Math Horror Movie

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18 Years!

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

(C)Copyright 2024, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Some things never change. Some things change drastically. And some things change out of necessity or just basic improvement.

Moira's grown from a child. Michele was pregnant for two years. Everyone was masked for more than a year.

And Ken, for once, knew enough to keep his thoughts to himself!

HAPPY 18 Years of (x, why?)!

Yes, I'm the first one to admit that there has not been a lot of updates in the past two years. I didn't mean to bail. I didn't mean to panic.

There even came a time recently where I had to say "I used to have a webcomic..." Thankfully, I haven't gone a full year without an update. Yes, that's a low bar to set.

Why the hiatus?

There wasn't one particular reason, but a bunch of factors. There are always factors. After all, it's a Math comic, first and foremost!

Demands on my time

There are two parts to this. This comic really flourished during the years I was substituting rather than teaching full-time. And then came the lockdown, which had me home a lot more. There was no travel time. Plus, when this started, I was teaching 15 minutes from my house. Now it's more like an hour and fifteen minutes.

Also, I'm doing more with the time that I do have. I have tried to get my writing career going again, which started in 2016 and kicked up a notch in 2020. I haven't found the success I'd like, but it's amusing to think that I'd start being a writer and started by a webcomic writer. And for a while, I was okay with that. But the bug bit me again.

And before the shutdown, I really got into walking around Brooklyn. During the shutdown and immediately after, it kicked into high gear, and I was walking everywhere. I walked enough places that I started another blog dedicated to that, Walkin' in Brooklyn. (No "g" in Walkin'.)

This left little time for me to spend on creating the comics. Even with better tools, it takes longer because I've tried to raise the bar on what's acceptable. So unless I just want to publish "Minis" and "School Life" comics (and maybe not those), I couldn't churn them out as quickly.

Story Lines and Other Things

While I didn't exactly write myself into a corner, I did leave a bit of a cliffhanger with that Total Eclipse of the Sun and the Heart in 2024. I did intend to resolve that, even if it had to wait until the summer was over. But it was going to take time to write that because it was going to be too wordy. It needed edits and then I had to figure who was going to be in the intervention comic, as it were.

Slightly sillier is that the above comic is number 1989. I'm closing in on 2000. I've been thinking about 2000 comics for years now. I wanted to do them right.

I didn't want that to happen during October Math Horror Movies or December Christmas Math Carols. The comics would fit the seasons. I still want to do them, and there's only a few more left, so I need to plan them.

Personal Life

We all have things going on. But I spent too many days in the past few years visiting hospitals and cleaning up someone else's place. Mike's family is modeled somewhat after my own. To differentiate, I only gave him one sister and didn't plan on making One-to-One relationships between the families. No one was to be anyone's avatar ... even if they did occasionally take on some personality traits.

But Art imitates Life no matter how you slice it. There's only one sister but I know which one she is because the older of the two passed away many years ago. Longtime readers might remember Mike's mother, particularly on Mothers Day. However, I stopped including her when my mother passed away. (It could be the Dad in me, or maybe it's just that I appreciate the Dad and Uncle characters enough to keep them around for a while.) And then in the past few years, I lost two of my brothers. Both had had their share of health issues, and I did a lot of visiting.

By the way, ever since I was child, I've hated hospitals, and that feeling hasn't changed. But I will go to them.

Moving Forward

Okay, now that I've brought the room down, let me look to the future. Yes, I would like to get back into the habit of creating comics. Yes, I want to make it to 2000 comics and beyond. However, as you can tell from the ads below, I'd like to keep writing as well.

We'll see how this all plays out.

