Yeah, yeah, we should have done this one a week ago. Feel free to transcribe your comments from the Methods Exam 2 discussion post. You can also check out the discussion on stackexchange, courtesy of Stog the Stirrer.
The question is awful, with the final part the pinnacle of awfulness. We’ll consider that part in some detail, but first the other awfulness.
Part (a)Part (b) could be interesting since finding the critical points amounts to solving a (nasty) cubic, but it is not interesting here. Here, it is meaningless CAS garbage.
- The wording in
Part (b)Part (c) is atrocious. If you mean the functions f(h-x) and f(x) are equal then damn well use the word “function”. And, why not define a new function, Fh or whatnot? You guys are forever, painfully, defining functions for no good purpose. Why not here, when there is actually a purpose? Of course, it also never occurs to anyone that one might prove that the two functions are equal for whatever h. Nope, just look at the damn picture.
- When does ga equal f? Seriously?
- Part (e)(i) is fine, but Part (e)(ii) contains possibly the worst sentence in human history. The question itself could be a good test of knowledge of trig symmetry, but of course here it is just a test of pushing buttons.
- Part (f) is good, although we wonder what students will make of it.
And now, Part (g), which is, at best, Magritte garbage. Is it worse than that? Yes, it is.
The question asks students to
Find the greatest possible minimum of ga.
There are (at least) six plausible interpretations of this question:
Interpretation 1 For each a, let Ma be the (absolute) minimum of ga. Find the maximum value of Ma over all possible a.
Interpretation 2 As for Interpretation 1, but find the minimum value of Ma over all possible a.
Interpretation 3 For each a, let La be the set of local minima of ga. Find, for each a, the maximal element of La.
Interpretation 4 As for Interpretation 3, but find, for each a, the minimal element of La.
Interpretation 5 As for Interpretation 3, but find the maximal element over (the union of) all La.
Interpretation 6 As for Interpretation 4, but find the minimal element over (the union of) all La.
Now, for the kind of reasons that commenter Tungsten suggests, it is likely that Interpretation 1 was intended, but it’s no gimme. In particular, Interpretation 2 is quite plausible; it takes a special born-that-way stupidity to use the term “greatest” when optimising negative quantities. Moreover, as John Friend and Glen have suggested, below and on the discussion post, Interpretation 3 is also very natural. Then, Interpretation 4 is not far behind. In any case, this is insane. Students shouldn’t need to engage in an idiotic guessing game at the end of the exam, for 1 mark, simply because the writers cannot write.
Anyway, guessing over, let’s assume Interpretation 1 is correct. What then do students do? Yep, as Tungsten suggests, they just fiddle with their buttons, note that Ma gives a minimum of -√2, and that Ma appears to be decreasing. That’s all they can reasonably do. Well, they can also reasonably scream out “This is meaningless garbage”, but that probably won’t score them the mark.
Note that there is a very nice and natural and easy proof that Ma has a minimum of -√2. See the stackexchange reply. But this is Methods. No one gives a damn.
A stupid, hateful question to end a stupid, hateful exam for a stupid, hateful subject. Utter lunacy.
Not a meaningful word in the exam report. A complete disgrace, and entirely predictable.