I’m giving an exam this morning (magnetic fields, circuits, magnetic forces on charges), which is always a carnival of boredom– happily, I have papers to grade during the test, which will keep me busy. Sadly, this is not a final exam, as Female Science Professor and others are making or grading right now– we still have three more weeks of class. Joy.
Anyway, this seems like a good time and topic for a Dorky Poll. So, bouncing off the FSP post, let me ask:
What’s your favorite trick question from an exam?
This could be an exam you’ve taken, or one you’ve given. All that’s required is that there be some sort of “trick” to the answer. You don’t need to give the answer, either, if you don’t want to– just post it in the comments, and let people guess.
Personally, I haven’t come up with a great many “trick” questions, but maybe that’s just because they don’t seem like tricks to me. I did have a mechanics question once that asked for the kinetic energy of a field-goal attempt at the peak of its flight, which got a dozen or so students to reflexively write down “0” without thinking about it. I usually put some variant of “Which falls faster, a heavy object or a light one?” on finals in intro mechanics, too, and it’s depressing how many students get tripped up by that one.
I’ve also been known to deliberately give quizzes where every answer is “B,” just to mess with students’ heads. I get this from my father, who used to give occasional true-false tests where all the answers were “True.”
My favorite “trick” question, though, comes from a colleague, who wrote a multiple choice question for an exam that was something like “A small 1kg lead sphere is at one end of a 1m long massless rod centered at the origin, while a large spherical collection of feathers with a total mass of 1kg is at the other. Where is the center of mass of the system located?”
From a seventh-grade science class:
What’s the closest star to the earth?
Ah, I needed that bit of relief. The next time I teach that question is being used on the exam covering center of mass.
I have vague memories that I encountered a few good ones in school, but they were (mumble) years ago and I have no memory of the details. It does make me think of the “bee flying between two trains” problem, which would work well when given in the context of a quiz on geometric series.
I call some of these “easy” questions. I.e., a question that requires thought rather than just instinctive application of a formula and a quick grab for the calculator.
After four years of teaching high school, I’ve realized that these “easy” questions are what sets physics apart from mathematics and the other sciences. By extension, seeing these questions also make students realize they need to actually think rather than apply recipes blindly (and often incorrectly) to every situation.
A friend of mine once had a question in a relativity class that went something along the lines of:
“A train is moving at 50 mph to the east. A person inside the train is running to the east at 5 mph with a flashlight pointed in front of him. A car is driving parallel to the track at 25 mph; what is the speed of the light emitted from the flashlight according to the car driver?”
Apparently nobody got the answer correct.
Not so much in the way of trick questions, but I had a math teacher in HS who gave midterms worth 200 points and finals for 400. We were expected to get about 100 and 200 points correct, respectively. Some questions we should be able to get completely correct, but mostly he just wanted to see if we knew the right approach/formulae. I had him for geometry and trig/pre-calc.
He would return test papers in descending order; the worse you did the longer you had to wait, although there was a fairly consistent order. I usually got mine back around the middle of the first half. Then he would curve on the fly. He would write all the scores on the board with the highest at the top working down. Then he’d glance at the column, draw a slash under one number and say, “Everything above this line is an A.” (Maybe 89 – 102 on a 200 point test). And so on thorugh B, C, D, F. On one occasion he ran out of blackboard with three scores to go. He put two of them on the wood below the chalk tray and then told the last student that his score would be posted later on the blackboard in the teacher’s lounge downstairs. I think the guy got 6 out of 200. He basically put his name and then wrote “x= ” on the first problem.
The subject of trick questions came up at a job interview I did some years ago. The chair of that department then dropped a pen onto the floor, waited until it stopped moving, and then asked me what the friction force was that was acting on the pen. (We assumed that the floor in question was level.) I gave the correct answer, but that wasn’t enough to get the offer.
Next time I teach a class that involves special relativity, I’m using gg’s question.
A roommate of mine took the GRE in physics and reported a wonderful one. There was a special relativity question which appeared to involve lots of special-relativistic calculations — it would easily take 10 minutes just to crunch through them. The actual question: “What is the speed of the second gamma ray?”
I’m not a physics person (maybe this helps, actually?) but I presume the correct answer to gg’s question is “c”?
