STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2017.

More STAAR problems.

Administered May 2017

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.





51. Which expression is equivalent to (7x³)²(x⁸)^1/2?

A 14x¹⁰
B 49x¹⁰
C 14x⁷
D 49x⁷

Answer: B 49x¹⁰

(7x³)²(x⁸)^1/2
= (49x⁶)(x⁴)
= (49x¹⁰)

For powers of powers, multiply. So 3*2 = 6 and 8*1/2 = 4
For the same base multiplied, add the powers. So 6+4 = 10.
The 7 was squared, so it becomes 49.



52. The function y = 3.75 + 1.5(x - 1) can be used to determine the cost in dollars for a taxi ride of x miles. What is the rate of change of the cost in dollars with respect to the number of miles?

F $1.50 per mile
G $3.75 per mile
H $4.25 per mile
J $5.25 per mile

Answer: F $1.50 per mile
The rate of change is the coefficient of x, which is 1.5, or $1.50.

53. Which graph best represents a function with a range of all real numbers greater than or equal to -6?

Answer: C
The range is the y-values. You want a graph where the minimum value for y is -6. Nothing can go below that.
Graphs B and D go down to negative infinity, below -6.
Graph A does not include values for -6 < y < 0



54. What is the value of x in the solution to this system of equations?

y + 2x = -1
y = 1/2 x + 4

F 6/5
G -2
H -10/3
J 3

Answer: G -2

y + 2x = -1
y = 1/2 x + 4
so 1/2x + 4 + 2x = -1
2 1/2 x + 4 = -1
2 1/2 x = -5
x = -2

Checking the answer:
y = 1/2 (-2) + 4 = -1 + 4 = 3

(3) + 2(-2) = -1
3 - 4 = -1
-1 = -1 (check)



END OF EXAM.

More problems to come. Comments and questions welcome.

More STAAR problems.

I also write Fiction! Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads. Thank you.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2017.

More STAAR problems.

Administered May 2017

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.





46. The graph of a quadratic function is shown on the grid

Which equation best represents the axis of symmetry

F y = 6
G x = 2
H y = 4
J x = 0

Answer: G x = 2
The Axis of Symmetry is the vertical line that would run down the middle of the parabola through the vertex, the turning point. That occurs when x = 2.



47. If p(x) = 5(x² + 1) + 16, what is the values of p(11)

A 690
B 736
C 622
D 626

Answer: D 626

p(11) = 5(11² + 1) + 16
= 5(121 + 1) + 16
= 5(122) + 16
= 610 + 16
= 626

58. The graphs of lines k₁ and k₂ are shown on the grid.

Which system of equations is best represented by this graph?

F 3x - y = 2 ; 4x + 9y = 36
G 3x - y = 6 ; 4x + 9y = 4
H x - 3y = -18 ; 9x + 4y = 9
J x y + = 10 ; 9x + 4y = 13

Answer: F 3x - y = 2 ; 4x + 9y = 36
Line k₁ has a positive slope. It has y-intercept of -2 and x-intercept of less than 1. There is another point at (1,1). It's slope is +3 (three units rise, 1 unit run).
Line k₂ has a negative slope. It has y-intercept of 4 and x-intercept of 9. It's slope is -4/9.

In Choices H and J, the slope of the second line is -9/4, not -4/9. Eliminate these.

In Choice F, 3(0) - (-2) = 2 and 3(1) - 1 = 2.
Additionally, 4(0) + 9(4) = 36 and 4(9) + 9(0) = 36.
Choice F is the correct answer.

Choice G has the same left hand sides as F, but the right hand sides are too small. This can be eliminated.



49. Which statement about the graph of y = (1/3)(2/3)^x is true?
Which inequality best represents the domain of the part shown?

A The graph has a vertical asymptote.
B The graph crosses the y-axis at (0, 2/9 ).
C The graph has an asymptote at y = 1/3.
D The graph decreases from left to right.

Answer: D The graph decreases from left to right.
Exponential functions do not have vertical asymptotes. Eliminate Choice A.

When x = 0, y = 1/3, not 2/9. When x = 1, y = 2/9. Eliminate Choice B.

When x = 0, y = 1/3, so y = 1/3 is NOT an asymptote.

The rate is less than one, so the graph will decrease from left to right: 1/3, 2/9, 4/27, etc.



50. The table represents some points on the graph of a linear function.

Which equation represents the same relationship?

F y + 268 = 1/12(x + 20)
G y + 20 = 1/12(x + 268)
H y + 268 = 12(x + 20)
J y + 20 = 12(x + 268)

Answer: H y + 268 = 12(x + 20)
(-20, -268) is a point on the line, with 20 being the x coordinate. So eliminate Choices G and J.

It comes down to whether the slope is 12 or 1/12.

m = (-40 - -124) / (-8 - -1)
= 84 / 7
= 12 Which is Choice H.

More to come. Comments and questions welcome.

More STAAR problems.

I also write Fiction! Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads. Thank you.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.

I had to put these on hold for a while. They're back now.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2017.

More STAAR problems.

Administered May 2017

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.





41. Which expression is a factor of 18x² - 15x + 2?

A 3x - 2
B 9x - 1
C x - 2
D 2x - 1

Answer: A 3x - 2
We can factor the trinomial, using "borrow & payback". Multiply (18)(2) = 36. What are two factors of +36 that add up to -15? They both have to be negative numbers.
Check them all: -1 and -36, no; -2 and -18, no; -3 and -12, bingo! (You can stop now)

18x² - 15x + 2
18x² - 12x - 3x + 2
Group the terms
(18x² - 12x) - (3x - 2)
Now find the GCF of each pair
6x(3x - 2) - 1(3x - 2)
(6x - 1)(3x - 2) are the factors
The answer is A.



42 The graph of linear function g is shown on the grid.

What is the zero of g?
Record your answer and fill in the bubbles on your answer document.

Answer: -6
The zero is where the line crosses the x-axis, which is -6.

43. Which quadratic function in vertex form can be represented by the graph that has a vertex at (3, -7) and passes through the point (1, -10)?

A y = 3/4 (x + 3)² + 7
B y = -3/4 (x + 3)² - 7
C y = 3/4 (x - 3)² + 7
D y = -3/4 (x - 3)² - 7

Answer: D y = -3/4 (x - 3)² - 7
The point (1, -10) is unnecessary information and no calculation is needed.
You are given the vertex and the four choices are in vertex form.
Choice D is the only possible answer as A, B, and C do not have vertices at (3, -7).

