UPDATE (09/09/21) The examination report is here (a Word document, because VCAA is stupid). Corresponding updates, including the noting of blatant errors (MCQ20, and see here, and Q5), are included with the associated question, in green.
UPDATE (31/12/20) The exam is now online.
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.)
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.
(09/09/21) 56% got this correct, which ain’t great.
MCQ3. A simple antidifferentiation question, although the 2x under the root sign will probably trick more than a few students.
(09/09/21) 86%, so students (or, more accurately, their CASes) weren’t tricked.
MCQ4. A routine trig question made ridiculous in the standard manner. Why the hell write the solutions to other than in the form ?
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.
(09/09/21) 50%, for God knows what reason.
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.
(09/09/21) 35%, for Christ’s sake. The examination report contains pointless gymnastics, and presumably students tried this and fell off the beam. (The function is squished by a factor of 2, so the area is halved. Done.)
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.
(09/09/21) 25%, obviously a direct consequence of VCAA’s idiotically cute form of answer.
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.
(09/09/21) In the General comments, the examination report admonishes students for poor decimalising:
“Do not round too early …”
It seems their idea is actually “do not round at all”.
MCQ15. A nice average value of a function question. It can be done very quickly by first raising and then lowering the function by units.
(09/09/21) 36%, presumably because everyone attempted the thoughtless and painfully slow approach indicated in the examination report.
MCQ16. A routine max-min question, which would be nice in a CAS-free world.
(09/09/21) 53%, for God knows what reason. The question is simple to do in one’s head.
MCQ17. A really weird max-min question. The problem is to find the maximum vertical intercept of a tangent to . 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.
(09/09/21) 42%, which is not surprising. The examination report gives absolutely no clue why the maximising tangent should be at x = 0.
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.
(09/09/21) 15%, which is worse than throwing darts. Although the darts would be better saved to throw at the writers of this stupid question.
MCQ20. All we can think is the writers dropped some acid. See here.
(09/09/21) 18%. Now, what did we do with those darts? As follows from the discussion here, the suggested solution in the examination report is fundamentally invalid. One simply cannot conclude that a = 2π in the manner indicated, which means that the question is at minimum a nightmare, and is best described as wrong. Either the report writers do not know what they are writing about, or they are consciously lying to avoid admitting the question is screwed. As to which of the two it is, we dunno. Maybe throw a dart.
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 ” 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 , but massively glitchy and poorly worded, and it’s still CAS shit. The use of subscripts is needless and irritating. More Fantasyland computation, calculating in part (a), and then considering the existence of 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 for which the graphs of and ,
where exists, are parallel and where “
We have no clue what was intended for part (g), a 1-marker asking students to “find” which values of result in having a tangent at some with -intercept at . 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.
(09/09/21) This could be a horror movie: Revenge of the 1-Pointers.
Part (c) was clearly intended to be an easy 1-pointer: just note that a (tangent) line without an x-intercept is horizontal. But, somehow 77% of students stuffed it up. So, how? The examination report sermonises, thusly:
“The concept of the ‘nature of a tangent line’ was not obvious for many students.”
This suggests that the report writers don’t understand the concept of a concept. It also indicates that the report writers didn’t read their own exam. Q5(c) reads as follows:
“State the nature of the graph of ga when b does not exist. [emphasis added]”
Three sub-questions ago, ga is defined to the be the tangent to a function, and b is defined to be the x-intercept of this tangent (even though it may not exist). So, what was obviously not obvious to the students was the meaning of a vaguely worded question framed in poor notation. God, these people are dumb. And sanctimonious. And dumb.
Part (g), another 1-pointer, is concerned with the function p(x) = x3 + wx. The question asks, badly, for which values of w is there a positive t such that the tangent to p at x = t will have x-intercept at -t. 3% of students were smart enough (or lucky enough) to get the right answer, and 97% of students were very smart enough to go “Fuck this for a joke”, and skip it.
The solution in the examination report is lazily incomprehensible, but the idea was to just do the work: equate p'(t) with the rise/run slope of the tangent and see for which w there is a positive t that solves the equation. It turns out that the equation simplifies to w + 5t2 = 0, and so as long as w < 0 there will be a solution. It also turns out that specifying t positive is entirely irrelevant. Which is what they do.
It is worth noting the question can also be nutted out qualitatively, if one knows what graphs like y = x3 + x and y = x3 – x look like. If w ≥ 0 then it it easy see the tangent to p(x) = x3 + wx will always hit the x-axis before crossing the y-axis, so no chance of giving a solution for the exam question. If w < 0 then look at tangents at points t between the two turning points. At a turning point the slope of the tangent is horizontal. Then as the slope goes negative the x-intercept of the tangent comes in from ∞ (or -∞), until eventually the x-intercept is 0. Somewhere along the way, there has to be a t that gives a solution for the exam question.
Part (h), another 1-pointer, is the final question on the exam, and is a stuff up. This time, 98% of students were very smart enough to skip the damn thing. As well, as mystery student PURJ pointed out to us, the examination report is also stuffed. The question again concerns the function p. It had been noted earlier that the tangents to p at t and -t are always parallel. Then Part (h) asks, in idiotic matrix notation, how p can not be translated or dilated to so that the new function still has this parallel tangent property. Yep, the question is framed in a negative manner, and the examiners whine about it:
“The key word in this part is restrictions.”
Nope. The key word in this part is “idiotic”. (And, “ungrammatical”.) In any case, the examination report indicates that the key to solving the question is that the transformed function must still be odd. This, as PURJ pointed out, is wrong. A vertical translation is just fine but the resulting function will not be odd. The correct characterisation is that the derivative of the transformed function must be even. In sum, this means one can transform as one wishes, except for horizontal translations. Which equates to the report’s matrix answer, without any noting of the “odd”, but not odd, contradiction.