Category: VCE

The VCAA Draft and its Third Rail

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March 25, 2021

12:32 am

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We’ve looked a little more closely at VCAA’s Draft for the new mathematics VCE subjects. Yes, the time for feedback has ended, unless it hasn’t: the MAV are offering a Zoom session TODAY (Thursday 25/3) for members. God knows how or why. But in any case, it’ll be a while before VCAA cements the thing in place: plenty of time to ignore everyone’s suggestions.

The following are our thoughts on the Draft and Overview. It will be brief and disorganised, since there is no point in doing more; as we wrote, the content doesn’t matter as much as the fact that, whatever content, VCAA will undoubtedly screw it up. Still, there are some clear and depressing points to be made. We haven’t paid much specific attention to what is new nonsense, and what is the same old nonsense; nonsense is nonsense.

GENERAL POINTS ON THE DRAFT

  • The draft looks like a primary school book report. Someone at VCAA really should learn \LaTeX.
  • “Computational Thinking” is meaningless buzzery, and will be endemic, insidious and idiotic. It will poison everything. Every step of Methods and Specialist is subject to the scrutiny of Outcome 3:

“On completion of this unit the student should be able to apply computational thinking and use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in practical situations requiring problem-solving, modelling or investigative techniques or approaches.”

“Statistical functionalities of technology”. And, there’s way more:

“key elements of algorithm design: sequencing, decision-making, repetition, and representation including the use of pseudocode.”

“use computational thinking, algorithms, models and simulations to solve problems related to a given context”

“the role of developing algorithms and expressing these through pseudocode to help determine and understand mathematical ideas and results”

“the purpose and effect of sequencing, decision-making and repetition statements on relevant functionalities of technology, and their role in the design of algorithms and simulations”

“design and implement simulations and algorithms using appropriate functionalities of technology”

This will all be the same aimless, pseudo-exploratory, CAS-drenched garbage that currently screws VCE, but much, much worse. Anybody who signs off on this idiocy should hang their head in shame.

  • CAS shit will now be worse than ever.
  • There should be no CAS exam, at all.
  • There should be no bound notes permitted in any exam.
  • Don’t write “technology”. It is pompous and meaningless. If you mean “CAS” then write “CAS”.
  • SACs have always been shit and will always be shit. The increased weight on them is insane.
  • The statistics is the same pointless bullshit it always was.
  • The presence of “proof” as a topic in Specialist highlights the anti-mathematical insanity of VCAA and ACARA curricula: proof has zero existence elsewhere. Much of what appears in the proof topic could naturally and engagingly and productively be taught at much lower levels. But of course, that would get in the way of VCAA’s constructivist fantasy, now with New and Improved Computational Thinking.

 

MATHEMATICAL METHODS

  • Not including integration by substitution is still and will always be the most stupid aspect of Methods.
  • Dilations must be understood expressed as both “parallel to an axis” and “from an axis”? But not in terms of the direction the damn points are moving? Cute.
  • The definition of independent events is wrong.
  • The demand that, for the composition \boldsymbol{f\circ g}, the range of \boldsymbol{g} must be a subset of the domain of \boldsymbol{f} is as pedantic and as pointless as ever.
  • “literal equations” is the kind of blather that only a maths ed clown could think has value.
  • The derivative of the inverse is still not in the syllabus, and everyone will still cheat and use it anyway.
  • “trapezium rule” is gauche but, more importantly, what is the purpose of teaching such integral approximation here? Yes, one can imagine a reasonable purpose, but we’ll lay odds there is no such purpose here.

 

SPECIALIST MATHEMATICS

  • The killing of mechanics is a crime.
  • The inclusion of logic and proof and the discrete topics could be good. But it won’t be. It will be shallow and formulaic and algorithmised, and graded in a painfully pedantic manner. Just imagine, for example, how mathematical induction will be assessed on exams: “Students often wrote \boldsymbol{n} instead of \boldsymbol{k}. Students should be aware of the proper use of these variables.”
  • There is no value here in “proof by contrapositive”, and it is confusing. Proof by contradiction suffices.
  • They’re really including integration by parts? Incredible.
  • The inclusion of cross products and plane equations makes some sense.

