It seems conventional wisdom that tests are generally gameable in the sense that an (most?) effective way to produce the best scores involves teaching password guessing rather than actually learning material deeply, i.e. such that the student can use it in novel and useful ways. Indeed, I think this is the case for many (most, even) tests, but also think it possible to write tests that are most easily passed by learning the material deeply. In particular, I don't see how to game questions like "state, prove, and provide an intuitive justification for Pascal's combinatorial identity" or "Under what conditions does f(x) = ax^3 + bx^2 + cx + d have only one critical point?'', but that's more a statement about my mind than the gameability of tests. I would greatly appreciate learning how a test consisting of such questions could be gamed, thereby unlearning an untrue thing; and if no one here can (or, at least, is willing to take the time to) explain how such a thing could be done, well, that's useful to know, too.
One easy way I can think of gaming such a test is to figure out ahead of time that those questions will be the ones on the test, then look up an answer for just that question, and parrot it on the actual test.
I know at my college, there were databases of just about every professor's exams for the past several years. Most of them re-used enough questions that you could get a pretty good idea of what was going to be on the exams, just by looking at past exams. A lot of people would spend a lot of time studying old exams to game this process instead of actually learning the material.
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