Saturday, June 23, 2018

Trigonometry Jones and the Running Gag, Part 3

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

(C)Copyright 2018, C. Burke.

You could say that brings us back to the origin.

Had I known that "Trigonometry Jones" would become A Thing, I might've planned for a compass to appear in that first run of strips. But then that would have compromised the first joke, which was that they were lost.

Seriously, T.J. started as extremely elaborate "right angle" joke. It all changed when I added the spiffy hat!

By the way, several months back, I started re-running own comics on Twitter on Saturday afternoons at 1pm ET, with the label #SaturdayMatinee.
This comic is timed to appear on Twitter the same time it appears on the blog!




Come back often for more funny math and geeky comics.




Friday, June 22, 2018

(x, why?) School Life #3

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

(C)Copyright 2018, C. Burke.

Condensed conversations for three panels, losing many awkward periods of silence.

If I hadn't tossed the script yesterday, it would've gone out the window today.
I toyed with Daisy only being called "Daisy" because she liked the flowers so much, but it wasn't actually her name. (Maybe that will still happen?)
But that's why this is an experiment, and I want to include these as "bonus" comics for the time being.

I added a line to Daisy's glasses. I think I like them better now. Thicker frames didn't work -- too raccoon-ish.




Come back often for more funny math and geeky comics.




L33t

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

(C)Copyright 2018, C. Burke.

1f y0u c4n r34d 7h15, y0u n33d 4 n3w h0bby.

This is Comic #1337, which means "leet" is "leetspeak", which is short for "elite", and was an offshoot of a hacker language that was popular back in usenet in the 90s (and probably earlier, but that's when I got onto usenet). It was a cipher, a secret code, replacing letters with numbers or a combination of symbols. So A could be 4 or @, T could be 7 or +, H might be ][ or |-| or even ]-[. You get the idea, or 1|)34.

Translating wasn't a big issue; it was the typing that was the problem. Plus, different generators have different defaults, which meant that I could pick and choose between them. But I wanted to ASCII (particularly because of the paint program) so I wasn't going to use, say, the registered trademark symbol for 'R'.

I don't think I could have imagined when I did the Roman Elite Guard back in Comic #220 (2009), that I'd still be doing this a thousand comics later!




Come back often for more funny math and geeky comics.




Thursday, June 21, 2018

(x, why?) School Life #2

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

(C)Copyright 2018, C. Burke.

Also, your fly is open.

The "funny" thing is that I wanted to use "Tell me something I don't know" for something totally different, as a setup for another punchline, later in the series.
I'll get there.




Come back often for more funny math and geeky comics.




Complete the Squares and Circles

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

(C)Copyright 2018, C. Burke.

Why give an equation in standard form when you can make students work for it, right?

The scene will continue in the next couple of (x, why?) School Life, which are on the way! No, for real, this time.




Come back often for more funny math and geeky comics.




June 2018 Common Core Algebra I Regents (mult choice)

The following are some of the multiple questions from the recent January 2018 New York State Common Core Algebra I Regents exam.

June 2018 Algebra I, Part I

Each correct answer is worth up to 2 credits. No partial credit. Work need not be shown.


1. The solution to 4p + 2 < 2(p + 5) is

Answer: (4) p < 4
Distributive property and inverse operations.
4p + 2 < 2(p + 5)
4p + 2 < 2p + 10
2p + 2 < 10
2p < 8
p < 4
There is no multiplication or division by a negative, so there is no need to flip the inequality symbol.


2. If k(x) = 2x2 - 3*sqrt(x), the k(9) is

Answer: (4) 153
Substitution and Order of Operations.
2(9)2 - 3(9)^(.5) = 2(81) - 3(3) = 162 - 9 = 153


3. The expression 3(x2 + 2x - 3) - 4(4x2 - 7x + 5) is equivalent to

Answer: (2) -13x2 + 34x - 29
Distributive property (including distributing a minus sign) and Combining Like Terms.
3(x2 + 2x - 3) - 4(4x2 - 7x + 5)
3x2 + 6x - 9 - 16x2 + 28x - 20
-13x2 + 34x - 29
Once you got -13, you could have eliminated choices 3 and 4. If you didn't get either choice 1 or 2, go back and check your signs.


