I know there are some math nerds out like @LionJim @IrishHerb among others and maybe they lived thru this! a lot to unpack in this crab trap.
OT the math question the SAT got wrong and other goodies
- Thread starter s1uggo72
- Start date
It is not some huge unexplainable mathematical paradox.
It isn't. It is simple, actually.
The question (as written) involves both the "length" of Rotation, and the Orientation (in this case, of the middle) of the smaller circle (which are two different things - and accumulate).
The people who wrote the test just assumed the "knee jerk" answer, based solely on length. The root issue is that the question was poorly (incorrectly) written.
It isn't. It is simple, actually.
The question (as written) involves both the "length" of Rotation, and the Orientation (in this case, of the middle) of the smaller circle (which are two different things - and accumulate).
The people who wrote the test just assumed the "knee jerk" answer, based solely on length. The root issue is that the question was poorly (incorrectly) written.
This just further confirms that biology was a better major choice than mathematics for me.
Last edited:
When I took the math Praxis exam years ago, I found a question that didn't have a correct answer. Much like this one, there was an answer that I assume they wanted you to select. I spoke with the proctor about it and they had me fill out a form explaining why I thought the problem was wrong and what the correct answer should be. Several weeks (maybe months) later I got a letter in the mail explaining that I was correct and the question was wrong.
No one ever interviewed me though!
No one ever interviewed me though!
Nice of you to say but nerdiness is a constant with me. Been that way for the longest time.
Yes, the "paradox" is nothing more than an optical illusion. Once you know what to focus on, the math is straightforward.
Suppose you have two coins of different sizes, and let the radius of the smaller coin be denoted as r. Assume that the radius of the second coin is nr, where n is some positive integer. Allow the coins to touch. The distance between the centers of the coins is the sum of the radii of the coins, r+nr=(n+1)r. Now, as we roll the small coin completely around the large coin so that the center of the small coin returns to its original location, the center of the small coin will travel 2π(n+1)r units. Since the circumference of the small coin is 2πr units, the small coin will revolve exactly n+1 times.
Ha that reminds me of the two Praxis tests that I took. After being an IE, I went back to school to do student teaching and was in the class to prepare students to take the Praxis tests, the professor showed us a math practice version, and I looked at it and told her I would be disappointed if I didn’t get a perfect score. Being an English professor, she tried to tell me how hard the test was and all that kind of nonsense. I told her that if I took the practice test and got 100% that they needed to just give me an A and let me not come to class the rest of the time. she laughed and said OK because she said no one in her classes had ever gotten a perfect score but then about 20 minutes later, I handed it back to her and she graded it. that was the easiest A ever.
when I took the praxis two test, I was in a room full of other people taking the same exam, about 20 of us. I believe they gave you 90 minutes to do the test, but I was done in about 30. When I handed the test to the proctor, she was very confused asking if I was sick, I told her it was really easy.
I had a similar but not matching experience. I took an education course to prepare for teaching. I was a Physics major and was taking quantum mechanics at the same time. Now it came time in education course for statistics , like average, mean, mode, median etc. There was almost a rebellion in the education course for all the math. I only remember I did very well in the education course, quantum mechanics?? weelllllll as they say......
Do you want me to now chaneg the geometry grade I gave you years ago?
Yes please, because + grades were not given out back in our day.Do you want me to now chaneg the geometry grade I gave you years ago?
Get unlimited access today.