Last one. We’re keen to hear.
We’ve now had a chance to look at the exam report. Of course blatantly lying about the screw up in 2(a) is not good, even if it’s par for VCAA’s gutless course. Our comments on this, and everything, are interlaced below, in green.
The exam report is now available, here. (Thanks, Sai.) Next week, Godot.
We haven’t looked at it yet, but will update with out thoughts asap.
The exam is now available, here. (Thanks, John.)
Well, our kissy-kissy with VCAA didn’t last long. Section B has got serious problems. Here are our thoughts:
Q1 A standard and OK partial fractions and graphing question, trivialised to meaninglessness by CAS. Part (d)(i) should have specified exactly two asymptotes.
Q2 As flagged by SRK, Part (a) is just wrong. And, (b) and (c) aren’t great. See here. (09/05/22) The examination report simply lies about the screw up in (a)(i). Belatedly flagging the existence of “an alternative solution” doesn’t cut it. Be a mensch. We make a few more comments here.)
Q3 An ok volumes of revolution and rates question, made worse, of course, by being more numerical than algebraic. Part (a) is poorly worded, a consequence of the micro-cutting of the question; it makes no sense to write “a definite integral in terms of y and H”, since once we integrate, y becomes a dummy variable. It would have been preferable, and preferable anyway, to ask directly for the volume of revolution. Part (b)(ii) would have be an excellent calculus problem if it hadn’t been destroyed by CAS.
Q4 Yes, a car crash. See here. (09/05/22) The question is still a car crash, but the examination report doesn’t provide much to add.
Q5 An ok and pretty straight-forward inclined plane problem, but the scenario is clunky and the wording throughout is extraordinarily clumsy.
Q6 Stats crap. We just cannot get ourselves to care. (11/11/21) But, writing “main daily sales” instead of “mean daily sales” is pretty damn sloppy.) (12/11/21) As SRK has noted, Part (d) to Part (e) switches from a 1% to a 5% confidence level, a repetition that wastes valuable testing time, and a change that is likely to be overlooked by many students.)(18/04/22) As John Friend notes, this error has been corrected without comment in the posted version of the exam. God, these people are sleazy.(09/05/22) The report notes the main-mean error, mostly to claim that students were not disadvantaged. This cannnot excuse the error, and it certainly cannnot excuse the airbrushing of the error from the published exam.
Section B is clearly going to be a slog, so we’ll first get the multiple choice questions out of the way.
In brief, and with respect to the stressed students newly commenting here, we liked the MCQ on this year’s exam. There were a couple clunks, but in general the questions seemed clear and good, readily solvable after a moment’s thought. Undoubtedly there was plenty of CAS gaming we didn’t see (or look for), but it was notable that we didn’t even think about Stupid CAS Tricks.
Whatever its intrinsic merits, that doesn’t mean there isn’t room to debate the length/difficulty or the unexpectedness of the MCQ as a whole. But as a decent test of mathematical knowledge and understanding, this year’s MCQ seems clearly better than any for years.
(09/05/22) Students did poorly on the MCQ, although maybe not as poorly as might be expected. Our quick calculation indicates an average score of 10.4/20, down from 11.4 in 2020 and 12.0 in 2019. That’s a notable, if hardly cataclysmic decline. Again, it doesn’t bother us. We liked the MCQ part of the exam; it was testing.)
Here are our question by question thoughts, including some quick suggestions of a (CAS-free) way to think about the questions (with no guarantees of being error-free).
MCQ1 A scary but good asymptotes question. It comes down to how many solutions
cos(3x) = -3/2 cos(3x) = -2/3 has on [-π/6,π], so how many solutions cos(t) = -3/2 cos(t) = -2/3 has on [-π/2,3π]. (Corrected 13/11/21. Thanks, SRK and John.)
MCQ2 A nice domain question, coming down to bx = e and bx = 1/e.
MCQ3 A very good max-min question, coming down to determining when the square thing in the denominator is smallest, so when cos(ax) = -1.
MCQ4 A good complex algebra question, most easily done by trying z = i, but can also readily be done in general: the numerator is |z|2 and the denominator is 2*Im(z). (09/05/22) The solution in the exam report is bad. Not wrong, but bad.
MCQ5 A good complex geometry problem, which is easy if one thinks about it, um, geometrically. See Damo’s and John Friend’s comments, below.
MCQ6 A good question damaged by poor wording; writing is needlessly confusing. The question itself is easy: the hypothesis implies that z is either purely imaginary or purely real. (09/05/22) Just 42% of students answered the question correctly. This could be due to the muddy wording. (The wording of the solution in the report is equally muddy. Do you guys never read what you’ve written?) It seems more likely, however, that students are simply not sufficiently familiar with the relationship between complex algebra and complex geometry.
MCQ7 A bad question. Very easy, but way too cute and poorly worded. The answer amounts to the length of quarter way around a circle.
MCQ8 A standard Euler’s method question. Presumably pointless, since any smart student will have Euler programmed into their machine.
MCQ9 A scary but nice, and easy, inflection point question; it’s simply a question of whether f” changes sign at some point.
MCQ10 A standard, and standardly poorly worded,
direction slope field question. One cannot possibly tell from a collection of unspecified dashes what the differential equation “is”.
MCQ11 A standard vector question screwed up by an idiotic inclusion of bearings.
MCQ12 A nice, and easy, dot product question. Nike method.
MCQ13 A nice, and easy, vector resolute question. Vector resolute = (scalar resolute) x (unit vector).
MCQ14 A standard and easy dynamics question.
MCQ15 A standard but nice statics question. A little calculation required, but straight-forward.
MCQ16 A very nice but difficult inclined plane problem. As John Friend notes, it’s probably better as an Exam 1 question.
MCQ17 A standard normal distribution question. It may have been preferable to have given the probabilities to ten decimal places rather than four.
MCQ18 An ok confidence interval question. In can be done quickly without CAS by doing rough calculations: the mean is about (and exactly) 73, and the population standard deviation is about 15.
MCQ19 A nice scaling of a distribution question. It can be quickly done approximately (and exactly) without CAS: the standard deviation has been scaled by 7/6, and we’re looking to go slightly above one standard deviation from the mean.
MCQ20 A standard difference of distributions question.