Everyone loves standardized tests, right? They are just super awesome in my book. SUPER AWESOME. Here in Louisiana there is the LEAP test. I don’t know all the details, but I think students have to have some minimum score in order to move to the next grade.

My wife showed me a question from the online practice test. You can see the whole thing here. It’s question number 10 from the Grade 8 practice math test. I don’t want to post the whole question here, so I will just make my own version.

A toy car starts at the beginning of a racetrack that looks like this:

Which of the following would be a graph of speed vs. time for the car on this track? (the question shows 4 possible graphs, but I will only show two).

The other two options weren’t very interesting.

What’s the answer?

This is the question my wife (who is awesome, btw) asked me. Here is my first response:

“Wait. Where did this question come from? No really? What’s this from? This question doesn’t even make any sense. The answer is that there is no answer. On top of that, this is a dumb question. What? This is a MATH question? How is this math? Well, I guess it doesn’t matter what it is since it’s wrong.

There is no correct answer. Well, maybe you could make a case for B, but it would be a stretch.

Here, maybe you should just play with this awesome PhET simulator. You can build your own track and see what happens.

Unfortunately, this particular applet can show a plot of energy vs. position but not a plot of speed vs. time.

But actually, this problem is even more challenging. Even if the top of the loop was at the same height as the starting point, the car wouldn’t make it over the loop. It still needs some velocity at the top so that it will be able to move in a circle. Try it out in the PhET simulator.

Why is this a bad question?

The question doesn’t give much information about the track or the car. With my expert level knowledge of toy cars, I would assume this is something like a Hot Wheels car. As it goes down the track, the car would increase in speed. When it goes on the part that goes up, it would decrease in speed. And here is the problem. The track goes higher than it started. In terms of energy, the car doesn’t have enough energy to go higher than it started.

Oh, but maybe the car started with some initial velocity. Right? Wrong. The speed graph option B shows clearly that the car starts at zero speed. Also, the question didn’t explicitly state that the car started from rest or moving. I would just assume it started from rest in this configuration.

What if it was a battery powered or wind up car? I guess that might work – but why would someone assume that?

You have to be careful writing questions

I suspect that this question came about like many questions are created for standardized tests (particularly in-state tests where the state doesn’t want to spend a whole bunch of money on the creation of the test). The Department of Education asks some teachers to write questions for the tests. They will then pay something like $10 – $40 per question (I really don’t know how much they pay, I’m just guessing). After that, the questions are sent to reviewers. The reviewers go through and pick out the useable questions. Seems like a good system, right? Again, I don’t know how it works for this particular test – I am just guessing.

The problem is that this question seems reasonably clear and straight forward. The car speeds up and then slows down. How difficult could that be? But it’s in those tiny details that things get complicated. Does the car start from rest? Is it already moving? Does the car have a motor? Could the car even make it to the top?

If you gave this question in a normal class, this could be the start of a very useful discussion. But on a standardized test like this, there is only right and wrong. Unfortunately, the author of the question is that one that is wrong.

Yes. This is only a practice question. Perhaps that is even more reason to make the question useful and meaningful.

Homepage image: Simona/Flickr