The one thing that (1, -10) tells you is that the parabola must open downward because -10 is below -7, so the number in the front must be negative.



44. The graph of part of linear function g is shown on the grid.

Which inequality best represents the domain of the part shown?

F -9 < x ≤ 2
G -9 ≤ x < 2
H -6 < g(x) ≤ 3
J -6 ≤ g(x) < 3

Answer: F -9 < x ≤ 2
The domain is the possible x values, and the range is the possible g(x) values. Eliminate Choices H and J.
There is an open circle at x = -9 that indicates it is not part of the solution, and a closed circle at x = 2 that indicates it is part of the solution. This means Choice F.



45. A student graphed f(x) = x and g(x) = f(x) + 3 on the same coordinate grid. Which statement describes how the graphs of f and g are related?

A The graph of f is shifted 3 units up to create the graph of g.
B The graph of f is steeper than the graph of g.
C The graph of f is shifted 3 units down to create the graph of g.
D The graph of f is less steep than the graph of g.

Answer: A The graph of f is shifted 3 units up to create the graph of g.
Whatever answer you would get for f(x), g(x) will always be 3 more than that. Since f(x) and g9x) are measured on the y-axis, adding through will move the points upward.
Adding or subtracting to a function will not affect its steepness. You would need to multiply.

More to come. Comments and questions welcome.

More STAAR problems.

I also write Fiction! Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads. Thank you.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.

I had to put these on hold for a while. They're back now.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2017.

More STAAR problems.

Administered May 2017

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.





36. What is the equation of the line that passes through the point (-2, 7) and has a slope of zero?

F x = 7
G y = -2
H x = -2
J y = 7

Answer: J y = 7
A line with a slope of 0 is a horizontal line in the form y = b. Since the point (-2, 7) is on the line, b must be 7.



37 Which ordered pair is in the solution set of y ≥ 1/3 x + 4?

A (-6, 1)
B (-1, 6)
C (6, -1)
D (1, -6)

Answer: B (-1, 6)
You don't need the provided graph, so I didn't include it in the answer. You could graph the inequality and check to see which point lies in the shaded region.
It would be quicker to just check the choices.
Is 1 ≥ 1/3 (-6) + 4?
1 ≥ -2 + 4
1 ≥ 2, X, not true, eliminate Choice A

Is 6 ≥ 1/3 (-1) + 4?
6 ≥ -1/3 + 4
6 ≥ 3 + 2/3, true. Choice B is the answer.

38. Which table does NOT show y as a function of x?

Answer: H
The only restriction on a function is that every imput has only one output.
In choice H, the value -0.2 repeats for the x value (input) but has two different y values (outputs) associated with it. This is not allowed in a function.
Consider a function to be like a function key on a calculator. You input a number and press the function key, you expect the same output every time you enter the same input. It can't be 5 sometimes and 8 other times.



39. A projectile is launched into the air from the ground. The table shows the height of the projectile, h(t), at different times.

Based on the table, which function can best be used to model this situation?

A h(t) = 99t² + 858
B h(t) = -4.9t² + 295t + 0.6
C h(t) = -4.9t² + 295t + 2
D h(t) = 99t² + 1,470.3

Answer: B h(t) = -4.9t² + 295t + 0.6
It's a projectile, so it is going to have negative acceleration. That is to say, it will be an upside-down parabola. You should also be aware that the leading coefficient is problems of these types is likely to be -16, -5, or -4.9, depending on if the question uses imperial units, and if they decide to round the numbers.
You can see that the height peaks at 30 and declines again. This means that the leading coefficient is negative. Choices A and D can be eliminated.
You can graph the other two in a graphing calculator and check the table of values, or you can do a quadratic regression in your calculator.
My graphing calculator lines out with 0.6 as the y-intercept, so +2 would be farther away.

Honestly, this is an odd problem in that B and C are so close together given the size of the values. The margin of error between them is miniscule.



40. Which value of x makes the equation 0.75(x + 20) = 2 + 0.5(x - 2) true?

F 64
G -64
H 56
J -56

Answer: J -56

0.75(x + 20) = 2 + 0.5(x - 2)
0.75x + 15 = 2 + 0.5x - 1
0.25x = -14
x = -56
I assume the "64" answers come from mathematical errors giving you either 16 or -16.

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.

I had to put these on hold for a while. They're back now.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

More STAAR problems.

Administered May 2017

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.





31. A student used f(x) = 5.00(1.012)^x to show how the balance in a savings account will increase over time. What does the 5.00 represent?

A The interest the savings account earned for the first year
B The annual interest rate of the savings account
C The number of years the savings account has earned interest
D The starting balance of the savings account

Answer: D The starting balance of the savings account
I hope the student was using a spreadsheet and showing what happens over many, many years, because $5.00 at 1.2% interest won't accrue to much of anything. And in the real world, banking fees would eat up that money, leaving the student owing money.
But as far as the test is concerned, 5.00 is the Principal, the starting money.



32. The graph of a function is shown on the grid.

Which ordered pair best represents the location of the y-intercept?

F (1/3, 0)
G (0, -2)
H (0, 1/3)
J (-2, 0)

Answer: G (0, -2)
At the y-intercept, the value of x is 0, so Choice F and Choice J are eliminated.
It's also below the x-axis, so the value of y is negative, making G the only Choice.
(1/3, 0) is a good approximation for the x-intercept.

33. Researchers in Antarctica discovered a warm sea current under a glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate of 0.06 m per day.

Which function can be used to find the thickness of the ice shelf in meters x days since the discovery?

A t(x) = 450 - 0.06x
B t(x) = -0.06(x + 450)
C t(x) = 450 + 0.06x
D t(x) = 0.06(x + 450)

Answer: A t(x) = 450 - 0.06x
The thickness of 450 is the initial value (the y-intercept) and doesn't take a variable. The 0.06 is a daily decrease, so it gets subtracted every day for x days.
Choice C is no good because that shows the ice increasing in size, not decreasing.



34. What is the positive solution to the equation 0 = (1/3)x² - 3?

Record your answer and fill in the bubbles on your answer document.

Answer: 3

0 = (1/3)x² - 3
0 = x² - 9
9 = x²
x = 3 (positive solution)
You could also have factored the Difference of Squares and continued from there, getting the same result.



