WitCH 49: Trigged Again

The question below is from the second 2020 Specialist exam (not online), and was flagged by commenter John Friend in the discussion here. John has spelled out the problems, but the question is bad enough to warrant its own post, and there’s arguably a little more to be said.

WitCH 48: Thesis Not Good

This combo WitCH comes courtesy of mystery correspondent, tjrb. They flagged three multiple choice questions from the 2018 Algorithmics exam (here, and examination report here), and we’ve added a fourth. tjrb also remarks, “There are probably a lot more errors in this paper (and the other algorithmics papers), but these were the most strikingly incorrect”.

For Q2, the examination report indicates that 41% of students gave the intended answer of A. By way of explanation, the report then remarks,

“Cobham theorised that problems that are feasibly computable (also known as easy problems) are those that are decidable in polynomial time.”

For Q6, the report indicate that both A (51%) and C (33%) were “accepted”, but is otherwise silent.

The report is silent on Q12 and Q16, except to indicate the intended answers: C (94%) and A (66%), respectively.

Feeling VCAA’s Draft: Discussion

It seems the VCAA has just released their draft of the new study design for Mathematics:

  • The current (pre-COVID) study design (pdf) is here.
  • The draft for the new study design (word) is here.
  • The key changes overview (work) is here.
  • The link for feedback (until March 9, 2021) is here.

We haven’t yet looked at the draft, because we’re scared. But, don’t let that stop others. May the discussion and the throwing of brickbats begin.

UPDATE (09/03/21)

We’ve written a post with some brief thoughts here.

Secret Specialist Business: Exam 2 Discussion

UPDATE (31/12/20) The exam is now online.

This is our post for teachers and students to discuss Specialist Exam 2 (not online). There are also posts for Methods Exam 1, Methods Exam 2 and Specialist Exam 1.

UPDATE (03/12/2020)

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.

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 \boldsymbol{z = a + bi} is introduced, but then plays no role; indeed, the question would have been vastly improved by having the offered answers expressed in terms of \boldsymbol{a} and \boldsymbol{b}. Requiring some extra algebraic manipulation to obtain the correct answer is needless, and a little contrived.

MCQ6. A very easy complex factorisation question.

MCQ7. Ugh! See here.

MCQ8. A nice complex algebra question.

MCQ9. Complete nonsense, as flagged by commenter Red Five, below. See here.

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.

MCQ16. A nice dot product and double angle formula question.

MCQ17. A straight-forward acceleration as a function of distance question.

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.

 

UPDATE (04/12/2020)

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.

Q2. An OK complex geometry question, which begins thusly:

Two complex numbers, u and v are defined as \boldsymbol{u = -2 -i} and \boldsymbol{v = -4 -3i}.

Jesus. What’s wrong with “Let \boldsymbol{u = -2 -i} and \boldsymbol{v = -4 -3i}“? The symbols \boldsymbol{u} and \boldsymbol{v} are pretty crappy choices for fixed complex numbers, and the later choice of \boldsymbol{z_c} 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.

Q3. The best question, graphing \boldsymbol{f(x) = x^2e^{-x}} and then finding the number of inflection points of \boldsymbol{g(x) = x^ne^{-x}} for \boldsymbol{n\in\mathbb Z}. 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.)

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 \boldsymbol{k} 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.

Secret Specialist Business: Exam 1 Discussion

UPDATE (31/12/20) The exam is now online.

This is our post for teachers and students to discuss Specialist Exam 1 (not online). There are also posts for Methods Exam 1, Methods Exam 2 and Specialist Exam 2.

UPDATE (29/11/2020)

We’ve finally gone through the exam, we’ve read the discussion below, and here are our thoughts.

In brief, the exam is OK but no better, and there are issues. There is some decent testing of skills, but the emphasis (as in the Methods 1 exam) appears to be on fiddly computation rather than deeper concepts. That isn’t great for a 1-hour sprint exam, and commenters have suggested the exam was overly long, but of course a 1-hour sprint exam is intrinsically insane. At a deeper level, some of the questions are contrived and aimless, which is standard, but it feels a little worse this year. And, there are screw-ups.

Here are our question-by-question thoughts:

Q1. The kind of pointless and boring mechanics question whose sole purpose is to make mechanics look bad. Part (a) asks students to compute the normal force, but to no end; the normal force is not required for the rest of the question.

Q2. An intrinsically nice question on integration by substitution, which shoots itself in the foot.

Q3. A routine and nice complex roots question.

Q4. A good inequality inequality question involving absolute values. The question is not difficult but, as commenters have suggested, it seems likely that students will do the question poorly.

Q5. A pretty nice vector resolute (projection) question, sort of a coherent version of last year’s debacle. Part (a) is contrived and flawed by having to choose the integer solution from the two roots of the quadratic; it’s not a hanging offence, but it’s the kind of oddity that would make a thoughtful writer think again.

Q6. A mess. See the comments below, and here.

Q7. An OK if (for a Specialist exam) unusual integration question involving continuity and differentiability of a “hybrid function”. The wording is clumsy, since all that is required is to demand that the function be differentiable; continuity of the function is then automatic, and the demanded continuity of the derivative is irrelevant. Sure, spelling out the continuity may simply be being nice, but including the continuity of the derivative suggests the examiners don’t really get it, or are planning a sleight of hand. We’ll see. Given the most authoritative (Methods) textbook makes a complete hash of this topic, it will be interesting to see if the examination report can get it right. We wouldn’t be betting the house on it.

Q8. An ok but ridiculously contrived volume of revolution question. Asking for the volume to be given in the form \boldsymbol{2\pi(\log_e(a) + b)} where \boldsymbol{a, b \in \mathbb R}  is needless, ill-defined and dumb.