MY NEWEST BOOK IS OUT Burke's Lore Briefs: Yesterday's Villains, the following to Tomorrow's Heroes is now available on Amazon and Kindle Unlimited. If Heroes who don't die live long enough to become the villain, what happens to Villains who live long enough? When do schemes of global conquest become dreams of a quiet place away from all those annoying people you once wanted to subjugate? And does anyone really want to rule over the world's ashes if it means we can't have nice things?
My older books include three more books in my Burke's Lore Briefs series, and the anthologies A Bucket Full of Moonlight and In A Flash 2020. Vampires, werewolves, angels, demons, used-car salesmen, fairies, superheroes, space and time travel, and little gray aliens talking to rock creatures and living plants. Plus pirates, spies, horror, and kindergarten noir! If you enjoy my books, please consider leaving a rating or review on Amazon or on Good Reads. Thank you!

Algebra Problems of the Day (Algebra Regents, August 2025 Part I)

This exam was adminstered in August 2025.

More Regents problems.

August 2025 Algebra Regents

Part I

Each correct answer will receive 2 credits. No partial credit.


1. Which expression is equivalent to 100x² − 16?

(1) (50x - 8)(50x + 8)
(2) (50x - 8)(50x - 8)
(3) (10x - 4)(10x + 4)
(4) (10x - 4)(10x - 4)

Answer: (3) (10x - 4)(10x + 4)

This is the Difference of Two Perfect Squares Rule. Take the square root of each term and write the conjagtes -- that is, write two binomials that are the same except that one is separated by addition (+) and one is separated by subtraction (-).

In Choices (1) and (2), 50x times 50x is 2500x², not 100x². Eliminate these.

In Choice (4), you are squaring (10x - 4), which will produce a constant of + 16, not - 16, as well as a middle term of -80x. Eliminate Choice (4).

Choice (3) is the Correct answer.

2. Josie has $2.30 in dimes and quarters. She has two more dimes than quarters. Which equation below can be used to determine x, the number of quarters she has?

(1) 0.35(2x + 2) = 2.30
(2) 0.25(x + 2) + 0.10x = 2.30
(3) 0.25x + 0.10(x + 2) = 2.30
(4) 0.25x + 0.10(x − 2) = 2.30

Answer: (3) 0.25x + 0.10(x + 2) = 2.30

If x is the number of quarters, then 0.25x is the amount that those quarters are worth. Eliminate Choices (1) and (2).

If there are 2 more dimes than quarters, then the number of dimes is x + 2, not x - 2. So the correct answer is Choice (3).

3. If g(x) = −2x² + 16 then g(−3) equals

(1) -20
(2) -2
(3) 34
(4) 52

Answer: (2) -2

Substitute and evaluate. Put -2(-3)² + 16 into your calculator.

g(-3) = -2(9) + 16 = -18 + 16 = -2, which is Choice (2).

4. What are the zeros of f(x) = x² − 8x − 20?

(1) 10 and 2
(2) 10 and -2
(3) -10 and 2
(4) -10 and -2

Answer: (2) 10 and -2

Since the constant term is negative, then one of the roots will be positive and the other will be negative. Eliminate Choices (1) and (4).

You can factor and solve the quadratic equation, or you can try the choices to see what works.

In Choice (2), (10)² - 8(10) - 20 = 100 - 80 - 20 = 0 is a true statement. Since we've already eliminated Choice (1), Choice (2) must be the correct answer.

You can check the other root: (-2)² - 8(-2) - 20 = 4 + 16 - 20 = 0, which is true.

Algebraically:

x² − 8x − 20 = 0
(x - 10)(x + 2) = 0
x - 10 = 0 or x + 2 = 0
x = 10 or x = -2

5. Which point lies on the graph of y = 3x² - 1/4 x + 3?

(1) (−2,15.5)
(2) (−1,5.75)
(3) (1,6.25)
(4) (2,15.5)

Answer: (1) (−2,15.5)

Check each x in the calculator to see if you get the correct y value. Or graph the function and look at the Table of Values.

In Choice (1), 3(-2)² - 1/4(-2) + 3 = 15.5, which is correct. Choice (1) is the correct choice.

In Choice (2), 3(-1)² - 1/4(-1) + 3 = 6.25, not 5.75. Eliminate Choice (2).

In Choice (3), 3(1)² - 1/4(1) + 3 = 5.75, not 6.25. Eliminate Choice (3).