35. The amount of fertilizer in a landscaping company’s warehouse decreases at a rate of 3% per week. The amount of fertilizer in the warehouse was originally 78,000 cubic yards.

Which function models the amount of fertilizer in cubic yards left after w weeks?

A f(w) = 0.97(78,000)^w
B f(w) = 1.03(78,000)^w
C f(w) = 78,000(0.97)^w
D f(w) = 78,000(1.03)^w

Answer: C f(w) = 78,000(0.97)^w
Eliminate the first two immediately. The number 78,000 represents the original amount that the decay rate will be applied to. Since it is decreasing (decaying) the rate has to be less than 1.00, so Choice D is eliminated.
A 3% decrease means subtract 1.00 - 0.03 = 0.97, which is the rate in Choice C.

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.

I had to put these on hold for a while. They're back now.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2017.

More STAAR problems.

Administered May 2017

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.





26. The graph models the linear relationship between the temperature of Earth’s atmosphere and the altitude above sea level.

Which of these best represents the rate of change of the temperature with respect to altitude
F -6.5°C/km
G -3.5°C/km
H -0.29°C/km
J -0.15°C/km

Answer: F -6.5°C/km
The graph drops from about (0, 15) to (10, -50). That a 65 degree drop at a run of 10 km. -65/10 = -6.5.



27. The value of y is directly proportional to the value of x. If y = 35 when x = 140, what is the value of y when x = 70?
Record your answer and fill in the bubbles on your answer document.

Answer: 17.5
Read this carefully. The value of x has been cut in half. If y is directly proportional, it is also cut in half, so it will be 17.5.
Be carefulat that you didn't swap those values in your head and double 140 to 280.

28. Which expression is equivalent to m² - 13m - 30?

F (m - 15)(m + 2)
G (m - 10)(m - 3)
H (m + 15)(m - 2)
J (m + 10)(m + 3)

Answer: F (m - 15)(m + 2)
Two factors of -30 that have a sum of -13. One must be positive and one negative. And the negative number has to have the larger magnitude (bigger absolute value). That's Choice F.
If you multiply the other binomials, you will get the same numbers, but the signs will change.



29. The line graphed on the grid represents the first of two equations in a system of linear equations.

If the graph of the second equation in the system passes through the points (-12, 20) and (4, 12), which statement is true?

A The only solution to the system is (10, 5).
B The only solution to the system is (0, 14).
C The system has no solution.
D The system has an infinite number of solutions

Answer: C The system has no solution.
If you were to plot the two points, (-12, 20) and (4, 12), you would see that each of them is 4 units above the first line. This means that second line is parallel to the first line, and there are no solutions.
"Infinite number" can be thrown out immediately because the two points were NOT on the first line.



30. What is the domain of f(x) = 9 = x²?

F f(x) ≥ 9
G All real numbers
H -3 ≤ x ≤ 3
J x ≤ 9

Answer: G All real numbers
Don't be fooled. You are asked for domain, which are the x values, not the range, which are the values.
And there is nothing stating that f(x) must be greater than 0.
There are no restrictions on x. There is no value of x for which f(x) is undefined.

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.

I had to put these on hold for a while. They're back now.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2017.

More STAAR problems.

Administered May 2017

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 population of Center City is modeled by exponential function f, where x is the number of years after the year 2015. The graph of f is shown on the grid.

Which inequality best represents the range of f in this situation?
A x ≥ 0
B y ≥ 250,000
C 0 ≤ x ≤ 110
D 250,000 ≤ y ≤ 1,000,000

Answer: B y ≥ 250,000
The range is composed of all the possible y values. This eliminates choices A and C.
The line starts halfway between 200,000 and 300,000. Both choices use 250,000. However the arrow at the end of the line indicates that the function continues upward, above the 1,000,000 line at the top of the graph. So the answer is B.



22. A sequence can be generated by using a_n = 4a_{(n - 1)}, where a₁ = 6 and n is a whole number greater than 1. What are the first four terms in the sequence?

F 6, 24, 96, 384
G 6, 10, 14, 18
H 6, 20, 100, 500
J 6, 20, 76, 300

Answer: F 6, 24, 96, 384
Each term in the sequence is FOUR TIMES larger than the previous one, with the first tern being 6. That means 6 X 4 = 24, 24 X 4 = 96, and 96 X 4 = 384, which is choice F.
Choice G would work if the sequence was a_n = 4 + a_{(n - 1)}, adding FOUR MORE than the previous term.
Choice H and J assume you made a blunder with the (n - 1) expression. Choice H multiplies by 5 X 4, instead of 6, but then multiplies by 5 after that for some reason. Choice J subtracts one from a_{(n - 1>} and then multiplies by 4.

23. What is the equation in slope-intercept form of the line that passes through the points (-4, 47) and (2, -16)?

A y = (-21/2)x + 979/21
B y = (-2/21)x + 979/21
C y = (-21/2)x + 5
D y = (-2/21)x + 5

Answer: C y = (-21/2)x + 5
The slope of the line is (y2 - y1) / (x2 - x1), which is (47 - -16) / (-4 - 2), so m = 63/-6 = - 21/2. This elimates B and D, which were done upside down.
Picking one of the points, you plug in what we know:

y = m x + b
-16 = (-21/2)(2) + b
-16 = -21 + b
5 = b
So the equation is y = (-21/2)x + 5, which is Choice C.



24. The graph of f(x) = x² is transformed to create the graph of h(x) = 2f(x). Which graph best represents f and h?

Answer: J
If h(x) = 2f(x), then h(x) = 2x², which is a parabola with a vertex of zero that will climb the graph more quickly than f(x) would. This is a dilation, not a translation.
Choice F is incorrect because it shifts (translates) the parabola two spaces up, instead of doubling the y-coordinate.
Choice H is incorrect because it shifts the parabola two spaces to the right.
Choice G looks correct, but it reverses functions f and h.
Choice J is correct.



25. A student is ordering a flower arrangement. She can choose any combination of roses and carnations for her flower arrangement, and she does not want to spend more than $30. If roses cost $3 each and carnations cost $2 each, which inequality represents all possible combinations of x roses and y carnations?