4. The zeros of the function p(x) = x2 - 2x - 24 are

Answer: (3) -4 and 6
Factoring to find zeros / roots / x-intercepts. What two factors of -24 have a sum of -2?
x2 - 2x - 24 = 0
(x - 6)(x + 4) = 0
x - 6 = 0 or x + 4 = 0
x = 6 or x = -4
I hope you didn't jump the gun after factoring and answer the question without solving for x, which flipped the signs.


5. The box plot below summarizes the data for the average monthly high temperatures in degrees Fahrenheit for Orlando, Florida.

The third quartile is

Answer: (2) 90
Box-and-whisker plots. Five-Number Summary.
The five-number summary for the plot shown are: Minimum is approximately 71. Q1 is 75. Median is approximately 83. Q3 is 90. Maximum is approximately 92.
"Approximately" because those numbers aren't labeled, but they can be inferred from the choices.
Not that the incorrect choices line up with another key portion of the plot.ut solving for x, which flipped the signs.


6. Joy wants to buy strawberries and raspberries to bring to a party. Strawberries cost $1.60 per pound and raspberries cost $1.75 per pound. If she only has $10 to spend on berries, which inequality represents the situation where she buys x pounds of strawberries and y pounds of raspberries?

Answer: (1) 1.60x + 1.75y < 10
Modeling inequalities
If x in the number of pounds of strawberries, which cost $1.60 per pound, then the first term is 1.60x. Eliminate choices 3 and 4.
She can't spend more than 10 dollars but and spend less than or exactly 10 dollars. So choice 1.


7. On the main floor of the Kodak Hall at the Eastman Theater, the number of seats per row increases at a constant rate. Steven counts 31 seats in row 3 and 37 seats in row 6. How many seats are there in row 20?

Answer: (1) 65
Sequences. Rate of Change.
If there are 6 more seats (37 - 31) when you go back 3 rows (6 - 3), then there is a rate of change of 2 seats per row.
If you go back another 14 rows (20 - 6), then there should be an additional 28 seats (14 * 2).
37 + 28 = 65 seats.
If x in the number of pounds of strawberries, which cost $1.60 per pound, then the first term is 1.60x. Eliminate choices 3 and 4.
She can't spend more than 10 dollars but and spend less than or exactly 10 dollars. So choice 1.


8. Which ordered pair below is not a solution to f(x) = x2 - 3x + 4?

Answer: (4) (-1, 6)
Graphing. Substitution. Evaluation.
Quickest way is to put the function into the graphing calculator and check the table of values. You will see that (-1, 8) is a solution, not (-1, 6).
If you change the settings, or use the Trace function, you will see that (1.5, 1.75) is a solution.


9. Students were asked to name their favorite sport from a list of basketball, soccer or tennis. The results are in the table below:
What percentage of the students chose soccer as their favorite sport?

Answer: (1) 39.6%
Statistics. Two-way frequency tables. Marginal frequencies. Percentages.
Find the number of student who prefer soccer. Find the total number of students. Divide the first by the second and multiply by 100%.
58 + 41 = 99 students like soccer
There are 42 + 84 + 58 + 41 + 20 + 5 = 250 total students
99 / 250 = 0.396 = 39.6%


10. The trinomial x2 - 14x + 49 can be expressed as

Answer: (1) (x - 7)2
Factoring. Perfect squares. Completing the squares
Even if you didn't recognize that this trinomial is a perfect square, you could have factored it quickly into (x - 7) and (x - 7), which is (x - 7)2.
Incorrect choices: Choice 2 would give + 14x as the middle term. Choice 3 has two conjugates, so there would be NO middle term. Choice 4 is just silly: -7 times 2 is not +49.


11. A function is definied as {(0,1), (2,3), (5,8), (7,2)}. Isaac is asked to create one more ordered pair for the function. Which ordered pair can be add(ed) to the set to keep it a function?

Answer: (4) (1, 3)
Functions. Relations.
You can't repeat the input (x) with a different output (y). Choices 1, 2, and 3 would cause the function to fail the Vertical-Line Test because they would duplicate x-values that already exist.


