## Saturday, February 27, 2021

### 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.

More STAAR problems.

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

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?

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

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.

## Friday, February 26, 2021

### (x, why?) Mini: Two Square Feet

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

It's great when someone can stand on their own two square feet.

I usually do a lot of Christmas comics but I wasn't able to do that this past December. This wouldn't have been one of them if I had. This is new, but it wasn't something worth holding for 10 months. I likely would've forgotten about it by then.

Come back often for more funny math and geeky comics.

### 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.

More STAAR problems.

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

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 an = 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 an = 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?

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.

## Thursday, February 25, 2021

### 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.

More STAAR problems.

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

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

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

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.

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.

## Wednesday, February 24, 2021

### Distance with Interest

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Remember the next time you RT any posting, you're going the D!

Alt tagline: If Kevin Costner does a math movie, it should be called Distance with Interest.

These two formulas gave me one of the most hilarious moments in teaching. I taught both of these formulas, along with other material, and had a quiz at the end of the week. Too tired to come up with different numbers for my version B quiz, I just flipped questions 4-6 with 7-9. This should have been immediately obvious to anyone who copied an answer after reading the question. It led to a student telling me that the time it takes a racecar traveling 200 mph to complete a 500 mile race was \$4,192.

Still a classic, after all these years.

The runner-up for that test was the kid who did long division to get 2 R1. ("This is Algebra. We don't 'remainder 1' here.") The student next to him wrote 2.1 without any indication how he got that answer. I had to explain "remainder 1" and "point 1" are usually not the same thing.

For anyone wondering, no, we don't cover modulo, the remainder function, in Algebra 1.

Come back often for more funny math and geeky comics.

## Tuesday, February 23, 2021

### Greatest Mathematicians

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Did they Blaise a trail for others to follow?

I almost said 'most influential', but that would've been a criterion.

My apologies for the lack of updates. I have been busy, both with classes and with writing. This is one of the reasons I like doing "Minis". My only hesitation was that I didn't want comic #1700 to be a mini. So you'll have to settle for a bad pun. It was going to be this one or the one coming up tomorrow.

As for the writing, I was working on a couple of short short stories that will be published in an anthology this summer. More details to come!

Come back often for more funny math and geeky comics.

## Tuesday, February 16, 2021

### (x, why?) Mini: One Dimension

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

You'd figure the round heads count as two-dimensional, but don't argue with the editor.

I've been putting a bit of effort into writing and rewriting a few stories, which has left me little time to work on the comics that I was planning on doing. And that's why I have these minis from time to time. Over 150 of them.

Come back often for more funny math and geeky comics.

## Wednesday, February 10, 2021

### Mandelbrot

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

My worst Mandelbrot joke. So far.

Granted, I've only had two, so maybe it's just worse than "mandlebrot".

Come back often for more funny math and geeky comics.

## Friday, February 05, 2021

### Mandelbar

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Just tri- it out for a while.

Why don't you take a closer look at it? Actually you won't have to.

The funny thing is when the search engines assume you meant "mandlebrot".

Come back often for more funny math and geeky comics.

## Wednesday, February 03, 2021

### (x, why?) Mini: By the C!

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Middle J, middle J, and I'm happy with B!

And to think, this joke was published:
"On 2/3, on 2/3, on 2 beautiful 3!!"

Oddly, this started as another lightspeed joke. Then it took a curve.

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## Monday, February 01, 2021

### Another Pirate Bit

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

A clipper ship between a pirate and a barber.

If I hadn't named him Art already, I would have gone with Joe. After all, Joe Dimagio was the Yankee Clipper.

Come back often for more funny math and geeky comics.