A 3x + 2y < 30
B 3x + 2y ≤ 30
C 2x + 3y > 30
D 2x + 3y ≤ 30

Answer: D 2x + 3y ≤ 30
This entire question boils down to knowing that "not ... more than $30" means "less than or equal to $30", with is Choice D.

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.

I had to put these on hold for a while. They're back now.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

More STAAR problems.

Administered May 2017

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.





16. What is the slope of the line represented by 5x - 12y = 24?

F -2
G 24/5
H -12
J 5/12

Answer: J 5/12
When a linear equation is written in standard form, it is Ax + By = c. In that case the slope of the line will be -A/B. In this example A = 5 and B = -12, and -5/-12 = 5/12.

Alternatively, you can rewrite the equation in slope-intercept form, y = mx + b.

5x - 12y = 24
-12y = -5x + 24
y = -5/-12 x + 24/-12
y = 5/12 x - 2
The slope is 5/12.



17. Which expression is equivalent to 6x² + 13x + 5?

A (2x + 5)(3x - 1)
B (2x - 5)(3x + 1)
C (2x + 1)(3x + 5)
D (2x - 1)(3x - 5)

Answer: C (2x + 1)(3x + 5)
I hope you didn't waste any time factoring this example when you had four choices with three easily eliminated options.
The constant is +5, which is positive, so both of the constants in the binomials need to be the SAME sign. This eliminates A and B.
The middle term is +13x, which is positive, so both constants have to be positive. This eliminates choice D.
Choice C is the answer, which you can check by multiplying.

18. A bus travels two different routes: the Green Route and the Blue Route. The routes are different lengths.
• On Monday the bus traveled the Green Route 6 times and the Blue Route 5 times, traveling a total of 52 miles.
• On Tuesday the bus traveled the Green Route 12 times and the Blue Route 13 times, traveling a total of 119 miles.
What is the length of the Green Route in miles?

F 4.4 mi
G 4.5 mi
H 6.4 mi
J 6.8 m

Answer: G 4.5 mi
Set up a system of equations and solve using elimination.

6g + 5b = 52
12g + 13b = 119
Double the first equation.
12g + 10b = 104
12g + 13b = 119
Subtract
3b = 15
b = 5
6g + 5(5) = 52
6g = 27
g = 4.5 mi



19. The table shows the heights and the lengths of several rectangles.

What does the correlation coefficient for the data indicate about the strength of the linear association between the height and the length of these rectangles?

A Weak negative correlation
B Strong negative correlation
C Weak positive correlation
D Strong positive correlation

Answer: C Weak positive correlation
Put the data into your graphing calculator and do a linear regression. You should get a correlation coefficient of approximately 0.15548, which is positive and very weak.



20. The expression ( x³)(x^-17) is equivalent to xⁿ. What is the value of n? Record your answer and fill in the bubbles on your answer document.

Answer: -14
Keep the base and add the exponents. If you add 3 + (-17), you get -14, which is n.

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

More STAAR problems.

Administered May 2017

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.





11. What is the solution to 8x - 3(2x - 4) = 3(x - 6)?

A 6
B 2
C 30
D No solution

Answer: C 30

8x - 3(2x - 4) = 3(x - 6)
8x - 6x + 12 = 3x - 18
2x + 12 = 3x - 18
30 = x



12. A lifeguard earns $320 per week for working 40 hours plus $12 per hour worked over 40 hours. A lifeguard can work a maximum of 60 hours per week.

Which graph best represents the lifeguard’s weekly earnings in dollars for working h hours over 40?

Answer: G
The most hours a lifeguard can work is 60, so the maximum number of hours over 40 is 60 - 40 = 20 hours. So Choices H and J are eliminated.

20 hours at $12 per hour is $240 on top of the $320. That means the maximum a lifeguard can earn is $540. This is Choice G.

13. A shoe company is going to close one of its two stores and combine all the inventory from both stores. These polynomials represent the inventory in each store:

Which expression represents the combined inventory of the two stores?

Answer: A 7/2 g² - 4/5 g + 15/4
Combine the like terms.

1/2 and 3 are 3 1/2 g² or 7/2 g²

- 4/5 g doesn't combine with anything.

7/2 + 1/4 = 14/4 + 1/4 = 15/4

Put it together and you get 7/2 g² - 4/5 g + 15/4



14. The graph of quadratic function f is shown on the grid.

What is the y-intercept of the graph of f ?

Record your answer and fill in the bubbles on your answer document.

Answer: 4
The parabola crosses the y-axis at (0, 4). That's a lot of setup for a very simple problem.

The y-intercept is usually the least important point on a parabola. The vertex and the roots are usually of more interest.



10. A particular type of cell doubles in number every hour. Which function can be used to find the number of cells present at the end of h hours if there are initially 4 of these cells?

A n = 4(1/2)^h
B n = 4(2)^h
C n = 4 + (2)^h
D n = 4 + (1/2)^h

Answer: B n = 4(2)^h
The problem describes exponential growth. Choice A shows exponential decay, as the growth factor is less than 1. Choices C and D are just silly because the initial number of cells is doubling, not being added to.

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

More STAAR problems.

Administered May 2017

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. The area of a rectangle is 54x⁹y⁸ square yards. If the length of the rectangle is 6x³y⁴ which expression represents the width of the rectangle in yards?

F 9x³y²
G 48x⁶y⁴
H 9x⁶y⁴
J 60x¹²y¹²

Answer: H 9x⁶y⁴
Divide 54x⁹y⁸ by 6x³y⁴

54 divided by 6 is 9.
x⁹ divided by x³ is x⁶, because 9 - 3 = 6
y⁸ divided by y⁴ is y⁴ becayse 8 - 4 = 4



7. The total number of seats in an auditorium is modeled by f(x) = 2x² - 6x, where x represents the number of rows of seats. How many rows are there in the auditorium if it has a total of 416 seats?

A 32
B 13
C 20
D 16

Answer: D 16
When does 2x² - 6x = 416? Set the equation equal to 0 and factor.

2x² - 6x - 416 = 0
x² - 3x - 208 = 0
What are two factors of -208 that add up to -3? They must be close together.
Knowing that 14² is 196, I might guess 13, which goes into 208 16 times. Good guess. Yeah, me!
-208 factors into -16 and 13
(x - 16)(x + 13) = 0
x = 16 or x = -13
We discard -13 because the number of rows must be positive.