12. The quadratic equation x2 - 6x = 12 is rewritten in the form (x + p)2 = q, where q is a constant. What is the value of p?

Answer: (3) -3
Quadratic functions. Parabolas. Minimum value. Vertex.
Two notes: first, "q is a constant" means that it will be some number, but we really don't care what that number will be; second, take note of the fact that there is a plus sign (+) in the rewritten form, not the usual minus sing (-). You don't have to "flip the sign" when reading your answer.
To complete the square, take half of -6, and square it. Add that to both sides.
x2 - 6x = 12
x2 - 6x + 9 = 12 + 9
(x - 3)2 = 21
The constant q is 21, but that isn't important. The value of p is -3.
You can check by graphing that these two equations are equivalent.

Final note: most of the above was unnecessary. Once you found b/2, -6/2 = -3, you had the answer. The rest was just checking.


13. Which of the quadratic functions below has the smallest minimum value?

Answer: (2) [graph]
Quadratic functions. Parabolas. Minimum value. Vertex.
The table in Choice 4 has a minimum of -6, but the graph in Choice 2 has a minimum of -10, so choice 4 is eliminated.
If you graph h(x) and k(x), you will see that neither one has a minimum of less than -10.
You could also have found the axis of symmetry, and plug them into the function.
For choice 1, the axis of symmetry was x = -2 / 2 = -1, and h(-1) = (-1)2 + 2(-1) - 6 = -7
For choice 3, the axis of symmetry is (-5 + -2) / 2 = -3.5, and k(-3.5) = (-3.5 + 5)(-3.5 + 2) = (1.5)(-1.5) = -2.25


14. Which situation is not a linear function?

Answer: (4) A $12,000 car depreciates 15% per year.
Linear functions have a constant rate of change.
Choices 1, 2, and 3 have constant amounts per month, per mile and per hour.
Choice 4 decreases by 15% per year. This is exponential decay. After one year, the value will be smaller, so 15% of that value will be a smaller decrease.


15. The Utica Boilermaker is a 15-kilometer road race. Sara is signed up to run this race and has done the following trains runs:

I. 10 miles
II. 44,800 feet
III. 15,560 yards

Which run(s) are at least 15 kilometers.

Answer: (1) I, only
Unit conversion.
From the back of the test booklet: 1 mile = 5280 feet, 1 mile = 1760 yards, 1 kilometer = 0.62 miles.
15 kilometers * (0.62 miles / kilometer) = 9.3 miles
10 miles > 9.3 miles
44,800 feet / (5,280 feet / mile )= 8.48 miles
15,560 yards / (1,760 yards / mile) = 8.8 miles.
Only 10 miles is at least 15 kilometers.


16. If f(x) = x2 + 2, which interval describes the range of this function?

Answer: (3) [2, infinity)
Domain and range.
Range is the set of possible y-values. The vertex of this function is (0, 2). The range is all values of y greater than or equal to 2, y > 2, or [2, infinity).


17. The amount Mike gets paid weekly can be represented by the expression 2.50a + 290, where a is the number of cell phone accessories he sells that week. What is the constant term in this expression and what does it represent?

Answer: (3) 290, the amount he is guaranteed to be paid each week.
Linear functions.
The initial value (y-intercept, when graphing) is 290, the constant term. The rate of change is 2.50, which repeats for every accessory sold.


18. A cubic function is graphed on the set of axes below.
Which function could represent the graph?

Answer: (2) g(x) = (x + 3)(x + 1)(x - 1)
Zeroes of a function. Factored form.
The zeroes of the function are -3, -1 and 1. So the function should have the terms (x + 3)(x + 1)(x - 1).


19. Mrs. Allard asked her students to identify which of the polynomials below are in standard form and explain why.

I. 15x4 - 6x + 3x2 - 1
II. 12x3 + 8x - 4
III. 2x5 + 8x2 + 10x

Which student's repsonse is correct?

Answer: (3) Fred said II and III because the exponents are decreasing
The Standard form of a polynomial is the term with the highest exponent goes first, then the next highest exponent, and so on.
They are not ordered by coefficients.