In Choice (2), 3(2)² - 1/4(2) + 3 = 14.5, not 15.5. Eliminate Choice (4).

6. Given f(x) = x² and g(x) = 8x − 15 graphed on the same set of axes, which value(s) of x will make f(x) = g(x)?

(1) 3, only
(2) 9, only
(3) 3 and 5
(4) 9 and 25

Answer: (3) 3 and 5

Graph both equations and check the Table of Values for 3, 5, 9 and 15. Or substitute and solve.

f(3) = 3² = 9 and g(3) = 8(3) - 15 = 24 - 15 = 9, so f(3) = g(3). This means the correct answer is either (1) or (3). Eliminate Choice (2) and (4).

f(5) = 5² = 25 and g(5) = 8(5) - 15 = 40 - 15 = 25, so f(5) = g(5). The correct answer is Choice (3).

Algebraically:

f(x) = g(x)
x² = 8x - 15
x² - 8x + 15 = 0
(x - 3)(x - 5) = 0
x - 3 = 0 or x - 5 = 0
x = 3 or x = 5

7. Which trinomial is written in standard form and has a constant term of five?

(1) x⁵ − 4x² + 10
(2) 2x² + 6x⁴ + 5
(3) 5x⁴ − 3x² + 1
(4) 4x⁵ − 8x² + 5

Answer: (4) 4x⁵ − 8x² + 5

A constant is a numerical term without a variable. Choice (1) has a constant of 10, and Choice (3) has a constant of 1. Eliminate them.

Choice (2) is not in standard form because the term with the highest exponent is not first. Eliminate Choice (2).

Choice (4) is the correct answer.

8. When solving x² + 6x = −8 for x, a student wrote x² + 6x + 8 = 0 as their first step. Which property justifies this step?

(1) associative property
(2) commutative property
(3) zero property of addition
(4) addition property of equality

Answer: (4) addition property of equality

Adding 8 to both sides of the equation is an example of the addition property of equality. This is Choice (4).
More to come. Comments and questions welcome.

MY NEWEST BOOK IS OUT Burke's Lore Briefs: Yesterday's Villains, the following to Tomorrow's Heroes is now available on Amazon and Kindle Unlimited. If Heroes who don't die live long enough to become the villain, what happens to Villains who live long enough? When do schemes of global conquest become dreams of a quiet place away from all those annoying people you once wanted to subjugate? And does anyone really want to rule over the world's ashes if it means we can't have nice things?
My older books include three more books in my Burke's Lore Briefs series, and the anthologies A Bucket Full of Moonlight and In A Flash 2020. Vampires, werewolves, angels, demons, used-car salesmen, fairies, superheroes, space and time travel, and little gray aliens talking to rock creatures and living plants. Plus pirates, spies, horror, and kindergarten noir! If you enjoy my books, please consider leaving a rating or review on Amazon or on Good Reads. Thank you!

Algebra Problems of the Day (Algebra Regents, January 2025 Part I)

This exam was adminstered in January 2025.

More Regents problems.

January 2025 Algebra Regents

Part I

Each correct answer will receive 2 credits. No partial credit.


17. A function is graphed on the set of axes below.

The domain of the function is

(1) {x | x > -2}
(2) {x | x > -2}
(3) {x | x > -4}
(4) {x | x > -4}

Answer: (1) {x | x > -2}

The open circle indicates greater than but not equal to. Eliminate Choices (2) and (4).

The domain is the x value and the lowest possible x value is -2. The correct answer is Choice (1).

Choices (3) and (4) confuse the domain with the range, except they use x instead of y. The range is {y | y > -4}.

18. Which ordered pair is a solution to the equation y − 1 = 2(x + 1/4)?

(1) (0.75,0)
(2) (1.25,4)
(3) (2.5,-6.5)
(4) (4,-9.5)

Answer: (2) (1.25,4)

Add 1 to both sides of the equation and check y = 2(x + .25) + 1 for each of the four choices.

Choice (1), y = 2(.75 + .25) + 1 = 3, not 0. Eliminate Choice (1).

