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.

(x, why?) Mini: Pseudo-

(Click on the comic if you can't see the full image.)

(C)Copyright 2020, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

One is derivative of another

In this case, this comic is derivative of two earlier ones, plus the more famous one from that other geeky, math/science/computer comic website. (You know which one.) I used a version of this when Leslie Nielsen passed away. And that time, I'd forgotten that I'd done an earlier version based on a Phil Collins song.

The "sudo" referenced here is the "sudo" computer command, which allows a user to run something with the privileges of another person (usu the "superuser"), even if they couldn't make the computer "do" it on their own.

As for the math, there is a tweet with a calendar problem for today from @GWOMaths about the Pseudo-Rhombicuboctahedron. If it was today's tweet, how did I know about it? Well, you might want to take a look at the answer tomorrow.

A Rhombicuboctahedron is an Archimedean solid with 26 faces: 18 squares and 8 equilateral triangles. A Pseudo-Rhombicuboctahedron is a similar object, but one section of it (top or bottom) is rotated by 45 degrees (1/8 of a full-rotations) or by some other odd multiple of 45. Being offset like this reduces some of the properties of the regular Rhombicuboctahedron.

The twisting is reminscent of the antiprism.

Come back often for more funny math and geeky comics.

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.

Quadratic Function Joke

(Click on the comic if you can't see the full image.)

(C)Copyright 2020, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

A five is nothing. Watch out for the zeroes!

If Ken is to be believed (never a sure bet), then the function would be in the form of y = a(x - 5)² - 4. Since we don't know the zeroes, we don't know what a is. Conversely, since we don't know a, we don't know the zeroes. However, if a = 1, then the zeroes are x = 3 and x = 7.

Come back often for more funny math and geeky comics.

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.

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.





11. Which expression is equivalent to x² − 17x − 60?

A (x - 20)(x + 3)
B (x - 5)(x - 12)
C (x - 20)(x - 3)
D (x + 5)(x - 12)

Answer: A (x - 20)(x + 3)
The minus sign in front of the 60 tells you that one factor is positive and one factor is negative. That eliminates Choices B and C.

What are two factors of -60 that add up to -17? -20 + 3 = -17, Choice A is the answer.



12. A zookeeper recorded the feeding schedule for a baby rhinoceros for 20 weeks. The table and scatterplot show the percentage of the baby rhinoceros’s body mass that was used to determine the amount of food given at each feeding as a linear function of its age in weeks.

What is the best prediction of the percentage of the baby rhinoceros’s body mass that should be used to determine the amount of food given at each feeding when it is 25 weeks old?

F 8.5%
G 6%
H 2.5%
J 10%

Answer: G 6%
Put the data into your graphing calculator and do a linear regression. You will get a = -.5448... and b = 19.80...
That makes your line of best fit, rounded to the nearest hundredth, y = -.54x + 19.80.
Substitute 25 for x and you get y = -.54(25) + 19.80 = 6.3, which is approximately 6%, which is Choice G.

13. What are the domain and range of f(x) = −37?

A Domain: All real numbers greater than or equal to −37; Range: All real numbers
B Domain: {−37} ; Range: All real numbers
C Domain: All real numbers ; Range: All real numbers greater than or equal to −37
D Domain: All real numbers ; Range: {−37}

Answer: D Domain: All real numbers ; Range: {−37}
The range is {-37}. No matter what the input is, the output is -37. That is the entirety of the range. That gives you exactly one option, Choice D.

The input is All real numbers. It doesn't matter what x is, and there are no restrictions on it. There are no values that are undefined.



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

If k(x) = x² and p(x) = k(x) + n, what is the value of n? Record your answer and fill in the bubbles on your answer document.

Answer:
The graph of the parent function k(x) = x² goes through the origin, (0, 0). The illustrated graph of p(x) has its vertex at (0, -6). Therefore, p(x) = x² - 6, which means that n = -6.

You can check this by substituting x = -3 or x = 3. Both numbers squared give 9 which after subtracting 6 becomes 3.



15. Two customers went to a post office to buy postcards and large envelopes. Each postcard costs the same amount, and each large envelope costs the same amount.

• • The first customer paid $12 for 14 postcards and 5 large envelopes.
• • The second customer paid $24.80 for 10 postcards and 15 large envelopes.

What was the cost in dollars of each large envelope?

A $1.42
B $0.35
C $1.15
D $0.63

Answer: A $1.42
The system of equations is as follows:

14x + 5y = 12
10x + 15y = 24.80
multiply the first equation by 3, and then subtract
42x + 15y = 36.00
10x + 15y = 24.80
32x = 11.20
x = 0.35, which is the cost of a postcard
14(.35) + 5y = 12
4.90 + 5y = 12
5y = 7.10
y = 1.42, which is the cost of a large envelope

More to come. Comments and questions welcome.

More STAAR problems.

Happy Thanksgiving 2020!

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(C)Copyright 2020, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

From start to finish, there's a strong aromatic sequence from one course to the next.

A lot of food for one small family of four, but how many people can cook smaller Thanksgiving dinners and still call it a Thanksgiving dinner? I mean, what are you going to leave out?

And you know that there will be "food runs" to the relatives who couldn't be there.

Happy Thanksgiving from (x, why?)!

Come back often for more funny math and geeky comics.

Call Me Mike

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(C)Copyright 2020, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

It just sounds wrong, right?

Students who keep in touch on social media still call me Mr. B, which is fine. But I've seen a couple socially, and they've tried not calling me that, and it doesn't work for them. Even though people younger than them have no problem.

This, of course, carries over to all of my parents' friends. Keep in mind, I'm older than Mike.

On a comic note: Moira (first time mentioning a name) was a student here when she was younger. She became a teaching student of Michele's shortly after the wedding.

Come back often for more funny math and geeky comics.