Friday, February 15, 2019

School Life #8: 4 Eva

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

(C)Copyright 2018, C. Burke.

There was no way to capture the squeals of delight in the cafeteria yesterday.

I saw this shirt a few days ago, without the accompanying dialogue, however.

Happy Valentines Day!




Come back often for more funny math and geeky comics.




Thursday, February 14, 2019

I<3U

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

(C)Copyright 2018, C. Burke.


Edit:

I may be less than 3 of U, but how do U and I measure up?

Happy Valentines Day!




Come back often for more funny math and geeky comics.




Wednesday, February 13, 2019

One Line

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

(C)Copyright 2018, C. Burke.

Euclider.

I originally planned to have Scotch plains, but the plaid would've been distracting.




Come back often for more funny math and geeky comics.




Monday, February 11, 2019

(x, why?) Mini: Shell Game

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

(C)Copyright 2018, C. Burke.

Funny or Na?

Now that he's gone the rest of the electrons are a perfect 10!

I know some day soon, I'll regret having used "Shell Game" for a title here. But, hey, I'll just re-use it.




Come back often for more funny math and geeky comics.




Friday, February 08, 2019

Straight Out of Content

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

(C)Copyright 2018, C. Burke.

Based on a true story -- although once they learn that I actually know math, they usually let teach math in math class.

This was originally title "Subbing Out of Content". And then it wasn't.




Come back often for more funny math and geeky comics.




Tuesday, February 05, 2019

Engagement and Discussion

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

(C)Copyright 2018, C. Burke.

Did Chuck predict an early wedding?

Michele prevented Chuck from proposing to Judy on New Year's Eve because that was the night she and Ken got engaged, and she wanted Judy to have her own day. (Or she wanted to her own day to herself?)

In reality, if I don't get around to doing tis, I'll forget it for so long that we'll all just drop the plot line.

Final note: I put some work into the four new girls I made last month. No firm thoughts on what their names might be.




Come back often for more funny math and geeky comics.




Monday, February 04, 2019

January 2019 Algebra 1 Regents, Parts III & IV

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

August 2018 Algebra I, Part III

Each correct answer is worth up to 4 credits. Partial credit can be given. Work must be shown or explained.


33. Marilyn collects old dolls. She purchases a doll for $450. Research shows this doll's value will increase by 2.5% each year.
Write an equation that determines the value, V, of the doll t years after purchase.
Assuming the doll's rate of appreciation remains the same, will the doll's value be doubled in 20 years? Justify your reasoning.

Answer:
2.5% = 0.025, which gets added to 100% = 1.00.
So the equation is V = 450(1.025)t
Substitute t = 20,
V = 450(1.025)20 = 737.377... = $737.38
$450 * 2 = $900, so the doll will not double in value.
Also, (1.025)20 is only 1.638... or 164%, which is less than double (200%).


34. The data given in the table below show some of the results of a study comparing the height of a certain breed of dog, based upon its mass.


Write the linear regression equation for these data, where x is the mass and y is the height. Round all values to the nearest tenth.
State the value of the correlation coefficient to the nearest tenth, and explain what it indicates.

Answer:
Place all the data into two lists in your graphing calculator and run a linear regression.
You should get a = 1.9 and b= 29.8, so y = 1.9x + 29.8.

Make sure you have DiagnosticsON, or you won't get r, the correlation coefficient.
r = .3, so it is a weak positive correlation.

Use this formula to find the value of V(3) and V(4) and subtract them to find the difference. (You can also graph this in your calculator and check the Table of Values)
V(3) - V(4) = 25000(0.815)4 - 25000(0.815)3
= 13533.584 - 11029.871 = 2503.713 = $2,503.71 depreciation between years 3 and 4.


35. Myranda received a movie gift card for $100 to her local theater. Matinee tickets cost $7.50 each and evening tickets cost $12.50 each.
If x represents the number of matinee tickets she could purchase, and y represents the number of evening tickets she could purchase, write an inequality that represents all the possible ways Myranda could spend her gift card on movies at the theater.
On the set of axes below, graph this inequality.