Choice (2), y = 2(1.25 + .25) + 1 = 4. Choice (2) is the correct answer.

In Choices (3) and (4), it should be obvious that the value of y for the given x will be positive and not negative, so both Choices (3) and (4) could be eliminated. However, if you didn't notice that, we can continue.

Choice (3), y = 2(2.5 + .25) + 1 = 6.5, not -6.5. Eliminate Choice (3).

Choice (43), y = 2(4 + .25) + 1 = 9.5, not -9.5. Eliminate Choice (4).

19. Elena’s fastest time for the 50-meter dash is 7 seconds. She wants to know how fast this is in inches per minute. Which expression can Elena use for a correct conversion?

Answer: (4) [See Image]

If you are changing meters per second into inches per minute than inches needs to appear once on top and minutes need to appear once on the bottom. The starting fraction needs to be meters/second, and both of those units need to be cancelled.

Choices (1) and (2) start with seconds per meter. Eliminate both of them.

Choice (3) has meters twice in the numerator, so neither one cancels. The end result will be meters² per min-in. Eliminate Choice (3).

Choice (4) has meters once in the numerator and once in the denominator, which cancel. It has seconds once in the numerator and once in the denominator, which cancel. The final result is in/meter. Choice (4) is the correct answer.

20. The table below shows the highest temperatures recorded in August for several years in one town.

The interquartile range of these data is

(1) 7
(2) 10
(3) 11
(4) 18

Answer: (3) 11

You can put the temperatures (not the years) into a list in your calculator and get a Five-Number Summary by doing 1-Var Stats.

Or you could arrange the data in order and do it yourself:

77, 78, 81, 84, 86, 88, 93, 95

There are 8 pieces of data, so the average of the fourth and fifth is the median, which is 85, but not important to this problem.

The median of the first four numbers is 79.5, which is Q1. The median of the last four numbers is 90.5, which is Q3. The IQR is Q3 - Q1, which is 90.5 - 79.5, which is 11. This is Choice (3).

21. The function f(x) = x² is multiplied by k, where k < −1. Which graph could represent g(x) = kf(x)?

Answer: (4) [See Image]

Multiplying a quadratic function by a factor greater than 1 will make it skinnier. Multiplying a quadratic function by a factor less than -1 will make it skinnier AND flip the direction of the parabola.

The given function, f(x) = x², opens upward. The new function, g(x), will open downward and be thinner than the original. This is Choice (4).

If 0 < k *lt 1, then Choice (1) would've been the correct answer.

If -1 < k < 0, then Choice (2) would've been the correct answer.

If k > 1, then Choice (3) would've been the correct answer.

22. Which graph is the solution to the inequality 6.4 − 4x ≥ −2.8?

Answer: (2) [See Image]

Since greater than or equal to is specified, the answer will have a closed circle. Eliminate Choices (1) and (3).

Next, you can check to see if x = 0 is in the solution set or not.

6.4 - 4(0) ≥ −2.8?
6.4 ≥ −2.8 (check)

Since 0 is in the solution set, the correct choice must be Choice (4) and not Choice (2).

Algebraically,

6.4 - 4x ≥ −2.8
-4x ≥ −9.2
x < 2.3

Remember that when you divide (or multiply) an inequality by a negative number, you have to flip the direction of the inequality symbol.

The correct answer is Choice (2).

23. The number of fish in a pond is eight more than the number of frogs. The total number of fish and frogs in the pond is at least 20. If x represents the number of frogs, which inequality can be used to represent this situation?

(1) x + 8x ≥ 20
(2) 2x + 8 ≥ 20
(3) x + 8x ≤ 20
(4) 2x + 8 ≤ 20

Answer: (2) 2x + 8 ≥ 20

The term 8x refers to 8 times as many fish as frogs, not 8 more than the number of frogs. Eliminate Choices (1) and (3).

The pond has at least 20 fish and frogs meaning that the combined number is greater than 20. The correct choice is Choice (2).

