Sample Math Problem from OECD International HS test

Couldn’t decide whether to put this in the MPSIMS thread.

This is a sample math problem from one of those “Chinese students are outstripping American ones in standardized testing…” tests. It was a nifty little problem. I got the right answer but felt I spent way too long on it (4 mins ish?) than what would constitute a “good” score.

http://www.businessinsider.com/pisa-revolving-door-question-2013-12
Just thought I’d mundanely and pointlessly share while posing a factual question.

Hm that took me about ten seconds to figure out. I think though that the prowess of Asian mathematics skills are greatly exaggerated, from my own anecdotal experience.

In this case, math is very simple - the question is understanding the problem which is more engineering than math.

Math that I remember from HS was more about understanding Cantor’s Theorem than problem solving.

This is what we used to do in HS… you get an equation and you have to work it to prove the equation… something like this… http://www.youtube.com/watch?v=YZwL1-tzk3c

Note: video is in Croatian.

Since I’m not seeing an actual question in the OP, let’s move this to MPSIMS.

Colibri
General Questions Moderator

It took me longer to load the page than to figure out the problem (aside: I really hate web pages that jump around while they’re loading). And then I had to read it over again to be sure there wasn’t some trick I was overlooking.

I know, the answer is pretty obvious - 10 seconds is about right. Why is this considered a difficult question?

Took me less than half a minute, including trying to find a scrap piece of paper to write out the solution for full marks. :slight_smile:

I’ve got two kids in hs. One freshman, one senior. Just for fun, I’m going to see how quickly they can solve it this evening.

i think you learn circumference in primary school, so you don’t even need a teenager to solve that. anyway, is this OECD International HS test taken by American students? if not, how do they compare the rankings?

They even show the door in the right position to visualize what’s needed.

I’m an engineer, took like 10 seconds.

This is where I fell, except I wasn’t very sure of my answer for some reason. I was like ‘well it really seems obvious the answer is _____, but… hmmm maybe there’s something I’m missing.’

Here are some rankings

That was the “duh” moment for me.

Well, I didn’t use any real math formula, but just sort of guessed using the 200 CM factor, but I would have at least mentioned the extra bit needed to keep it sealed. I might have scored the points - but most likely the only points in the entire math section for me.

Is their answer off by a factor of 2?

The diagram shows the arc subtends a 120 degree angle. A circle is 360 degrees and 2Pi radians in angle. Therefore Pi radians is 180 degrees, Pi/3 radians is 60 degrees, and 2Pi/3 radians is 120 degrees. The arc subtends a 120 degree = 2Pi/3 radian angle. The definition of angle is radians is arc length over radius. So the angle T = S/R where S is the (unknown) arc length, R = radius = 100 cm, and angle T is 2Pi/3 radians (= 120 degrees). So the arc length (S) is RT or 2Pi/3 times 100 cm or 200 cm * Pi/3. Their answer is 100 cm * Pi/3.

Or did I do something wrong again?

Took me longer than that, but I’ve been taught to distrust diagrams in word problems. I had to convince myself that what looked like 50% was really 50%.

In my defense, I haven’t done a geometry proof in 33 years. If I’d thought to have kids to help with their homework, I’d be better at this kind of stuff.

I do agree that this wasn’t particularly difficult. When I first looked at the problem, i was expecting to have to calculate the length of a chord intersecting the circle and then I would have been sunk.

Typo Knig, you’re supposed to find the length of each opening.

As soon as I realized that each door opening was 1/6 of the circumference, the answer was obvious.

if American students are also taking the same tests, then i must have misunderstood the point in the OP’s link. i had assumed it was “the Asian students weren’t as smart as they claim, the tests were simply easy.” btw what was your factual question, pancakes3?

D’Oh! I thought they would not make such a basic mistake. That’s my speciality. :frowning:

Based on the article, I was worried that I over-simplified the problem, but it was as simple as I thought and my intuitive answer was correct. I think it would have been more difficult without a diagram, but then it’s only difficult because of the setup.

IMO, this is something that anyone with geometry ought to be able to answer fairly easily, and likely many people with less education, as long as they know the formula for the circumference of a circle ought to be able to get it right. Frankly, considering that geometry is a required subject, if this is one of the hardest questions, it sounds like this is a fair test for a high school education.

If that’s one of the most difficult questions, I shudder to think what the easy ones are like. Possibly:

Solve for x: 1 + 1 = x

If the vast majority of high school students in America can’t solve the linked problem, then we might as well close the doors and shut off the lights on the country, since we are doomed to become a second or third rate society.