I’ve subscribed to the AP Students sub-reddit, principally to read what questions students studying for physics have, and to learn what resources they find helpful. This question caught my eye:
I know it’s probably much easier because when taking their diagnostic tests I ended up getting 30/35 on both of them, when I would think that I would get much less. Can someone who has taken the mechanics exam tell me how much it differs in difficulty?
This motivated me to go have a look at the Varsity Tutors diagnostic tests.
I headed off with the intention of evaluating so I could give my opinion arriving here. I wanted to evaluate the questions in a time efficient way. Given the set up, you are required to answer a question to move on, So I read questions, diagnosed them when I saw questions that struck me as odd, I took a screenshot, superimposed the url on the question. Then I then clicked answers at random and submitted so I could see the next question. I looked at 35 questions.
Here’s a question that caught my eye:
Am I hearing “But … !!!!?????!!!!!” If you are asking that: double plus good for you! If you picked 6N…. uhhmmm… no. If you picked 4N… well, we’ll talk about that in a minute.
Varsity Tutors claims the answer is 6N. Their explanation is shown to the right. Uhmm…
Perhaps your wondering why I’m writing “Uhmm”? Let’s look at this three ways.
- Assume the book “held” and “kept” from sliding down the wall– as stated. Perhaps I am mistaken, but I take this wording to mean the force of friction is sufficient to keep the book motionless. Given the problem statement it would appear the frictional force and the force of gravity are the only vertical forces. So if the force of friction keeps the book from sliding down, the friction force must balance the book’s weight.
Assuming this is all happening on earth: Ffriction = m g ~ 1 kg * 10 m/s2 = 10 N. That’s Newton’s first law. If the book is not accelerating, forces must balance. So this should always the right answer. (BTW: this is an important thing for students to know and the AP Physics C often have questions involving static friction and Newton’s law. Newton’s law always trumps Fs = μs FN, because, among other things Fs ≤ μs FN. That the inequality appears in that relation is considered a very important point for a student to understand.)
- Now, lets suppose we ignore the fact the question tells us the friction force keeps the book from sliding and consider the possibility it is slding. In that case, we use the coefficient of kinetic friction which is 0.2, and Ffriction= 0.2 * 20 N = 4 N. Given our previous answer we would also conclude that if the book is sliding, the book must be accelerating downward because this force is less than the downward force due to gravity.
- If we use the solution Varsity Tutors gives– which is the correct value for the maximum possible force due to fiction, we get 6N. Ok. That’s what Varsity Tutors claims.
But now ask yourself this: Is an upward force of 6K sufficient to “keep[[.]] the 1kg book from sliding”?
Nope. At least not if this is taking place on earth because 6N is less than the 10N. So we should conclude that the force of static friction is insufficient to prevent the book from sliding down the wall. Unless some other upward vertical force is applied (perhaps by a helium balloon), the book is going to slide.
The ‘person holding a book against the wall’ is a classic introductory physics problem. One hopes a student preparing for the AP Physics C came to a stop and scratched their head when coming across this version. A well prepared student should know it’s screwed up.
What about the other questions? Some of the other questions at that practice site were ok, but in my opinion, often not “AP Physics C like”. For example:
- I saw questions that required unit conversion and/or required kids to know the meaning of prefixes in SI. Kids should know how to do unit conversions andwhat “c”, “m”, “K” and so on mean. However, the number of conversions on the AP Physics C exam range from none to almost none with none seeming the more frequent situation; the same goes for use of “c”, “m” and so on. So: not as AP Phys C like as they should be.
- At least one question seemed physically odd to me. For example: there was one about a mouse walking in toward the central axis of a spinning turntable. The intention was to use conservation of angular momentum. I grew up with turntables. We still own one. I’m pretty sure torque is always applied to real turntables when they are spinning. Perhaps this is ok for students who never saw a turntable and have no idea how they work and who likely recognizes the intention is to test whether they know how to apply conservation of angular momentum. But the College Board usually avoids questions where the real situation doesn’t conform to the assumptions the student is supposed to make.
