Math Exams with Only One Question

According to legend, this was once the actual Β final exam at my high school. But according to legend, England chose kings by sword-yanking contests, so, you know.

It’s like Scattergories, except the category is always “fractions.”
Mega bonus points if it’s recognizably similar to the Himalayas. And mega MEGA bonus points if it’s recognizably similar to the Frostfangs.
Precalculus is just Algebra but more so, right?
(Try not to write a long test, since you’ll be taking one from everyone else in the class.)
And to help you out, the same vase oriented vertically vs. horizontally will count twice.
I did this as a whole-class activity once., with everyone creating an expression that reduced to something simpler, and then combining them… I’m pretty sure it had like 97 errors in it.

15 thoughts on “Math Exams with Only One Question

  1. I just wish I could start learning math all over again. I had such a phobia. Now I pretend I understand it. But I don’t. I still think it’s quite cool. That’s why I love this blog. Makes sense, finally.

  2. You can systematically generate ALL the fractions between 5/8 and 5/7 by a modified version of the Stern-Brocot mediant procedure. The first number we generate is (5+5)/(8+7) = 10/15 which reduces to 2/3. Then we compute the mediant of 5/8 and 2/3, namely 7/11, and the mediant of 2/3 and 5/7, namely 7/10. And so on. It turns out that every rational number between 5/8 and 5/7 eventually turns up. This is a special case of a conjecture of mine that was proved by Dhroova Aiylam:

    1. There’s an easier path when you consider there will be a time limit. Work the test, not the problem.

      Assuming the teacher won’t accept un-reduced fractions, we need a big prime. I happen to remember 1,000,003 is a prime.
      5/8 = 0.625
      5/7 =~ 0.714286

      You have an hour for the test. Start writing:
      650,000 / 1,000,003
      650,001 / 1,000,003

      How many can you write in an hour? I feel like I could easily write 600 in an hour if my hand doesn’t cramp up, and even that seems leisurely when you start production lining writing them down the page(s). And remember, you are highly likely to get an extra point for each unique one. If you’re worried someone might happen to remember the same large prime, start the numerator at 662,917 and go from there.

      I woulda killed on this test.

  3. Calculus — take your cool mountain range from your aglebra exam 3 years ago. Find a function that smooths off the peaks and valleys (continuous and differentiable)…

    I think I atually had that one — find a polynomial that goes through this set of points and has derivative = ??? at some other set of points.

    1. It the beginning the world was created. This has generally been considered a “bad move”, and has been followed by many centuries of conflict and strife.

    2. First the earth cooled. Then the dinosaurs came. They got to big and fat and then they died and turned into oil. And then the Arabs came, and they all bought Mercedes Benzes. Then Prince Charles started wearing all lady Di’s clothing. He took her best dress out of the closet and put it on. I couldn’t believe it.

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