A classical problem from AI: take a chessboard with two squares removed from opposite (diagonal) corners. You’re given a set of dominoes; each domino can be placed horizontally or vertically on the chessboard, such that it covers two adjacent squares. Place the dominoes on the board such that all the squares are covered.
A bear falls of a cliff. Given the height of the cliff and the time it takes the bear to fall, what colour is the bear?
chris @ #6: I had a high school teacher who curved the same way, and I hated it–when you’re the only person at the top, and the whole class knows it and is *looking* at you, well, it’s not a lot of fun.
(I know, I know, pity the poor smart girl who was getting good grades. Still, even today I don’t think that much detail was necessary.)
An undistorted tetrahedral sp3-hybridized carbon atom bears four independent, freely rotating, rigorously identical (including isotopic substitution) substituents, CR_4. Said carbon is a chiral center. Provide a general case and a specific example.
The answer is painfully obvious. PAINFULLY obvious. “Discovery is seeing what everybody else has seen, and thinking what nobody else has thought,” Albert Szent-Gyorgyi.
I like #10’s as a for fun trick question. I’d personally ask what the bears favorite color is and accept either a statement about there not being enough information or a statement about it liking any color that means the bear is not really falling off the cliff.
My high school calculus teacher would occasionally have “Jeopardy!” days where students were divided into teams and answered questions. The day before such contests, the students would be assigned to write up 5 questions each. I titled my category “Oh” and then wrote 4 questions with the answer of “zero”. (Integration limits that are equal, symmetric integration of an odd function, etc.) The final $500 question was “What is 1 less than the lowest prime number?” I wasn’t in class that day, but apparently multiple teams guessed the same wrong answer, and eventually realized that the category topic was not “Zero” but “Oh” as in the sound you make when someone finally tells you the correct answer.
I wouldn’t call this a ‘favorite’, but if you want to be particularly obnoxious, there’s always “what weighs more, a pound of gold or a pound of feathers?”.
So what’s the answer to the lead sphere/feathers one — the origin? It seems so obvious that I’m afraid I’m falling for the trick…
In mathematical questions, anything appearing long, complex, and ridiculously convoluted that ends up equaling 42 and has a simple shortcut if you’re bright enough to notice it also works well in my book.
In questions with non-numeric answers, anything that requires a Monty Python quote or any good classic/cult Sci-Fi reference in the answer is good. Bonus points for multiple quotes and references in the same answer.
Personally I don’t have any such questions I can give off the top of my head but it shouldn’t be too hard to come up with something.
My HS physics teacher once asked the class about an insect flying at a fixed velocity headlong at a train, also travelling at a fixed velocity. I can’t remember the specifics, but the way he worded it seemd to suggest that for an instant, when the fly crashes into the train both it and the train remain stationary for a brief moment in time, meaning the fly could stop the train.
Another of his famous trick questions was to ask us how many forces are operating on a ball attached to a piece of string if you swing it around your head. not many got that right either, with answers ranging from 2 to 9.
Kate@11:
It was a pretty competitive boarding school so it was the ones at the end of the receiving line that got stared at. For my part I breezed through algebra, geometry, and trig with A’s and B’s and then hit calculus as a senior where I barely got a D+ even with the help of a tutor. I tried, but I just couldn’t see it. When asked a question like, “water is flowing into a pool of z dimensions at x rate, and leaking out the bottom at y (less than x), given the pool was empty at the start, how long to overflow the pool?” I would wonder why they didn’t just plug the hole.
Here’s one we used to do in new hire classes to make sure people were listening:
“You start your work day driving the #10 bus through downtown. At the first stop 6 passsengers get on. At the second stop, 2 passengers get off and 8 more get on. At the third stop, and so on, etc, with some passengers getting off and some getting on at each stop. At the end we then ask, “How old is the bus driver?”
Okay, Uncle Al, I’ll bite: How can an undistorted sp3-hybridized carbon with four identical freely-rotating substituents be a chiral center?
I shouldn’t ask, because any answer will make me sorry: I’ll either kick myself for not seeing an answer that probably would have been obvious to me 15 years ago when I was taking organic, or I’ll kick myself for getting sucked into asking Uncle Al for the answer.