- Some questions were ill-posed. One asked the student to compute the coefficient of friction of a car with known speed taking a turn around a circle of known radius. However, the question did not say that the speed was the maximum possible speed. So, technically, the correct answer should be “not enough information”. As worded there is only enough information to find the lower bound on the coefficient of static friction. Based on the information given, it could be infinite. (But it’s multiple choice so a student will probably get the answer the question writer was seeking. Still…. Knowing that the formula for computing static friction is an inequality is a very important point the AP Physics C tests. So: bad question that has the potential for feeding a misconception.)
That said: the site is free, and most questions were mostly ok. In my opinion, they are not not especially useful for testing how well you’d do on the AP Physics C exam. Since many resources exist, I would not send a student prepping for the AP Phys C test to that site. Other resources are a better use of their time.
Like what? I would advise that student to find old AP Physics C exams written by the College Board. Those who hang out at reddit can find plenty.
That’s a relief – I got 10N and looked in vain for the answer among the four choices. The next question was what would I have picked in a test, not seeing 10N. I was leaning towards 6N, but was desperately wondering whether I had gone mad and it wasn’t just F=mg.
I used to love physics puzzles “in the olden days” but haven’t attempted any for a long time. Don’t suppose I’d do well these days. (I didn’t take physics but some pals did, and I liked to pretend that I could still answer the questions without taking the course (A-level: for age 16-18 in the UK.))
Has this post really been up for a week without drawing a comment?
lucia: “If we use the solution Varsity Tutors gives– which is the correct value for the maximum possible force due to fiction,”
The question probably started as “Is the friction force sufficient to keep the book from sliding?” But that only has two possible answers, so it got thoughtlessly edited. When you know what a question is supposed to mean, it can be very hard to see how it might be “misread”. But I would think that material that is going to be widely used would be tested before release.
I have long believed that in writing a test question, one should start with a clear idea of the concept or skill being tested and make sure that the question actually tests that, and not something else. But all too often, tests are just collections of problems that the students ought to be able to do. Then if a question is not hard enough, people throw in something extra, like a units conversion, to make it harder.
p.s. I just noticed that lucia wrote “force due to fictionâ€. Very appropriate, even if unintentional.
Yep. Not a very interesting post. 😉
Yep. But of course, not all students being tested know what it is “supposed” to mean nor what it “must” mean.
I suspect many students will pick the answer Varsity Tutors thinks is “right”. But in some sense, they are the “problem” because they will significantly overlap the group who will use the wrong principle when the AP like question shows up. They all know it “must” mean use Fs= μs N because they think that’s right. The AP question will have μs N give the wrong answer. Questions testing that appear frequently– and it’s precisely to catch out students who think the friction force is always μs N.
AP tests are.
What Varsity Tutors does is offer their tutors a small amount of money per question. I don’t know what the fee is. It’s not high. But it’s per question.
The Tutors submit problems and then someone or another approves them. I don’t think there is any extensive testing. I suspect Jit’s theory is exactly correct. The person making the question modified a classic problem quickly, entered, submitted, got their $5 or so.
Yep. What I can say for AP tests:
1) The College Board has a set of learning objectives and the tests cover a good distribution of them (and topics.)
2) No unit conversions. One of my students wants to take the Physics subject matter tests and I got their booklet on that. It contains two practice test. Zero unit conversions.
The fact is: it’s easy to make a test harder. As you noticed: change questions to have screwy units. You can also ‘test’ projectile motion with questions that require the maximum amount of algebra. Throw in stuff that was mentioned in class but that is not the ‘core’ so students are left guessing what’s in the test. Give insufficient time. Always throw in distracting irrelevant information in the problem– picking what almost at random. On problems where kids need to do a lot of conceptual thinking, also knock of points for wrong rounding and/or wrong significant figures. Be inconsistent about whether the test using g=9.8 m/s2, g=9.81 m/s2 or g=10 m/s2. Be a bear about significant figures, and then make it a “rule” that g=10 m/s2 is to be treated as an “exact” value rather than ’rounded to 1.” Turn the wording of an “idealized” problem with a figure into a “real world” problem without taking care that the students are now expected they should know they need to neglect something they shouldn’t neglect. Use jargon.