8. The graph of an exponential function is shown on the grid.

F Line q
G Line r
H Line s
J Line t

Answer: H Line s
In an exponential graph, the asymptote is the horizontal line that the function draws nearer and nearer to, without ever intersecting, even if it's own by a millionth of a unit.



9. Which situation best represents causation?

A When the number of bus stops increases, the number of car sales decreases.
B When fewer firefighters report to a house fire, the damage caused by the fire decreases.
C When ice cream sales increase, incidents of sunburn increase.
D When it rains several inches, the water level of a lake increases.

Answer: D When it rains several inches, the water level of a lake increases.
If it rains, water levels will rise. One causes the other.

Increasing bus stops doesn't necessaily affect car sales. People aren't suddenly going abandon their cars in favor of taking the bus.

If there are fewer firefighters, fire damage would likely increase since for lack of people to put out the fire.

Ice cream sales will spike in the summer at the same time that sunburn incidents increase. But these are both caused by the heat of the Sun. One doesn't cause the other.



10. The graph of a quadratic function is shown on the grid.

Which function is best represented by this graph?

F f(x) = x² + 3x - 4
G f(x) = -x² - 3x + 4
H f(x) = x² - 3x - 4
J f(x) = -x² + 3x + 4

Answer: J f(x) = -x² + 3x + 4
The parabola opens downward, so the a value must be negative. Eliminate Choices F and H.

You could graph the other two. Or you could find the zeroes. Or rewrite them into vertex form, etc. You could also substitute -4 and 1 for x and see if you get 0.

Choice G has -3x for the b term and J has +3x. If you look for the Axis of Symmetry, then x = -b/2a.
Either x = -(-3)/(2(-1)) = 1.5 or x = -(3)/(2(-1)) = -1.5
From the graph, the Axis of Symmetry is x = -1.5, so we need the b term to be +3, which is Choice J.

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

More STAAR problems.

Administered May 2017

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. Which expression is equivalent to SQRT(147)?

A 3 SQRT(7)
B 7 SQRT(3)
C 21 SQRT(7)
D 49 SQRT(3)

Answer: 7 SQRT(3)
Factor the number in the square root, and pair the like factors up.

SQRT(147) = SQRT(3 * 7 * 7) = 7 SQRT(3)

The square root of 49 is 7, and 49 is a factor of 149, so it can be separated and rooted.



2. A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote. They wrote a total of 46 songs.

Which system of equations models this situation if the drummer wrote d songs and the guitarist wrote g songs?

F g = 2d - 8 ; g + d = 46
G g = 8 - 2d ; g = 46 - d
H d = 2g - 8 ; d = 46 - g
J d = 8 - 2g ; d + g = 46

Answer: F g = 2d - 8 ; g + d = 46
Please understand why Choices F and H can be eliminated immediately. The first equation in both choices would work if there were a total of 8 songs written. Think of the difference of having $20 less than you had originally, and originally having $20 and spending some amount of money.

Translate guitarist wrote 8 fewer than twice the drummer into
g equals subtract 8 from two times d, or g = 2d - 8

The total output of the two writers is 46 is g + d = 46. That being said, the other ways it is written -- g = 46 - d and d = 46 - g -- are not incorrect.

3. Which graph best represents the solution set of y ≤ -4x?

Answer: C
The ≤ symbol tells us that we will be shading underneath a solid line. The -4 cofficient of x tells us that it is a steep slope down and to the right.

That is Choice C. Choices A and D have the line y = -4, not y = -4x. Choice B has a broken line and is graphed above.



4. The graph of f(x) = x² was transformed to create the graph of g(x) = (x - 7.5)². Which of these describes this transformation?

F A horizontal shift to the right 7.5 units
G A horizontal shift to the left 7.5 units
H A vertical shift down 56.25 units
J A vertical shift up 56.25 units

Answer: F A horizontal shift to the right 7.5 units
This is pretty much a definition question, but you could graph them both in your calcultor and see the shift.

The vertex of a parabola is at the point (h, k) in the formula

y = a(x - h)² + k The vertex of f(x) = (0, 0) and the vertex of g(x) = (7.5, 0). That means a shift 7.5 units to the right.

Had the 7.5 been the k instead of the h, the graph would have shifted up or down, but only by 7.5 spaces.



5. A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f(x) = 20x + 4.

What is the range of the function for this situation?

A {0, 1, 2, 3, 4, 5, 6}
B {4, 24, 44, 64, 84, 104, 124}
C {0, 2, 4, 6}
D {4, 44, 84, 124}

Answer: C
The range is the output, the dependent variable, the f(x) values, y. All that.

If the valid inputs are 0, 1, 2, 3, 4, 5, 6 because you can you that many pairs of weights, then the outputs are 4, 24, 44, 64, 84, 104, 124.

Choice A is the Domain. Choice C is the domain if you misread the question concerning the pairs of weights. Choice D is the range if you misread the question regarding pairs of weights.

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2018, cont.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

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.





51. What is the slope of the line that passes through the points (5, −11) and (−9, 17)?

A -2
B -1/2
C 7
D 2

Answer: A -2
Change in y divided by change in x

(17 - -11) / (-9 - 5) = 28 / -14 = -2



52. What is the x-value of the solution to this system of equations?

x = 2y − 4
7x + 5y = −66

F -2
G -19/7
H -8
J -62/19

Answer: F -2
Substitute (2y - 4) for x in the second equation

7(2y - 4) + 5y = -66
14y - 28 + 5y = -66
19y = -38
y = -2

An odd coincidence that two answers in a row were the first choice, which was -2.

53. Which expression is equivalent to SQRT(96)?

A 24
B 8 SRT(6)
C 48
D 4 SQRT(6)

Answer: D 4 SQRT(6)
96 is not a perfect square, so it will not have an integer square root. Choices A and C are eliminated.
The factors of 96 are 2 x 2 x 2 x 2 x 2 x 3. (I got that by dividing 96 by 2 repeatedly until I only had 3 remaining.
Group the factors into pairs: SQRT( (2x2) x (2x2) x 2 x 3 )
That equals 2 x 2 x SQRT( 2 x 3 ), which is 4 SQRT(6).



54. Which line appears to have an x-intercept of -5 and a y-intercept of 3?

Answer: G
An x-intercept of -5 means the point (-5, 0) is on the line. A y-intercept of 3 means the point (0, 3) is on the line.

The graph that shows this is Choice G.