My favorite was not on an exam, but rather on a list of short projects for an introductory circuit design class (everyone had to choose a project and had a week or so to build it): build a circuit to translate 3-bit binary numbers into 4-bit binary numbers using a distance 2 code.
When I was in eighth grade, our science teacher was always on about reading the quiz entirely before beginning. On one particular quiz, the final question wasn’t a question at all, but a statement, “Disregard all previous questions.”
Most of the class got burned on that one.
Pretty basic, but I never forgot about it!
Fun computer science one: Devise an efficient algorithm for factoring large (i.e. 2048-bit) prime integers. What is the running time?
This isn’t a trick question so much as a trick answer. The Boyfriend was teaching a thermo class and one of the short-answer questions on the final exam was, “Can you cool a room by putting a refrigerator in the middle of it, turning it on and opening the door? Explain your answer.” One student wrote, “No, because if you could, they’d sell it at the store for that purpose.”
He gave her partial credit.
dexoigmn–You almost had me on that one! O(1)
You’re sitting in a boat in the middle of a still pond, with a very large rock also in the boat. You pick up the rock and drop it into the pond, where it sinks to the bottom. Does the water level go up or down?
Chirality lacks all improper axes of rotation: mirror plane, inversion point, higher S_n axes. Reduce a regular tetrahedron, point group T_d, to point group T in two ways:
1) CR_4 and CS_4 where R,S is the Cahn-Ingold-Prelog system. C(lactate)4.
2) In mathematics, that way and a more colorful way.
Helicity depends on point of view (left-handed relativistic beta-rays). Then chirality with one coordinate’s signs reversed. Then parity with all three coordinates’ signs reversed. Parity is quantifiable. Uncle Al sent a perfectly parity divergent molecule to NIST. NIST rewrote its commercial stereochemistry software. Why wasn’t NIST grateful?
This was from a high school chemistry exam.
You have a glass of water sitting in a room at 50 degrees C. At equilibrium, what is the state of matter of the water?
The answer is: not enough information, as the state of matter also depends on the air pressure.
“what weighs more, a pound of gold or a pound of feathers?”
As Aaron says, this one is particularly obnoxious. To see the answer, look up Troy weight.
Expand:
(x-a)(x-b)(x-c)(x-d)( … )(x-y)(x-z)
Consider a string of letters a,b,c,d,…
A string has an “inversion” if a later letter appears before an early letter. For example, the string “bac” has 1 inversion, because b comes before a, but all other pairs of letters are in order.
Consider the letters {a, b, c, d, e}. What is the average number of inversions over all 5-letter no-repeat strings?
I had this on a test in a discrete mathematics course, but used my physicist sensibilities to solve it in 1 line!
On my human anatomy exams I like to use this question:
True or False? Females have paired corpora cavernosa.
Most people immediately think of the corpora cavernosa of the penis and answer ‘false’, forgetting that females have a pair of ccs in their clitorises. The question works well in the other direction, too, using males and mammary glands. The miss rate for these questions is awfully high, considering that the information is straightforward and most people do get the right answers if they just stop and think. I call that tricky.
@5 Isn’t the answer speed of light through the train’s particular atmosphere + 25 mph?
@30 No. Never again, not if my life depended on it.
@33:
look at the third-to-last term.
Not exactly a trick question but my electromagnetics exam had
“The primary seat of DC electromotive force in a typical automobile is on what order of magnitude?
10^0 10^1 10^2 10^3 ”
only half the class figured out that this means “about how many volts is a car battery?”
you needed the answer for the next four questions. theoretical physicists suck 😛
My friend had a class where the answers to the other section’s exam were “abababab…”, the teacher gave her class a version that went “aaaaa..bbbbb”. Anyone who knew someone in the other section got a 50.
gg: A friend of mine once had a question in a relativity class that went something along the lines of:
“A train is moving at 50 mph to the east. A person inside the train is running to the east at 5 mph with a flashlight pointed in front of him. A car is driving parallel to the track at 25 mph; what is the speed of the light emitted from the flashlight according to the car driver?”
Oh, yeah.
I’ve used that one a lot, to great effect. It really helps sort out who was paying attention…
nanoAl: My friend had a class where the answers to the other section’s exam were “abababab…”, the teacher gave her class a version that went “aaaaa..bbbbb”. Anyone who knew someone in the other section got a 50.