What is the maximum number of matinee tickets Myranda could purchase with her gift card? Explain your answer.

Answer:


13 movies. 13 is the highest whole number on the x-axis lower than the x-intercept. (13, 0) is in the solution set. (14, 0) is not.


36. One spring day, Elroy noted the time of day and the temperature, in degrees Fahrenheit. His findings are stated below.
At 6 a.m., the temperature was 50°F. For the next 4 hours, the temperature rose 3° per hour.
The next 6 hours, it rose 2° per hour.
The temperature then stayed steady until 6 p.m.
For the next 2 hours, the temperature dropped 1° per hour.
The temperature then dropped steadily until the temperature was 56°F at midnight.
On the set of axes below, graph Elroy's data.

State the entire time interval for which the temperature was increasing.
Determine the average rate of change, in degrees per hour, from 6:00 p.m. to midnight.

Answer:


The temperature is increasing on the graph between 6am and 4pm. (6am, 4pm)
At midnight (12) the temperature is 56. At 6pm, the temperature is 74.
Calculate the rate of change: (56 - 74) / (12 - 6) = -18 / 6 = -3 degrees per hour. The temperature is falling at an average rate of 3 degrees per hour. (If you write it the second way, "falling" implies the negative.)

August 2018 Algebra I, Part IV

A correct answer is worth up to 6 credits. Partial credit can be given. Work must be shown or explained.


37. A recreation center ordered a total of 15 tricycles and bicycles from a sporting goods store.
The number of wheels for all the tricycles and bicycles totaled 38.
Write a linear system of equations that models this scenario, where t represents the number of tricycles and b represents the number of bicycles ordered.
On the set of axes below, graph this system of equations.
Based on your graph of this scenario, could the recreation center have ordered 10 tricycles? Explain your reasoning.

Answer:

The equations that you want to graph are

t + b - 15
3t + 2b = 38

You could graph them this way, or rewrite them as
t = 15 - b
t = 38/3 - 2b/3

The slope of the first line is -1. The slope of the second line is -2/3.
The two lines intersect at (8, 7), which is 8 tricycles and 7 bicycles.
Based on the graph, the recreation center could NOT have order 10 tricycles because t=10 is not the point of intersection. (They ordered 8.)

End of Exam

How did you do?

Questions, comments and corrections welcome.

Friday, February 01, 2019

Move the Chains!

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

(C)Copyright 2018, C. Burke.

Move 10 chains and we'll get there 'fore long.




Come back often for more funny math and geeky comics.




Thursday, January 31, 2019

January 2019 Algebra 1 Regents, Part II

The following are some of the multiple questions from the January 2019 New York State Common Core Algebra I Regents exam.

January 2019 Algebra I, Part II

Each correct answer is worth up to 2 credits. Partial credit can be given. Work must be shown or explained.


25. Solve algebraically for x: 3600 + 1.02x < 2000 + 1.04x

Answer:
Subtract 2000 from both sides. Then subtract 1.02x from each side.
Finally, divide both sides by 0.02.


3600 + 1.02x < 2000 + 1.04x
1600 < 0.02x
80000 < x



26. The number of people who attended school's last six basketball games increased as the teamed neared the state sectional games. The table below shows the data.

Game131415161718
Attendance348435522609696783

State the type of function that best fits the given data. Justify your choice of a function type.

Answer: Note that you don't need to understand anything about basketball or what "sectional games" are.
A linear function is best because there is a constant rate of change of 87.
435 - 348 = 87
522 - 435 = 87
609 - 522 = 87, etc.
At this point, even if the rest weren't exactly 87, a linear function would still be the best fit.


27. Solve x2 - 8x - 9 = 0 algebraically
Explain the first step you used to solve the given equation.

Answer: If you graph it on the calculator, you will not get full credit. However, you can graph it if you wish to check your answer.
If you look for the factors of -9 that add up to -8, you will get -9 and +1


So x2 - 8x - 9 = 0 factors into
(x - 9)(x + 1) = 0
Then x - 9 = 0 or x + 1 = 0
So x = 9 or x = -1

You could have also, for example, completed the square or used the quadratic formula. In either case, you needed to explain what you were doing to get the second point.