20. Which graph does not represent a function that is always increasing over the entire interval -2 < x < 2?

Answer: (3) [graph]
The function in Choice 3 is decreasing when 0 < x < 2, so it doesn't increase over the entire interval specified in the question.
Choice 4 does not start decreasing until after x > 2.


21. At an ice cream shop, the profit, P(c), is modeled by the function P(c) = 0.87c, where c represents the number of ice cream cones sold. An appropriate domain for this function is

Answer: (2) an integer > 0
The domain should be an integer, not a rational number. Cones are sold as whole units. You wouldn't sell, for example, 3 1/2 cones.


22. How many real-number solutions does 4x2 + 2x + 5 have?

Answer: (3) zero > 0
Find the discriminant: b2 - 4ac = (2)2 - 4(4)(5) = 4 - 80 = -76.
There are no real solutions.
You could also graph this function. You will see that it never touches the x-axis, so it has no solutions. (The minimum occurs at (-.25, 4.75).)
Note that the answer "Infinitely many" is silly. A quadratic equation can only have 0, 1, or 2 solutions.
The only time is could be infinitely many is if both sides of the equation are quadratic expressions which are equivalent.


23. Students were asked to write a formula for the length of a rectangle by using the formula for its perimeter, p = 2L + 2W. Three of their responses are shown below.

Which response are correct?

Answer: (2) II and III, only> 0
To solve for L in terms of p and W, you need to use inverse operations to isolate L.
In this case, that means subtract 2w and then either divide by 2, or multiply by 1/2. So responses II and III are equivalent.
Response I isn't good because the 1/2 was only applied to the p term and not the W term.


24. If an = n(an-1 and a1 = 1, what is the value of a5?

Answer: (2) II and III, only> 0
a1 = 1,
a2 = 2(a1) = 2(1) = 2,
a3 = 3(a2) = 3(2) = 6,
a4 = 4(a3) = 4(6) = 24,
a5 = 5(a4) = 5(24) = 120.
Give yourself a pat on the back if you realized that this was the factorial function.

End of Part I

How did you do?

Questions, comments and corrections welcome.

Wednesday, June 20, 2018

Text From the Ex

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

(C)Copyright 2018, C. Burke.

They were childhood friends, so it's probably something innocent, and possibly sad news.




Come back often for more funny math and geeky comics.




Tuesday, June 19, 2018

Straight Lines

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

(C)Copyright 2018, C. Burke.

And, of course, it's the shortest distance between two pun-ts.

The Co-medians haven't taken to the stage in quite a while. About time they had a new gig.




Come back often for more funny math and geeky comics.




Monday, June 18, 2018

(x, why?) Mini: My Other Favorite Schools

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

(C)Copyright 2018, C. Burke.

Particularly if is filled with fresh pasta.

I've always thought "scolapasta" was a great word from the first time I heard it, even though it sometimes sounded like "-basta" or even "-bassa". I had to look up the proper spelling.
Kind of a "duh!" moment -- of course, it would contain the word "pasta" since it's job is to contain the pasta!




Come back often for more funny math and geeky comics.




Sunday, June 17, 2018

Happy Fathers Day 2018!

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

(C)Copyright 2018, C. Burke.

Someone's a little envious that they don't have kids yet.
Yes, this comic is a little late because despite being "my" day, it was still a busy one getting the house ready for company. And as much as I might have wanted to relax, that wasn't going to happen for the whole of the day -- and definitely not long enough for this to appear.
Which is probably a good thing, because this strip was originally so much more complicated in my head, and yet boiled down to the same thing.
I'm sure "Dad" ("Grandpa") will appear again soon.




Come back often for more funny math and geeky comics.




Saturday, June 16, 2018

Trigonometry Jones and the Running Gag, Part 2

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

(C)Copyright 2018, C. Burke.

Since this is Part 2, it actually is a running gag now!

Part 1 appeared back in 2015, Comic 990.




Come back often for more funny math and geeky comics.




Friday, June 15, 2018

Opposite and Adjacent

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

(C)Copyright 2018, C. Burke.

I have this conversation every term. Sometimes multiple times.




Come back often for more funny math and geeky comics.