24. Which graph below represents a function that is always decreasing over the entire interval −3 < x < 3?

Answer: (4) [See image]

Always decreasing means as x gets bigger, y gets smaller. The graph is always going down and to the right.

Choice (1) is increasing in the interval −3 < x < 3. Eliminate Choice (1).

Choice (2) is increasing in the interval −3 < 0 and then starts decreasing. Eliminate Choice (2).

Choice (3) is increasing in the interval −3 < x < 3. Eliminate Choice (3).

Choice (4) is the correct answer.

End of Part I. Comments and questions welcome.

MY NEWEST BOOK IS OUT Burke's Lore Briefs: Yesterday's Villains, the following to Tomorrow's Heroes is now available on Amazon and Kindle Unlimited. If Heroes who don't die live long enough to become the villain, what happens to Villains who live long enough? When do schemes of global conquest become dreams of a quiet place away from all those annoying people you once wanted to subjugate? And does anyone really want to rule over the world's ashes if it means we can't have nice things?
My older books include three more books in my Burke's Lore Briefs series, and the anthologies A Bucket Full of Moonlight and In A Flash 2020. Vampires, werewolves, angels, demons, used-car salesmen, fairies, superheroes, space and time travel, and little gray aliens talking to rock creatures and living plants. Plus pirates, spies, horror, and kindergarten noir! If you enjoy my books, please consider leaving a rating or review on Amazon or on Good Reads. Thank you!

Algebra Problems of the Day (Algebra Regents, January 2025 Part I)

This exam was adminstered in January 2025.

More Regents problems.

January 2025 Algebra Regents

Part I

Each correct answer will receive 2 credits. No partial credit.


9. When the formula p = 2l + 2w is solved for w, the result is

(1) w = (2l + p) / 2
(2) w = (p - 2l) / 2
(3) w = p/2 + l
(4) w = l - p/2

Answer:(2) w = (p - 2l) / 2

Use inverse operations to isolate w.

p = 2l + 2w

p - 2l = 2w

(p - 2l) = w

The correct answer is Choice (2).

10. Market Street Pizza kept a record of pizza sales for the month of February. The results are shown in the table below.

Of all the pizzas sold in February, what percent were plain, deep-dish pizzas?

(1) 20%
(2) 30%
(3) 40%
(4) 50%

Answer: (1) 20%

There were 200 plain, deep-dish pizzas sold. The percentage would be 200 divided by the total number of pizzas sold. Find the grand total of all pizzas in the table.

300 + 200 + 80 + 25 + 120 + 105 + 100 + 70 = 1000 pizzas sold.

200/1000 = 0.20 = 20%, which is Choice (1).

11. When solving -2(3x - 5) = 9/2 x - 2 for x, the solution is

(1) 8/7
(2) 10/11
(3) -16/21
(4) -16/3

Answer: (1) 8/7

You can solve this with the calculator but be sure to use parentheses when substituting.

-2(3x - 5) = 9/2 x - 2

-6x + 10 = 9/2 x - 2

-12/2 x + 10 = 9/2 x - 2

-21/2 x = -12

-21x = -24

x = -24/-21

x = 8/7

The correct Choice is Choice (1).

12.The expression x^{2a + b} is equivalent to

(1) x^2a + x^b
(2) x^a + x^{a + b}
(3) x^a * x^{a + b}
(4) x^{a + b} * x^{a + b}

Answer: (3) x^a * x^{a + b}

Terms with different exponents CANNOT be combined because they are not Like Terms. Terms with the same base can be multiplied. When multiplying terms with the same base, the exponents are added.

The first two choices cannot be added together because they are not like terms. Eliminate Choices (1) and (2).

In Choice (3), x^a * x^{a + b} = x^{2a + b}, which is the correct answer.

In Choice (4), x^{a + b} * x^{a + b} = x^{2a + 2b}. Eliminate Choice (4).