A Choice of Difficults

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March 10, 2021

8:28 pm

40 Comments on A Choice of Difficults

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You have a choice. The two questions below come from different exams:

Each question was (arguably) last year’s most difficult exam question on the most difficult mathematics subject in that state. Each question was effectively allocated just under 20 minutes to complete (11/100 x 180 and 13/80 x 120).

Now, you must choose: which question is better, in any sense of the word “better”?

 

NSW  (Formula Marking guide and sample solution are here.)

 

VIC  (Briefly discussed here, marking guide and sample solution are in your dreams.)

VCAA’s Draft Feedback Due TODAY

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March 9, 2021

11:21 am

11 Comments on VCAA’s Draft Feedback Due TODAY

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We’ve been remiss in not writing further on VCAA’s draft for the new mathematics VCE subjects. It’s just, for reasons we’ll explain briefly here and flesh out elsewhere, we’ve struggled to face up to this new nonsense.

But, feedback is due TODAY (midnight? – see links below), and we really oughta say something. So, here are our brief thoughts and then, after that, why we believe none of it really matters:

  • “Computational thinking and algorithms” is pure snake oil.  Inevitably, it will be nothing but wafer-thin twaddle for the training of data monkeys.
  • The increased weight on these meaningless, revolting SACs is insidious.
  • If we read it correctly, more weight will be placed on the non-CAS Methods/Specialist exams; it is not remotely close to enough, but it is good.
  • Statistics was and is and will always be an insane topic to emphasise in school.
  • Foundation Mathematics: Who Cares?
  • General Mathematics: Who Cares?
  • Mathematical Methods: same old swill.
  • The deletion of mechanics from Specialist Mathematics is criminal, but the topic had already been so bled to meaningless that it hardly matters.
  • In principle, the inclusion in SM of “logic” and “proof and number” and “combinatorics” is a good thing. We’ll see.
  • Similarly, in principle the making of SM12 presumed knowledge for SM34 is good; in practice, it is almost certainly bad. Currently, a good teacher at a good school will take the freedom in SM12 to go to town, to show their students some genuine mathematics and real mathematical thought. In the future, that will be close to impossible, and SM12 will likely become as predictable and as dull as MM12 (and MM34 and SM34).

And now, why doesn’t any of it matter? Because, fundamentally it doesn’t matter what you teach, it matters how you teach. What matters is the manner in which you approach your subject and your students, and none of that will change in other than a microscopic manner. Nothing in VCAA has changed, nothing in the general culture of Victorian education had changed. So, why the Hell would twiddling a few dials on utterly insane subjects assessed in an utterly insane manner make any meaningful difference?

Everything VCAA touches, they will turn to shit. That will continue to be true until there is a fundamental cultural shift, in VCAA and generally.

I hate this place.

LINKS

  • 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.

Feeling VCAA’s Draft: Discussion

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November 24, 2020

4:14 pm

41 Comments on Feeling VCAA’s Draft: Discussion

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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

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November 20, 2020

2:09 pm

56 Comments on Secret Specialist Business: Exam 2 Discussion

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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

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November 20, 2020

2:08 pm

31 Comments on Secret Specialist Business: Exam 1 Discussion

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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

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November 20, 2020

2:08 pm

43 Comments on Secret Methods Business: Exam 2 Discussion

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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.

Secret Methods Business: Exam 1 Discussion

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November 20, 2020

2:08 pm

57 Comments on Secret Methods Business: Exam 1 Discussion

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UPDATE (31/12/20) The exam, and all the exams, are now online. (Thanks to Red Five for the flag.)