Choice J flips those numbers.

Choice F flips and negates those numbers.

Choice H negates those numbers.



END OF EXAM.

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2018, cont.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

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.





46. Scientists are studying a bacteria sample. The function f(x) = 245(1.12)^x gives the number of bacteria in the sample at the end of x days.

Which statement is the best interpretation of one of the values in this function?

F The initial number of bacteria is 12.
G The initial number of bacteria decreases at a rate of 88% each day.
H The number of bacteria increases at a rate of 12% each day.
J The number of bacteria at the end of one day is 245.

Answer: H The number of bacteria increases at a rate of 12% each day.
Taking apart the function: 245 is the initial number, and 1.12 indicates a 12% increase.

The initial number is not 12. The bacteria are increasing, not decreasing. The starting value is 245, not the amount after 1 day.



47. The daily cost of hiring a plumber, y, to work x hours on a repair project can be modeled using a linear function. The plumber charges a fixed cost of $80 plus an additional cost of $45 per hour. The plumber works a maximum of 8 hours per day.

For one day of work, what is the range of the function for this situation?

A 0 ≤ x ≤ 8
B 80 ≤ y ≤ 440
C 0 ≤ x ≤ 10
D 45 ≤ y ≤ 685

Answer: B 80 ≤ y ≤ 440
The plumber charges $80 before any hours of work have been done. This will be the minimum charge. Only one choice, B, has this as the minimum.

Choice A refers to the amount of hours he might work. Choice C doesn't seem to make any sense. Choice D has the equation backward with a fixed $45 and $80 per hour.

48. The graph of g(x) = x² was transformed to create the graph of h(x) = -(x/4)². Which of these describes the transformation from the graph of g to the graph of h?

F A reflection over the x-axis and a horizontal stretch
G A reflection over the y-axis and a horizontal stretch
H A reflection over the x-axis and a vertical stretch
J A reflection over the y-axis and a vertical stretch

Answer: F A reflection over the x-axis and a horizontal stretch
You can put both of these in your graphing calculator and just look at them.

The negative coefficient means that the parabola means that it will be flipped upside down, reflected across the x-axis. The 1/4 (which will become 1/16 when it's squared) will flatten out the curve, which is to say that is will be stretched out horizontally.



49. Which expression is equivalent to

(10q²w⁷) / (2w³) X (4(q⁶)²) / (w^-5)
for all values of q and w where the expression is defined?

A (32q⁷) / w
B 20q¹⁷w⁹
C 32q⁷w⁹
D 20qw

Answer: B 20q¹⁷w⁹

In the first fraction, simplify 10/2 to get 5. Simplify w⁷ / w³ to get w⁴.

In the second fraction, (q⁶)² becomes q¹². Also, w^-5 in the denominator becomes w⁵ in the numerator.

At this point, there is nothing left in the denominator.

In the numerator, there is (5)(4) = 20, w⁴ * w⁵ = w⁹, q⁵ * q¹² = q¹⁷.



50. A graph of a quadratic function is shown on the grid.

Which coordinates best represent the vertex of the graph?

F (2.4, 0)
G (0, −1)
H (−0.4, 0)
J (1, −2)

Answer: J (1, −2)
The vertex is that minimum point at the bottom of the curve. The x-coordinate is 1, and the y-coordinate is -2. (1, -2).

Choices F and H appear to be the zeroes (roots) of the function. Choice G is the y-intercept, which is rarely important with quadratic functions (in my own opinion).

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2018, cont.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

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.





41. The area of a rectangular trampoline is 112 ft². The length of the trampoline is 6 ft greater than the width of the trampoline. This situation can be represented by the equation w² + 6w − 112 = 0.

What is the width of the trampoline in feet?

A 7 ft
B 16 ft
C 8 ft
D 14 ft

Answer: C 8 ft
If the length X the width of a rectangle is 112 ft², what are the possible lengths and widths? Hint: They have to have a difference of 6 because the length is 6 more than the width.

The factors of 112 are (1, 112), (2, 56), (4, 28), (7, 16), (8, 14). The last pair has a difference of 6. The width is 8 and the length is 14.



42. The table shows the linear relationship between the balance of a student’s savings account and the number of weeks he has been saving.

Based on the table, what was the rate of change of the balance of the student’s savings account in dollars and cents per week?

Record your answer and fill in the bubbles on your answer document.

Answer: $7.00 per week
It's a linear relationship, so any two points can give you the rate of change. As always, if I have a chance to use 0 or 1, I'll take it. If I can use smaller numbers instead of bigger numbers, I'll do that, too.

Rate of change: (39 - 32) / (1 - 0) = 7 / 1 = 7
$7.00 per week.

43. The graph of a linear function is shown on the grid.

Which equation is best represented by this graph?

A y + 7 = −3(x − 4)
B y + 1 = −3(x + 2)
C y − 4 = 3(x + 7)
D y − 2 = 3(x − 1)

Answer: A y + 7 = −3(x − 4)
The slope is negative, so choices C and D are eliminated.

According to the other choices, either (4, -7) or (-2, -1) should be a point on the graph. We can see that (4, -7) is on the graph, but (-2, -1) is not. In fact, the graph doesn't even go through any part of Quadrant III.



44. Which expression is a factor of 9r² − 4r + 1?

F 3r − 1
G r − 1
H 9r − 1
J There are no real factors.

Answer: J There are no real factors.
What are two factors of (9)(1) that add up to -4? Answer: there are none.

If you graph this function, you will see that it doesn't cross the x-axis.



45. The graph of 2x − 5y = 10 is shown on the grid.

Which ordered pair is in the solution set of 2x − 5y ≥ 10?
A (0, 5)
B (5, 0)
C (−2, 5)
D (−5, 2)

Answer: B (5, 0)
Look at the point (0, 0). Is 2(0) - 5(0) ≥ 10? Is 0 - 0 ≥ 10? Obviously not. So (0, 0) is not is the solution set. Therefore, the solution is not above the line, but below the line. So which of these points is pn or below the line?

The other way to look at it is this: Plot the four points. Choice A is above the line. Choice B is on the line. Choice C is above the line. Choice D is above the line. Three of the choices are above the line, which means that they are ALL solutions or NONE of them are solutions. Since they can't all be, then none of them are. The answer is B.

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2018, cont.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

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.