The best “mess with cheaters” story I heard was from a large section where the professor announced that there would be four different versions of the exam, and thus students shouldn’t even bother trying to copy. On exam day, the tests were passed out, on four different colors of paper.
Of course, the four different colors didn’t correspond to the four different versions, so students with yellow papers cheerfully copied off other students with yellow papers, and failed badly…
@33
What distinguishes Relativity from the Newtonian Mechanics is that the speed of light is a constant regardless of the relative motions of the source and observer. This requires other thing which, in the Newtonian view, were supposed to be absolute (mass, length, time) actually be variable. Being in an atmosphere would change things due to the delay when photons are absorbed and then re-emitted, but the motion of the train through the atmosphere is _not_ added or subtracted from the speed of light. Any relativity student who doesn’t understand this is really doing what Feynman called “cargo-cult” Physics.
@37
I don’t think that’s quite right. Once you have an atmosphere, you have a preferred frame: the rest frame of the gas. Thus, it’s not unreasonable to expect that the speed of light observed in the rest frame of the gas is different from the speed of light while measured in relative motion to that gas.
While the atmosphere is nearly vacuum, I don’t think #33’s answer can be dismissed so quickly as you purport.
Chad drives for a layup. At the top of his leap, how far has the earth recoiled as a result of his jump?
apropos #26: You drink a glass of water from the pond, does the water level go up or down? 😉
If you want to trick your E+M students, give them a problem where they have to draw a free-body diagram (say a conductor of known weight in a transverse B field hanging at an angle from wires with a known modulus) and see if they can still do a statics problem to figure out how much the wires stretch. (Student: “That was last semester!”)
But if you really want their attention, try giving them the Force Concept Inventory and see how they do on those conceptual questions. Many people are convinced the force in a collision is bigger on the smaller vehicle, no matter how much physics they know. Sort of like the “Monty Hall” problem is to statisticians.
Trickiest exam I ever took? A true-false final exam in integral calculus. Wrong answers probably culled from old student exams.
I once gave a quiz that was, in its entirety, “Spell Bremsstrahlung”
I didn’t just say it. I wrote it on the board.
Two students got it wrong.
freshman physics, a take home exam consisting of one question, that began “Imagine a cosmic twinkie…”, the punch line of which was to figure out how much such a twinkie would change the orbit of the earth relative to the sun. The same question was given to that professor’s senior astrophysics course. The difference was that us lowly freshmen were allowed to assume constant density, while the astrophysics jocks were supposed to take into account the creamy filling.
#38 wrote: “Once you have an atmosphere, you have a preferred frame: the rest frame of the gas. Thus, it’s not unreasonable to expect that the speed of light observed in the rest frame of the gas is different from the speed of light while measured in relative motion to that gas.”
I don’t know if anyone’s still reading this post at this point, but one can detect differences between the speed of light in moving and non-moving matter. One of the early ‘aether’ experiments was by Fizeau in 1850, in which he measured interferometrically the differences between light moving in a stationary fluid and in a moving fluid. The change in the velocity of light (approximately) goes as du = fv, where v is the velocity of the medium and f = 1 – 1/n^2, where n is the refractive index. Air, with a refractive index of roughly 1.0008, differs very little from pure vacuum. At the very least, one can say that the effective shift in light speed is far, far less than any relative motion of observers.
At some point in the near future I’ll try and blog about this experiment some more, as it’s actually quite interesting.
This isn’t so much a trick question, as a “trick quiz”. One day last fall I was snowbound and cancelled my Relativity class. I emailed students with link to a video online of Kip Thorne giving a lecture on the equivalence principle or something. I told students this was NOT OPTIONAL, and was a replacement for the missed class, and that I would start class on Monday assuming that everyone had watched it. But how could I be sure who had and who hadn’t?
So Monday morning, I came into class and passed out a mostly-blank sheet to the students with a title like “General Relativity and the Equivalence Principle: QUIZ” at the top. I told them to get out a pen and get ready to take a quiz. There was a nervous mutter from the class as I fired up the projector. I put a Keynote slide up on the screen pictures of four physicists giving lectures in front of a classroom and the question…
“WHICH ONE IS KIP THORNE?”
The 1/2 second of confusion on their faces before they figured out what I was up to and why was PRICELESS.
@30:
I don’t get it…