OK, we should have thought of this earlier. This post is for teachers and students (and fellow travellers) to discuss Methods Exam 1, which was held a few days ago. (There are also posts for Methods Exam 2, Specialist Exam 1 and Specialist Exam 2. We had thought of also putting up posts for Further, but decided to stick to mathematics.) We’ll also update with our brief thoughts in the near future.

Our apologies to those without access to the exam, and unfortunately VCAA is only scheduled to post the 2020 VCE exams sometime in 2023. The VCAA also has a habit of being dickish about copyright (and in general), so we won’t post the exam or reddit-ish links here. If, however, a particular question or two prompts sufficient discussion, we’ll post those questions. And, we might allow (undisplayed) links to the exams stay in the comments.

UPDATE (21/11/20) The link to the parent complaining about the Methods Exam 1 on 3AW is here. If you see any other media commentary, please note that in a comment (or email me), and we’ll add a link.

UPDATE (23/11/20) OK, we’ve now gone through the first Methods exam quickly but pretty thoroughly, have had thoughts forwarded by commenters Red Five and John Friend, and have pondered the discussion below. Question by question, we didn’t find the exam too bad, although we didn’t look to judge length and coverage of the curriculum. There was a little Magritteishness but we didn’t spot any blatant errors, and the questions in general seemed reasonable enough (given the curriculum, and see here). Here are our brief thoughts on each question, with no warranty for fairness or accuracy. Again, apologies to those without access to the exam.

Q1. Standard and simple differentiation.

Q2. A “production goal” having the probability of requiring an oil change be m/(m+n) … This real-world scenarioising is, of course, idiotic. The intrinsic probability questions being asked are pretty trivial, indeed so trivial and same-ish that we imagine many students will be tricked. It’s not helped by a weird use of “State” in part (a), and a really weird and gratuitous use of “given” in part (b), for a not-conditional probability question.

Q3. An OK question on the function tan(ax+b). Stating “the graph is continuous” is tone-deaf and, given they’ve drawn the damn thing, a little weird. The information a > 0 and 0 < b < 1 should have been provided when defining the function, not as part of the eventual question. Could someone please send the VCAA guys a copy of Strunk and White, or Fowler, or Gowers, or Dr. Seuss?

Q4. A straight-forward log question.

Q5. For us, the stand-out stupidity. See here.

Q6. An OK graphing-integration question, incorporating VCAA’s \boldsymbol{f = f^{-1}} fetish. Interestingly, solving the proper equation in (b) is, for a change, straight-forward (although presumably the VCAA will still permit students to cheat, and solve \boldsymbol{f = x} instead). As discussed in the comments, the algebra in part (c) is a little heavier than usual, and perhaps unexpected, although hardly ridiculous. The requirement to express the final answer in the form \boldsymbol{\frac{a - b\sqrt{b}}6}, however, is utterly ridiculous.

Q7. This strikes us as a pretty simple tangents-slopes question, although maybe the style of the question will throw students off. Part (c) is in effect asking, in a convoluted manner, the closest point from the x-axis to a no-intercepts parabola. Framed this way, the question is easy. The convolution, however, combined with the no-intercepts property having only appeared implicitly in a pretty crappy diagram, will probably screw up plenty of students.

Q8. A second integration question featuring VCAA’s \boldsymbol{f = f^{-1}} fetish. Did we really need two? The implicit hint in part (c) and the diagram are probably enough to excuse the Magritteness of part (d), but it’s a close call. Much less excusable is part (b):

“Find the area of the region that is bounded by f, the line x = a and the horizontal axis for x in [a,b], where b is the x-intercept of f.” 

Forget Dr. Seuss. Someone get them some Ladybird books.

 

MAV’s Trials and Tribulations

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September 25, 2020

4:30 pm

113 Comments on MAV’s Trials and Tribulations

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Yeah, it’s the same joke, but it’s not our fault: if people keep screwing up trials, we’ll keep making “trial” jokes. In this case the trial is MAV‘s Trial Exam 1 for Mathematical Methods. The exam is, indeed, a trial.