28. The graph of f(t) models the height, in feet, that a bee is flying above the grown with respect to the time it traveled in t seconds.


State all time intervals when the bee's rate of change is zero feet per second. Explain your reasoning.

Answer:
When the bee's rate of change is zero, the slope of the line will be zero. This means the parts of the graph that are horizontal line segments.
This intervals are between 2 and 6 seconds and again at 14-15 seconds.


29. Graph the function f(x) = 2x - 7 on the set of axes below.
If g(x) = 1.5x - 3, determine if f(x) > g(x) when x = 4. Justify your answer.

Answer:
The graph will look like the exponential parent function y = 2x but translated seven units down.

g(4) = 1.5(4) - 3 = 6 - 3 = 3.
f(4) = 24 - 7 = 9. (You didn't have to show this if you included the point (4, 9) on the graph.
So f(4) > g(4).
You also could have graph g(x) to compare the points. If you did this, be sure to label both lines!


30. Determine algebraically the zeroes of f(x) = 3x3 + 21x2 + 36x

Answer:
As with the earlier problem, if you graph the equation, you can check your answer, but you will not get full credit for doing it that way.
Any time you have a number greater than one as a coefficient for the first term, or if the exponent is greater than 2, look for common factors you might be able to remove.
3 is a factor of all three terms, and so is x.

f(x) = 3x3 + 21x2 + 36x
f(x) = 3x(x2 + 7x + 12)
f(x) = 3x(x + 3)(x + 4)

If 3x(x + 3)(x + 4) = 0 then
x = 0 or x = -3 or x = -4.
The zeroes of f(x) are 0, -3 and -4.


31. Santina is considering a vacation and has obtained high-temperature data from the last two weeks for Miami and Los Angeles.


Which location has the least variability in temperatures? Explain how you arrived at your answer.

Answer:
The range of temperatures in Miami is 87 - 60 = 27
The range of temperatures in Los Angeles is 74 - 61 = 13
Los Angeles had less variability.

A similar question came up on the August Regents, and there were multiple acceptable answers.
For example, you could have used the Interquartile Range (Q3 - Q1), which you could have gotten if you had put all the data into two separate lists on your calculator and performed "1-Var Stats".
Or you could have compared standard deviations, similarly by making lists in your calculator.
These methods require extra work. Some students may have chosen these because comparing the range might appear to be "too easy".


32. Solve the quadratic equation below for the exact values of x.

4x2 - 5 = 75

Answer:
Since there is no x1 term, it would be easier to use square roots than trying to factor the equation (in this blogger's opinion).
Add 5 to both sides: 4x2 = 80
Divide by 4: x2 = 20
Square root: x = + SQRT(20)

Note that "exact value" means leave it in radical form. DO NOT write a rounded decimal, not even one that has 10 decimal places. It won't be the exact value.

End of Part II

How did you do?

Questions, comments and corrections welcome.

Get Hype!

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

(C)Copyright 2018, C. Burke.

But can you avoid SIN?




Come back often for more funny math and geeky comics.




Tuesday, January 29, 2019

Data-Driven

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

(C)Copyright 2018, C. Burke.

''Discussion'' that I've overheard after different types of tests.

Yes, I get that "data" is important, but giving everyone the same exact multiple-choice test in a math class? For every exam? Ridiculous. And then people who should know better wonder why students have problems with open-ended problems on standardized testing. Or why they just can't explain a concept.

And don't get me started on how easy it is to cheat on a single-version multiple-choice test. At least, let me make two versions and I'll key in the results myself! (The problems with multiple versions of a computerized exam start with the kids needing to know in advance who has which version of the test and having to mark their bubble sheet accordingly. And if they mark it incorrectly or not at all, it's a waste of effort.)




Come back often for more funny math and geeky comics.




Friday, January 25, 2019

(x, why?) Mini: Log n

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

(C)Copyright 2018, C. Burke.

Because the Math/Pain Scale is logarithmic.




Come back often for more funny math and geeky comics.