Q9. An OK but ridiculously contrived arclength question. The introduction of the symbol \boldsymbol{s} for the arclength is gratuitous and confusing. And (reviews notes), asking for the arclength to be given in the form \boldsymbol{\log_e(m) + n\log_e(p)} where \boldsymbol{m,n, p \in \mathbb Q}  is needless, ill-defined and dumb.

Secret Methods Business: Exam 2 Discussion

UPDATE (31/12/20) The exam is now online.

This is our post for teachers and students to discuss Methods Exam 2 (not online). There are also posts for Methods Exam 1, Specialist Exam 1 and Specialist Exam 2.

UPDATE (21/11/20) A link to a parent complaining about the Methods Exam 2 on 774 is here.

 

UPDATE (24/11/20 – Corrected) A link to VCAA apparently pleading guilty to a CAS screw-up (from 2010) is here. (Sorry, my goof to not check the link, and thanks to Worm and John Friend.)

 

UPDATE (05/12/2020)

We’ve now gone through the multiple choice component of the exam, and we’ve read the comments below. In general the questions seemed pretty standard and ok, with way too much CAS and other predictable irritants. A few questions were a bit weird, generally to good effect, although one struck us as off-the-planet weird.

Here are our question-by-question thoughts:

MCQ1. A trivial composition of functions question.

MCQ2. A simple remainder theorem question.

MCQ3. A simple antidifferentiation question, although the 2x under the root sign will probably trick more than a few students.

MCQ4. A routine trig question made ridiculous in the standard manner. Why the hell write the solutions to \boldsymbol{\cos 2\theta = b} other than in the form \boldsymbol{\theta = \alpha + k\pi}?

MCQ5. A trivial asymptotes question.

MCQ6. A standard and easy graph of the derivative question.

MCQ7. A nice chain rule question. It’s easy, but we’re guessing plenty of students will screw it up.

MCQ8. A routine and routinely depressing binomial CAS question.

MCQ9. A routine transformation of an integral question. Pretty easy with John Friend’s gaming of the question, or anyway, but these questions seem to cause problems.

MCQ10. An unusual but OK logarithms question. It’s easy, but the non-standardness will probably confuse a number of students.

MCQ11. A standard Z distribution question.

MCQ12. A pretty easy but nice trigonometry and clock hands question.

MCQ13. The mandatory idiotic matrix transformation question, made especially idiotic by the eccentric form of the answers.

MCQ14. Another standard Z distribution question: do we really need two of these? This one has a strangely large number of decimal places in the answers, the last of which appears to be incorrect.

MCQ15. A nice average value of a function question. It can be done very quickly by first raising and then lowering the function by \boldsymbol{a} units.

MCQ16. A routine max-min question, which would be nice in a CAS-free world.

MCQ17. A really weird max-min question. The problem is to find the maximum vertical intercept of \boldsymbol{f(x) = -log_e(x+2)}. It is trivial if one uses the convexity, but that is far from trivial to think of. Presumably some Stupid CAS Trick will also work.

MCQ18. A somewhat tangly range of a function question. A reasonable question, and not hard if you’re guided by a graph, but we suspect students won’t do the question that well.

MCQ19. A peculiar and not very good “probability function” question. In principle the question is trivial, but it’s made difficult by the weirdness, which outweighs the minor point of the question.

MCQ20. All we can think is the writers dropped some acid. See here.

 

UPDATE (06/12/2020)

And, we’re finally done, thank God. We’ve gone through Section B of the exam and read the comments below, and we’re ready to add our thoughts.

This update will be pretty brief. Section B of Methods Exam 2 is typically the Elephant Man of VCE mathematics, and this year is no exception. The questions are long and painful and aimless and ridiculous and CAS-drenched, just as they always are. There’s not much point in saying anything but “No”.

Here are our question-by-question thoughts:

Q1. What could be a nice question about the region trapped between two functions becomes pointless CAS shit. Finding “the minimum value of the graph of \boldsymbol{f'} ” is pretty weird wording. The sequence of transformations asked for in (d) is not unique, which is OK, as long as the graders recognise this. (Textbooks seem to typically get this wrong.)

Q2. Yet another fucking trig-shaped river. The subscripts are unnecessary and irritating.

Q3. Ridiculous modelling of delivery companies, with clumsy wording throughout. Jesus, at least give the companies names, so we don’t have to read “rival transport company” ten times. And, yet again with the independence:

“Assume that whether each delivery is on time or earlier is
independent of other deliveries.”

Q4. Aimless trapping of area between a function and line segments.

Q5. The most (only) interesting question, concerning tangents of \boldsymbol{p(x) = x^3 +wx}, but massively glitchy and poorly worded, and it’s still CAS shit. The use of subscripts is needless and irritating. More Fantasyland computation, calculating \boldsymbol{b} in part (a), and then considering the existence of \boldsymbol{b} in part (b). According to the commenters, part (d)(ii) screws up on a Casio. Part (e) could win the Bulwer-Lytton contest:

“Find the values of \boldsymbol{a} for which the graphs of \boldsymbol{g_a} and \boldsymbol{g_b},
where \boldsymbol{b} exists, are parallel and where \boldsymbol{b\neq a}

We have no clue what was intended for part (g), a 1-marker asking students to “find” which values of \boldsymbol{w} result in \boldsymbol{p} having a tangent at some \boldsymbol{t} with \boldsymbol{x}-intercept at \boldsymbol{-t}. We can’t even see the Magritte for this one; is it just intended for students to guess? Part (h) is a needless transformation question, needlessly in matrix form, which is really the perfect way to end.