Regular readers of this blog will be aware that we’re not exactly a fan of the MAV (and vice versa). The Association has, on occasion, been arrogant, inept, censorious, and demeaningly subservient to the VCAA. The MAV is also regularly extended red carpet invitations to VCAA committees and reviews, and they have somehow weaseled their way into being a member of AMSI. Acting thusly, and treated thusly, the MAV is a legitimate and important target. Nonetheless, we generally prefer to leave the MAV to their silly games and to focus upon the official screwer upperers. But, on occasion, someone throws some of MAV’s nonsense our way, and it is pretty much impossible to ignore; that is the situation here.

As we detail below, MAV’s Methods Trial Exam 1 is shoddy. Most of the questions are unimaginative, unmotivated and poorly written. The overwhelming emphasis is not on testing insight but, rather, on tedious computation towards a who-cares goal, with droning solutions to match. Still, we wouldn’t bother critiquing the exam, except for one question. This question simply must be slammed for the anti-mathematical crap that it is.

The final question, Question 10, of the trial exam concerns the function

\color{blue}\boldsymbol{f(x) =\frac{2}{(x-1)^2}- \frac{20}{9}}

on the domain \boldsymbol{(-\infty,1)}. Part (a) asks students to find \boldsymbol{f^{-1}} and its domain, and part (b) then asks,

Find the coordinates of the point(s) of intersection of the graphs of \color{blue}\boldsymbol{f} and \color{blue}\boldsymbol{f^{-1}}.

Regular readers will know exactly the Hellhole to which this is heading. The solutions begin,

Solve  \color{blue}\boldsymbol{\frac{2}{(x-1)^2}- \frac{20}{9} =x}  for  \color{blue}\boldsymbol{x},

which is suggested without a single accompanying comment, nor even a Magrittesque diagram. It is nonsense.

It was nonsense in 2010 when it appeared on the Methods exam and report, and it was nonsense again in 2011. It was nonsense in 2012 when we slammed it, and it was nonsense again when it reappeared in 2017 and we slammed it again. It is still nonsense, it will always be nonsense and, at this stage, the appearance of the nonsense is jaw-dropping and inexcusable.

It is simply not legitimate to swap the equation \boldsymbol{f(x) = f^{-1}(x)} for \boldsymbol{f(x) = x}, unless a specific argument is provided for the specific function. When valid, that can usually be done. Easily. We laid it all out, and if anybody in power gave a damn then this type of problem could be taught properly and tested properly. But, no.

What were the exam writers thinking? We can only see three possibilities:

a) The writers are too dumb or too ignorant to recognise the problem;

b) The writers recognise the problem but don’t give a damn;

c) The writers recognise the problem and give a damn, but presume that VCAA don’t give a damn.

We have no idea which it is, but we can see no fourth option. Whatever the reason, there is no longer any excuse for this crap. Even if one presumes or knows that VCAA will continue with the moronic, ritualistic testing of this type of problem, there is absolutely no excuse for not also including a clear and proper justification for the solution. None.

What of the rest of the MAV, what of the vetters and the reviewers? Did no one who checked the trial exam flag this nonsense? Or, were they simply overruled by others who were worse-informed but better-connected? What about the MAV Board? Is there anyone at all at the MAV who gives a damn?

*********************

Postscript: For the record, here, briefly, are other irritants from the exam:

Q2. There are infinitely many choices of integers \boldsymbol{a} and \boldsymbol{b} with \boldsymbol{a/\sqrt{b}} equal to the indicated answer of \boldsymbol{-2/\sqrt{3}}.

Q3. This is not, or at least should not be, a Methods question. Integrals of the form \boldsymbol{\int\!\frac{f'}{f}\ }  with \boldsymbol{f} non-linear are not, or at least are not supposed to be, examinable.

Q4. The writers do not appear to know what “hence” means. There are, once again, infinitely many choices of \boldsymbol{a} and \boldsymbol{b}.