36. Which expression is equivalent to (h² + 9h − 1)(−4h + 3)?

F −4h³ − 33h² + 31h − 3
G 4h³ + 39h² − 23h − 3
H −4h³ − 39h² + 23h + 3
J 4h³ + 33h² − 31h + 3

Answer: F −4h³ − 33h² + 31h − 3
It should be obvious that the leading term will be the product of h² and -4h, which will be -4h³. That eliminates G and J.

Likewise, the final term is the product of (-1) and (3), which is -3, which eliminates H.

If you needed to work it out, do the following:

(h² + 9h − 1)(−4h + 3)
-4h³ + 3h² - 36h² + 27h + 4h - 3
-4h³ - 33h² + 31h - 3



37. There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7 inches or 12 inches. The diameter of all 15 plates combined is 140 inches.

Which system of equations can be used to find the number of 7-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet?

A x + y = 140 ; 12x + 7y = 15
B 7x + 12y = 140 ; 7x + 12y = 15
C x + y = 15 ; 7x + 12y = 140
D x + y = 15 ; 12x + 7y = 140

Answer: C x + y = 15 ; 7x + 12y = 140
The total number of plates is 15, so x + y = 15. Eliminate A and B.

The variable x is defined to be the 7-inch plates, so the total number of inches in diamter is 7x, not 12x. Likewise, the number of 12-inch plates is y, so we need 12y.

If you were solving this problem on your own, and the variables had not been pre-defined for you, then there would be no difference in using either C or D to solve the problem, as long as you knew which varaible stood for which object.

Choice A is backward with its 140 and 15 -- 140 dishes have a combined diameter of 15 inches? It must be a miniatures collection, or toys in a tiny doll house. Choice B has a pair of parallel lines, which has no solution.

38. The graph of quadratic function f is shown on the grid.

Which of these best represents the domain of f ?

F −3 ≤ x ≤ 2
G All real numbers
H y ≥ 5.5
J All real numbers less than −3 or greater than 2

Answer: G All real numbers
Domain is the valid x values that can be input to the function. There are no numbers for which this quadratic is undefined. Just because only −3 ≤ x ≤ 2 is shown doesn't mean that that is the entirety of the graph. (Note the arrows at the ends of the line.)

Choice H would be correct for the Range. When you see something like this, always go back and reread the question. Make sure it said what you thought it said. (You'd be surprised at the number of times a person can misread something and instead read what they expected to see instead of what was there.)



39.What is the equation in slope-intercept form of the line that passes through the point (2, −2) and is perpendicular to the line represented by y = 2/5 x + 2?

A y = 5/2 x − 7
B y = 5/2 x + 7
C y = −5/2 x − 3
D y = −5/2 x + 3

Answer: D y = −5/2 x + 3
The slope of a line perpendicular to another line must be the inverse reciprocal of the slope of the original line. That is, the two slopes will have a product of -1.

The inverse reciprocal of 2/5 is -5/2. Eliminate A and B.

Substitue x = 2 into the other equations, and see which gives you -2.
y = -5/2 (2) - 3 = -5 - 3 = -8
y = -5/2 (2) + 3 = -5 + 3 = -2.

To work it out, if there weren't any choices, use slope-intercept form:

y - (-2) = -5/2 (x - 2)
y + 2 = -5/2 x + 5
y = -5/2 x + 3



40. Which graph best represents f(x) = 2(5)²?

Answer: F
When x = 0, 5^x = 5⁰ = 1, and 2(1) = 2.

When x = 1, 5^x = 5¹ = 5, and 2(5) = 10.

The only graph with (0, 2) [approximately] and (1, 10) is graph F.

Choice J looks like f(x) = 5(2)^x.

Choice H looks like f(x) = 10(2)^x.

Choice G looks like f(x) = 5^x.

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2018, cont.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

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.





31.Which expression is a factor of 21x² + 13x - 20?

A 3x − 4
B 7x − 5
C 7x + 4
D 3x + 5

Answer: B 7x − 5
What are the factors of (ac) that add up to b?

(21)(-20) = -420. What factors of -420 have a sum of +13.
If you start with, say, -10 and 42, which add up to 32, you can see that you need to get the numbers closer together. -14 and 30 is +16, which is closer. -15 and 28 gives you the result you're looking for.

Rewrite 21x² + 13x - 20 as 21x² - 15x + 28x - 20
Now separate them and factor: (21x² - 15x) + (28x - 20)
3x(7x - 5) + 4(7x - 5)
= (3x + 4)(7x - 5)



32. What are the equation and slope of the line shown on the grid?

F y = 6; slope is -1/6.
G x = 6; slope is zero.
H y = 6; slope is 6.
J x = 6; slope is undefined.

Answer: J x = 6; slope is undefined.
The slope of a vertical line is undefined. It is not zero. A slope of zero would be a horizontal line.
Vertical lines have equations like x = a, where a is the coordinate of the x-axis. There is no y in the equation.

33. In the year 1900, the total number of metric tons of copper produced in the world was 495,000. Each year since 1900, the total number of metric tons of copper produced has increased on average by about 3.25% over the amount produced the previous year.

Which function models the total number of metric tons of copper produced in the year that is x years since 1900?

A c(x) = 495,000(1.0325)^x
B c(x) = 495,000(0.9675)^x
C c(x) = 495,000x^1.0325
D c(x) = 495,000x^0.9675

Answer: A c(x) = 495,000(1.0325)^x
If the amount has increased, then the rate will be over 100%. An increase of 3.25% means that the rate is 103.25%, or 1.0325, which is Choice A.

Choice B represents a 3.25% reduction every year. Choices C and D are meaningless nonsense, created by mixing up the elements of the function.



34. What is the solution to 34x + 95 = 3(14x + 9)?

Record your answer and fill in the bubbles on your answer document.

Answer: 8.5 or 8 1/2

34x + 95 = 3(14x + 9)
34x + 95 = 42x + 27
95 = 8x + 27
68 = 8x
8.5 = x



35. The graphs of linear functions f and g are shown on the grid.

Which function is best represented by the graph of g?

A g(x) = f(x) - 4
B g(x) = 1/3 f(x)
C g(x) = f(x) - 2
D g(x) = 3f(x)

Answer: B g(x) = 1/3 f(x)
This is an interesting problem for me because it's not something that we encounter in New York in Algebra 1. In New York, when discussing transformations of functions, the focus is on translations, rigid motions, not dilations.

