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.
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.
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 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.
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.
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 where is needless, ill-defined and dumb.
Q9. An OK but ridiculously contrived arclength question. The introduction of the symbol for the arclength is gratuitous and confusing. And (reviews notes), asking for the arclength to be given in the form where is needless, ill-defined and dumb.
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.)