13. The inputs and outputs of a function are shown in the table below.

This function can best be described as

(1) linear
(2) quadratic
(3) exponential
(4) absolute value

Answer: (3) exponential

There is no common difference but there is a common ratio. You can see from the bottom three lines that 0.5 times 2 is 1 and 1 times 2 is 2. You can check the others as well. Going up the table, each decimal is half as large as the one below it.

Since the table has a common ratio, it is exponential, which is Choice (3).

14. Stephanie is solving the equation x² - 12 = 7x - 8. Her first step is shown below. Given: x² - 12 = 7x - 8
Step 1: x² - 4 = 7x

(1) associative property
(2) commutiative property
(3) distributive property
(4) addition property of equality

Answer: (4) addition property of equality

To get from the Given equation to the Step 1, Stephanie added 8 to both sides of the equation. This is possible because of the addition property of equality.

The correct answer is Choice (4).

15. What is the sum of 8√(3) and √(3)?

(1) 8√(6)
(2) 9√(6)
(3) 7√(3)
(4) 9√(3)

Answer: (4) 9√(3)

The sum of 8x and x is 9x. This is true whether x is apples, kittens, -27, or √(3).

Choice (4) is the correct answer.

16. The dot plots below represent test scores for 20 students on a math test.

The mode for this math test is 80 and the median is 85. Which dot plot correctly represents this data?

(1) I
(2) II
(3) III
(4) IV

Answer: (1) I

The mode of a dot plot is the number with the highest columns of dots. That eliminates Choices (2) and (4).

The median of 20 students is the average of the 10th and 11th score. In plot I, the 10th and 11th dots are both 85. In plot III, the 10th and 11th dots are in the 80 column.

Eliminate Choice (3).

Choice (1) is the correct answer.

More to come. Comments and questions welcome.

MY NEWEST BOOK IS OUT Burke's Lore Briefs: Yesterday's Villains, the following to Tomorrow's Heroes is now available on Amazon and Kindle Unlimited. If Heroes who don't die live long enough to become the villain, what happens to Villains who live long enough? When do schemes of global conquest become dreams of a quiet place away from all those annoying people you once wanted to subjugate? And does anyone really want to rule over the world's ashes if it means we can't have nice things?
My older books include three more books in my Burke's Lore Briefs series, and the anthologies A Bucket Full of Moonlight and In A Flash 2020. Vampires, werewolves, angels, demons, used-car salesmen, fairies, superheroes, space and time travel, and little gray aliens talking to rock creatures and living plants. Plus pirates, spies, horror, and kindergarten noir! If you enjoy my books, please consider leaving a rating or review on Amazon or on Good Reads. Thank you!

Algebra Problems of the Day (Algebra Regents, January 2025 Part I)

This exam was adminstered in January 2025.

More Regents problems.

January 2025 Algebra Regents

Part I

Each correct answer will receive 2 credits. No partial credit.


1. When factored, the expression x³ - 36x is equivalent to

(1) (x + 6)(x - 6)
(2) (x + 18)(x - 18)
(3) x(x + 6)(x - 6)
(4) x(x + 18)(x - 18)

Answer: (3) x(x + 6)(x - 6)

If the expression is third-degree, that is, it has x³ in it, then there must be three factors of x when factored. Eliminated choices (1) and (2).

The Greatest Common Factor of the two terms is x. When you factor the x, you get x(x² - 36).

That binomial is the difference of two perfect squares which factors into (x + 6)(x - 6) because (6)(-6) equals -36 and (6) + (-6) = 0.

The correct answer is Choice (3).

You can put y = x³ - 36x into your graphing calculator and then graph the four choices. You will see that the Choices (1) and (2) are parabolas and that Choice (4) does not match the original graph. You can also look at the Table of Values if the graph goes off the screen.

2. Which equation represents the line that passes through the points (-1,8) and (4,-2)?

(1) y = -2x + 6
(2) y = -2x + 10
(3) y = -0.5x + 7.5
(4) y = -0.5x + 8.5

Answer: (1) y = -2x + 6

Find the slope of the line and then check which choice has an equation that works for both points.

