UPDATE (31/12/20) The exam is now online.
We’ve now gone through the multiple choice component of the exam, and we’ve read the comments below. In brief, and ignoring the screw-ups, most of the questions seemed good, and a number of questions were hard (which is good). We haven’t thought much about the extent to which the questions are trivialised by CAS/Mathematica, although this is of course extremely important; the comments below on this aspect are well worth a careful read.
Here are our question-by-question thoughts:
MCQ1. A decent and non-trivial stationary point question. A pretty mean way to begin.
MCQ2. A contrived and tricky range of function question. A very mean way to continue.
(11/09/21) 42% correct, which is no surprise. The problem was to find the range of g(x) = |bcos-1x -a|, given a, b > 0, and (weirdly) a < bπ/2. The note in the examination report suggests to “Use transformations on g …”, which is incomprehensible. Simplest is to note the extreme values of cos-1x are 0 and π, and then note that we pass through 0 along the way.
MCQ3. A rather weird piecewise constant acceleration question.
MCQ4. A good and not so easy composition of functions question.
MCQ5. Intrinsically a routine and good complex algebra question, but the presentation is a mess. The notation is introduced, but then plays no role; indeed, the question would have been vastly improved by having the offered answers expressed in terms of and . Requiring some extra algebraic manipulation to obtain the correct answer is needless, and a little contrived. (11/09/21) Plus, the gratuitous and stupid use of “equivalence”.
MCQ6. A very easy complex factorisation question.
MCQ7. Ugh! See here.
(11/09/21) 26% correct, solely down to the question being tricked-up garbage. The problem was to choose the partial fraction form of 1/ax(x2 + b), where b < 0. What kind of asshole does that? Plus, as discussed here, the non-appearance of the factor 1/a in the correct answer is absurd.
MCQ8. A nice complex algebra question.
MCQ9. Complete nonsense, as flagged by commenter Red Five, below. See here.
(11/09/21) 35%, which is to be expected on a question that is meaningless crap. VCAA has absolutely no excuse for including such garbage on an exam.
MCQ10. A routine tank mixture problem.
MCQ11. A screw-up, and perhaps a semi-deliberate one, as flagged by commenter John Friend, below. See here.
MCQ12. A straight-forward but nice Euler’s method problem.
MCQ13. A standard linear dependence problem. As noted by commenter John Friend, the problem is trivial with 3 x 3 determinants, which is not on the syllabus but which is commonly taught for this very purpose.
MCQ14. A straight-forward force component question.
MCQ15. A nice parametrised curve question.
(11/09/21) 38%, which is ridiculous. The question is completely routine.
MCQ16. A nice dot product and double angle formula question.
MCQ17. A straight-forward acceleration as a function of distance question.
(11/09/21) 58%, on a trivial question. It can be done in one’s head in 5 seconds.
MCQ18. A straight-forward but nice string tension question.
MCQ19. A cricket ball with a mass of 0.02 kg? Otherwise, a nice change of momentum question.
MCQ20. A straight-forward but nice force and acceleration question.
We’ve now gone through Section B (extended question) of the exam, and we’ve read the comments below. There do not appear to be any significant screw-ups, but most of it is pretty poor. In the main, the questions are aimless and badly written, with CAS washing away the potentially good effect of any decent content. Nothing is quite a WitCH or PoSWW, but almost everything is close.
Here are our question-by-question thoughts:
Q1. A strikingly aimless parametrised motion question. Seriously, who gives a shit about any of it? Part (b)(i) asks for dy/dx as a function of t, to “hence” obtain the equation of the tangent at t = π, when it is more natural and simpler to first evaluate dy/dt and dx/dt at π. Then, (b)(ii) asks for the velocity at π, for which you need … This is stupid with a capital stupid.
(11/09/21) In an ever-changing world, there is something reassuring about the clockwork predictability of VCAA’s pedants whining about a “missing dt” in an integral.
Q2. An OK complex geometry question, which begins thusly:
Two complex numbers, u and v are defined as and .
Jesus. What’s wrong with “Let and “? The symbols and are pretty crappy choices for fixed complex numbers, and the later choice of for the centre of a circle is really crappy. Part (d), finding the centre and radius of this circle, would be a nice question in a CAS-free world.
(11/09/21) Part (c) was a vaguely worded 1-pointer, asking for the “geometric interpretation” of the graph |z – u| = |z-v| (with u and v fixed); but, at least the examination report indicates that “A variety of reasonable responses were accepted”. Similarly, Part (d)(ii) is a 1-pointer required students to graph an open ray, whose endpoint had already been plotted; the examination report does not indicate fussing about the endpoint. There was nasty fussing, however, in the very next question. Part (d)(i) casually asks students to “Write down” the equation of the function Arg(z-u) = π/4 in cartesian form, with no emphasis in the original. And, of course, 3/4 of students scored 0/1:
While a high proportion of students gave the correct rule, many did not fully describe the function as they did not include the domain.
Anybody want to “fully describe” this dickishness? And, if we’re going to play pedant games, Part (e) asks students to find a and b, but the solution in the report instead uses m and n. Of course. Because it’s in the nature of these pig-ignorant bullies to fuss endlessly over trivia in student work, and to fuss zero-ly over the quality and accuracy of their own writing.
Q3. The best question, graphing and then finding the number of inflection points of for . Much of the goodness is killed by CAS. It is not entirely clear what is meant by “asymptotes” in part (b). (See the discussion here.)
(11/09/21) As commenters have noted, the final Part (e) was an insane amount of work for 2 marks, and the grading was consequently insane to match. Previous parts of the question, which were “handled well” (by the machines), involved calculating g”(x) and then solving g”(x) = 0. In effect – and summarised incomprehensibly in the examination report – students had worked out that there were no solutions of g”(x) = 0 for n < 0, and for nonnegative n,
Part (e) then required students to fill in a table, indicating for each n whether g(x) had 0, 1, 2 or 3 inflection points. Even assuming that students had suitably organised their previous work, and even given that apparently no working on Part (e) was required, that’s a hell of a lot for 2 marks. And, with a catch. The xn factor means that, for n >1, there is an inflection point at x = 0 if n is odd, but not if n is even. Then, presumably 1 mark out of 2 was deducted for a single error. (And, two marks deducted for two errors?) A final average of 0.2/2 was the inevitable result. Utter madness.
Q4. Another parametrised motion question, this one involving a pilot seemingly unaware of the third dimension. Pointless and boring CAS nonsense.
Q5. An absolute mess of a dynamics question. The diagram is shoddy. The appropriate range of the frictional parameter should be given or determined before asking students to compute a Fantasyland acceleration. Part (e), which feels like an afterthought, involves a jarring and needless switch from the algebraic to numeric, with a specific velocity and implausible force plucked from thin air.