Q5. “Appropriate mathematical reasoning” is a pretty fancy title for the trivial application of a (stupid) definition. The choice of the subscripted \boldsymbol{g_1} is needlessly ugly and confusing. Part (c) is fundamentally independent of the boring nitpicking of parts (a) and (b). The writers still don’t appear to know what “hence” means.

Q6. An ugly question, guided by a poorly drawn graph. It is ridiculous to ask for “a rule” in part (a), since one can more directly ask for the coefficients \boldsymbol{a}, \boldsymbol{b} and \boldsymbol{c}.

Q7. A tedious question, which tests very little other than arithmetic. There are, once again, infinitely many forms of the answer.

Q8. The endpoints of the domain for \boldsymbol{\sin x} are needlessly and confusingly excluded. The sole purpose of the question is to provide a painful, Magrittesque method of solving \boldsymbol{\sin x = \tan x}, which can be solved simply and directly.

Q9. A tedious question with little purpose. The factorisation of the cubic can easily be done without resorting to fractions.

Q10. Above. The waste of a precious opportunity to present and to teach mathematical thought.

UPDATE (28/09/20)

John (no) Friend has located an excellent paper by two Singaporean maths ed guys, Ng Wee Leng and Ho Foo Him. Their paper investigates (and justifies) various aspects of solving \boldsymbol{f(x) = f^{-1}(x)}.

Bernoulli Trials and Tribulations

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September 23, 2020

11:29 am

47 Comments on Bernoulli Trials and Tribulations

VCE

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This one feels relatively minor to us. It is, however, a clear own goal from the VCAA, and it is one that has annoyed many Mathematical Methods teachers. So, as a public service, we’re offering a place for teachers to bitch about it.*

One of the standard topics in Methods is the binomial distribution: the probabilities you get when repeatedly performing a hit-or-miss trial. Binomial probability was once a valuable and elegant VCE topic, before it was destroyed by CAS. That, however, is a story is for another time; here, we have smaller fish to fry.

The hits-or-misses of a Binomial distribution are sometimes called Bernoulli trials, and this is how they are referred to in VCE. That is just jargon, and it doesn’t strike us as particularly useful jargon, but it’s ok.** There is also what is referred to as the Bernoulli distribution, where the hit-or-miss is performed exactly once. That is, the Bernoulli distribution is just the n = 1 case of the binomial distribution. Again, just jargon, and close to useless jargon, but still sort of ok. Except it’s not ok.

Neither the VCE study design nor, we’re guessing, any of the VCE textbooks, makes any reference to the Bernoulli distribution. Which is why the special, Plague Year formula sheet listing the Bernoulli distribution has caused such confusion and annoyance:

Now, to be fair, the VCAA were trying to be helpful. It’s a crazy year, with big adjustments on the run, and the formula sheet*** was heavily adapted for the pruned syllabus. But still, why would one think to add a distribution, even a gratuitous one? What the Hell were they thinking?

Does it really matter? Well, yes. If “Bernoulli distribution” is a thing, then students must be prepared for that thing to appear in exam questions; they must be familiar with that jargon. But then, a few weeks after the Plague Year formula sheet appeared, schools were alerted and VCAA’s Plague Year FAQ sheet**** was updated:

This very wordy weaseling is VCAA-speak for “We stuffed up but, in line with long-standing VCAA policy, we refuse to acknowledge we stuffed up”. The story of the big-name teachers who failed to have this issue addressed, and of the little-name teacher who succeeded, is also very interesting. But, it is not our story to tell.

 

*) We extend our standard apology to all precious statisticians for our language.

**) Not close to ok is the studied and foot-shooting refusal of the VCAA and textbooks to use the standard and very useful notation q = 1 – p.

***) Why on Earth do the exams have a formula sheet?

****) The most frequently asked question is, “Why do you guys keep stuffing up?”, but VCAA haven’t gotten around to answering that one yet.