.

More STAAR problems.