The first thing you notice about the graph is that the slope has changed, and the two lines intersect. This cannot happen in a translation, so Choices A and C are eliminated.

The new function has a smaller (less steep) slope than the original. Even without checking the points, it should be obvious that the slope must be 1/3 and not 3. If you check the graph, you can see that f(3) = 3 and g(3) = 1, f(6) = 6 and g(6) = 2. g(x) is 1/3 of f(x).

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2018, cont.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

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.





26.Which function is equivalent to f(x) = -4(x + 7)² - 6?

F f(x) = −4x² − 56x − 202
G f(x) = −4x² + 14x + 43
H f(x) = −4x² − 56x − 172
J f(x) = −4x² + 190

Answer: F f(x) = −4x² − 56x − 202
Look at the constant terms in the four choices. They are all different. Two of them make no sense at all.

The final term has to be (7)² X (-4) - 6. That cannot be a positive number, so G and J are eliminated.
(7)² X (-4) - 6 = -202. So it is Choice F.

Working it out would give you:

f(x) = -4(x + 7)² - 6
= -4(x² + 14x + 49) - 6
= -4x² - 56x - 196 - 6
= -4x² - 56x - 202



22. A paper airplane was thrown from the top of a tall building. The height of the paper airplane above the ground can be found using the function y = −1.5x + 60, where x is the time in seconds the airplane has been in the air.

How many seconds did it take the paper airplane to reach the ground?
Record your answer and fill in the bubbles on your answer document.

Answer:
The graph isn't necessary. In fact, graphing a slope of -1.5 when the scale is 5 might even be confusing. (It's actually the same as if the scale was 1, as far as counting boxes goes.)

0 = -1.5x + 60
-60 = -1.5x
40 = x
After 40 seconds the airplane will reach the ground.

28. Which expression is equivalent to (q⁴)^-3/q^-15

F q²⁷
G 1/q²⁷
H q³
J 1/q³

Answer: H q³
(q⁴)^-3/q^-15 = q^{(4)(-3) - (-15)} = q³



29. Which graph best represents a quadratic function that has only one zero?

Answer: B
A quadratic function with only one zero only touches the x-axis once. That means that the vertex must be on the x-axis itself as either a minimum or a maximum. That is choice B.

Choices A and C have two zeroes. Choice D has no zeroes. (Zero zeroes if you will.)



30. What is the solution set for −4x + 10 ≥ 5x + 55?

F x ≥ 5
G x ≥ 45
H x ≤ −5
J x ≤ −45

Answer: H x ≤ −5

−4x + 10 ≥ 5x + 55
−9x + 10 ≥ + 55
−9x ≥ 45
x ≤ −5
Don't forget to flip the inequality symbol around.

More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2018, cont.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

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 ft²/gal
B 1/200 ft²/gal
C 400 ft²/gal
D 1/400 ft²/gal

Answer: C 400 ft²/gal
If you go to 1 gallon on the x-axis, that lines up with 400 ft² on the y-axis. Change in y / Change in x, it is 400 ft² / gal.



22. What are the solutions to (x + 7)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 < x < 3
B -1 < y < 3
C 5.3 < x < 27
D 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

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.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2018, cont.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

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.





16. The water level of a river was measured each day during a two-week period. The graph models the linear relationship between the water level of the river in feet and the number of days the water level was measured.

Which statement best describe the y-intercept of the graph?

F The water level increased by 0.25 ft per day.
G The maximum water level was 19.5 ft.
H The initial water level was 16 ft.
J The water level was measured for 14 days.

Answer: H The initial water level was 16 ft.
The y-intercept represents the initial amount in a graph or fuction.

The other statements are all true, but have nothing to do with the y-intercept. In F, the incease in water level per day is the slope. In G, the maximum water level is a part on the graph, but not the initial point. In J, we've established the domain, 0 - 14, which concerns the x values, not the y values.



17. There are 1,024 players in a tennis tournament. In each round, half the players are eliminated. Which function can be used to find the number of players remaining in the tournament at the end of x rounds?

A f(x) = 1,024(1.50)^x
B f(x) = 1,024(0.50)^x
C f(x) = 1,024(1.05)^x
D f(x) = 1,024(0.05)^x

Answer: B f(x) = 1,024(0.50)^x%
If half the teams are eliminated, then the rate of decay is .50, or 50%.

Choice A shows a 50% increase, meaning more players are joining the tournament. Choice C shows a 5% increase. Choice D shows a 95% decrease, with only 5% advancing to the next round.

18. Which statement about g(x) = x² − 576 is true?

F The zeros, −288 and 288, can be found when 0 = (x + 288)(x − 288).
G The only zero, 288, can be found when 0 = (x − 288)².
H The zeros, −24 and 24, can be found when 0 = (x + 24)(x − 24).
J The only zero, 24, can be found when 0 = (x − 24)².

Answer: H The zeros, −24 and 24, can be found when 0 = (x + 24)(x − 24).
The Difference of Squares rule states that x² - n² can be factored into (x + n)(x - n). The "inner" and "outer" terms when multiplied form a zero pair and cancel out.

In this problem, 576 represents n², so n is SQRT(576), which is 24, not 288.



19. Which graph best represents the solution set -4x < 6y - 54?

Answer: A
Two questions to ask yourself: Is it a solid or a broken line? Is (0, 0) part of the solution?

Since we want "less than or equal to" (<) and not just "less than" (<), the graph needs to have a solid line, so Choices B and C are eliminated.
Substitute (0, 0) and we get 0 < 0 - 54, which is not a true statement. Therefore, (0, 0) is not a part of the solution, and that side of the line cannot be shaded. Choice D is eliminated.

The longer method involves rewriting the problem into slope-intercept form.

-4x < 6y - 54
6y - 54 > -4x
6y > -4x + 54
y > -4/6 x + 9
At this point, you can see that the line needs to be shaded above, not before. Also, you can see that choice A have a slope of -4/6 (or -2/3), while D has a slope of -6/4 (or -3/2).



20.Given f(x) = 1/3 (4 - x)², what is the value of f(16)?

Record your answer and fill in the bubbles on your answer document.

Answer:

f(16) = 1/3 (4 - 16)²
= 1/3 (-12) ²
= 1/3 (144)
= 48

More to come. Comments and questions welcome.

More STAAR problems.