You don’t need to do any of this to have kids get wrong answers in physics.
The College Board doesn’t make any of their questions hard with those sorts of tricks. In fact, unless the language is specific to physics (e.g. displacement vs. distance), they even make sure the text is very clear. They would never use “hang time” for “time the object is in the air”. Nor would they use “apex” for “object is at the top of the trajectory”. The AP tests is given to kids in other countries; their language is very clear. For many idealized problems they provide a sketch. They also go out of their way to make it pretty easy to pick numbers off a graph.
In contrast to the Varsity Tutors problems, the AP questions are good. I didn’t like their page turn on the most recent Physics EM problem especially since their “slab” picture had an aspect ratio of L/d ~2, and on the previous page the students were told L>>d. But you have to put a page turn somewhere.
(WRT to page turn: I read the sub question on the second page of a free response question, said, are they really asking a 3dim question. On this test which doesn’t expect students to do that level of math. I flipped back, reread and then the sub-question could be done very quickly. A pressured student might have thought “OMG!” and started trying, had an attack and fallen out of their chair. That happens on tests. But still, the question was good– and it was an appropriate test of what they knew. Students do need to have some test taking skillz and know to flip back to reread if the question seems ridiculously hard. )
Hi Lucia,
The FAA used to rate the questions in their pilots’ exams question pool for percent of test-takers who got them right. I can’t remember, if I ever knew, what the cut-offs were, but questions which were answered correctly more than 90% of the time were deemed uninformative and rewritten as were questions which were answered correctly less than 70% of the time.
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Many of the things one must know to fly safely must be known exactly, close can kill. Accordingly there was a precision to the wording of the questions which I found exquisite.
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Questions are multiple choice, with the usual supply of very plausible wrong answers which can catch you up if you didn’t really understand the issue.
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I took three of these things in the ’70s and marveled each time at how clever the questions were.
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I would hope the process for question generation and validating on other exams follows this practice.
I just noticed this post and, like Jit, I immediately looked for “9.8 N” in the answers, thinking they were trying to trick people into choosing the $latex \mu_s * F_N $ answer. Then the penny (or the book?) dropped, and it struck me that that there was insufficient friction to hold up the book.
I have an alternate theory of how this question came about. Perhaps the original question had the normal force at, say, 200 N, rather than 20 N. Certainly sufficient to hold the book in place. And then someone figured that 200 N was on the high side for a horizontal force exerted by someone’s arm, at least for a 50 kg student standing upright. So the normal force was reduced to a more reasonable value, not realizing that this is insufficient to pin the book to the wall.
I did what Jit did, but in between picked 39.2, getting confused by the units and figuring Newton is British so 16*2.2 for my answer, not realizing this is 35.2.
HaroldW
Also possible. That’s the sort of thing someone who wrote an excel spread sheet to create “random” variations would do if they didn’t think about ‘the problem’.
Lucia,
Oh, I thought it was interesting. I just didn’t have anything to add [say regarding].
For my part (not that this is interesting, but since I opened my mouth anyway) I did indeed say ‘uhmm, but…’ but in my case I lacked sufficient confidence to believe the problem was wrong. Because I almost never work with these types of problems I just assumed I was somehow missing something and the problem had it right. Your post certainly clarified!
Lucia,
Maybe the dumbest question evah! It is the kind of question which could only be written by someone who doesn’t really understand much physics.
SteveF,
Or was just writing quickly to get the fee, didn’t care and just….
For what it’s worth, the person writing it would have been a tutor for the service at the time they wrote it.