The slope of a line is (y2 - y1) / (x2 - x1) = (-2 - 8) / (4 - (-1)) = 10 / (-5) = -2. Eliminate Choices (3) and (4).

At this point, you can graph the first two lines and check the Table of Values. Or you can do it algebraically.

y - (-2) = -(2)(x - 4)
y - (-2) = -2x + 8
y = -2x + 6

Once again, you could have graph all four lines and checked the Table of Values to find a match.

The correct answer is Choice (1).

3. A geometric sequence is shown below.

1/2, 2, 8, 32, ...

What is the common ratio?

(1) 1/4
(2) 2
(3) 1/2
(4) 4

Answer: (4) 4

The common ratio is what you multiply each term by to get the next term. There are four 1/2's in 2, and 2 goes into 8 four times, etc.

The correct Choice is Choice (4).

If the common ratio was a fraction, like, 1/2 or 1/4, then the sequence would be getting smaller.

If the common ratio was 2, the sequence would've been 1/2, 1, 2, 4, 8, 16, 32, ...

4. What is the constant term of the polynomial 2x³ - x + 5 + 4x²?

(1) 5
(2) 2
(3) 3
(4) 4

Answer: (1) 5

The constant term is the one without a variable. It's a constant because its value doesn't change!

The constant in this polynomial is the + 5.

Choice (1) is the correct answer.

5. A landscaping company charges a set fee for a spring cleanup, plus an hourly labor rate. The total cost is modeled by the function C(x) = 55x + 80. In this function, what does the 55 represent?

(1) the set fee for the cleanup
(2) the hourly labor rate for a cleanup
(3) the profit earned by the company for one cleanup
(4) the number of hours of labor required for one cleanup

Answer: (2) the hourly labor rate for a cleanup

The variable represents the number of hours worked. That is the only thing unknown. The variable is multiplied by the hourly labor rate, which in this function is 55.

The correct answer is (2).

6. Which expression is equivalent to (5x² - 2x + 4) - (3x² + 3x - 1)?

(1) 2x² + x + 3
(2) 2x² - 5x + 5
(3) 2x⁴ + x² + 3
(4) 2x⁴ - 5x² + 5

Answer: (1) 2x² + x + 3

When adding or subtracting polynommials, the exponents DO NOT change. You can only combine like terms, like counting puppies and kittens. Eliminate Choices (3) and (4).

Distribute the minus sign and combine like terms.

(5x² - 2x + 4) - (3x² + 3x - 1)

5x² - 2x + 4 - 3x² - 3x + 1

2x² - 5x + 3

The correct answer is Choice (1).

7. A system of inequalities is graphed on the set of axes below.

Which point is a solution to this system?

(1) (1,1)
(2) (2,-2)
(3) (1,8)
(4) (4,2)

Answer: (4) (4,2)

The solution to the system of inequalities is the set of points in the double-shaded (criss-cross) area as long as they are NOT on the broken line. The broken line is not in the solution set. It represents a boundary that isn't part of the solution.

Choice (1) is the intersection of the broken and solid lines. Eliminate Choice (1).

Choice (2) is on the broken line. Eliminate Choice (2).

Choice (3) is a solution to only one of the two inequalities. Eliminate Choice (3).

Choice (4) is in the double-shaded area. This is the correct answer.

8. In an arithmetic sequence, the first term is 25 and the third term is 15. What is the tenth term in this sequence?

(1) -20
(2) -25
(3) 70
(4) 75

Answer: (1) -20

The sequence is getting smaller, not bigger, so 70 and 75 are just silly. Eliminate Choices (3) and (4).

The difference is -10 after 2 terms, so each term is going down by 5. You could easily write this out:

25, 20, 15, 10, 5, 0, -5, -10, -15, -20.

The correct choice is Choice (1).

Algebraically, if each term subtracts 5 and the tenth term is nine terms after the first term, then the tenth term must be:

25 - 5(9) = -20

This is useful if you need to find a bigger number or if the common difference isn't an "easy" number like 5.

More to come. Comments and questions welcome.

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