Methods Exam 1 was today. We’ve been handballed a copy of the exam but haven’t looked at it yet, and we’ve not yet heard any reactions. People are free to give their thoughts in the comments below, and we’ll update this post as the dust settles.
OK, we’ve now been through the exam report. Since the exam was relatively benign, and too easy, the report doesn’t bring up a lot else. But there is Q9, on which the report is disgraceful. We hammer this below, in green.
We shall also make one quick comment here on the report’s summary advice to students. While advising on the proper use of notation, the report reminds students that they should:
Ensure the variable used in the naming of a function is consistent with the rule. In Question 9ci., g(θ) was needed, not g(x).
Well, yes. Who can object? Except, VCAA committed this exact error in the previous year’s Methods 2 Exam and, of course, never acknowledged their error. It is such dishonesty and such hypocrisy that makes VCAA so much loved by so many.
We will post on some sleaziness in the exam report soon. But, it is worth noting that, after waiting five months for the report to come out, there is an error in the report on Question 1. Seriously, are you VCAA guys drunk?
The exam report is now available, here.
The exam is now available, here.
Alright, it’s time for us to stop wagging school and get down to work. Obviously Methods 2 and Specialist 2 were the, um, more interesting exams, but we’ll begin with the relatively straight-forward ones.
There’s not much to say about Methods 1. It was too easy,* except for the final question Q9, which was nasty and, in parts, stupid. Other than that, there were no real issues that we could see. Below are our question by question thoughts.
*) In general “too easy” is significantly worse than “too hard”, although this is probably not the day to be trying to convince Specialist students of that.
Q1 Easy differentiations.
(22/04/22) It’s quite poetic for VCAA to make everyone wait a millennium for the examination report, and then have screwed up the answer to the very first question.
Q2 Way too easy antidifferentiation.
Q3 Easy trig question.
Q4 Easy enough graphing question, although there’s enough minus signs to probably catch people.
Q5 Easy and meaningless question on polynomial functions and transformations. The x-intercepts of g and h are most easily found by thinking of transformations, but presumably most students will do it the long way.
Q6 A nice binomial distribution question.
Q7 A very easy probability question, with pdf f(x) = k/x2 on [1,2]. The clarification that “k is a positive real number” is needless and clumsy. There’s also some standard and pointless pedantry, declaring the pdf to be “0 elsewhere”, rather than just sticking to the natural domain.
Q8 An OK antidifferentiation question. Part (b) is most easily done with the second derivative test, which is not part of Methods. (We assume SDT is nonetheless permissible in Methods, although we have heard from an unreliable source that this is not the case.)
(23/04/22) As noted by SRK below, the exam report has officially sanctioned the use of the second derivative test. This is good.
Q9 Not an intrinsically awful question, but an extrinsically awful question. As commenters have noted, it was nasty and idiotic to have all the difficulty in the exam concentrated in one final 20% question. And, as commenters have noted, there are parts of the question for which it is likely that many students will know exactly what is going on but will be tricked and slimed out of proper reward.
(22/04/22) Well, that went swimmingly. An average score of 1/8 on the question. But of course this is not in any sense because VCAA might have stuffed up.
Part (a) in effect requires students to “show” that the line is tangent to the circle . As commenter John Friend noted, the question is most naturally and most easily done by plugging the line into the circle, and showing there is just the one solution. BUT, as John also noted, the VCAA assessors have traditionally and idiotically interpreted “show” to mean something like “derive”, precluding natural and completely valid “we know where we want to get to” proofs. It is difficult to believe that VCAA would be so stupid to enact such a policy on this question, but VCAA assessors can be pretty damn stupid.
(22/04/22) And, yes, it would appear that VCAA is, yet again, that damn stupid. Our reading of the report is that John Friend’s most natural proof, indicated above, would have been considered invalid. In the summary advice to students, the report notes:
A reminder that ‘show that’ questions require a reasoned argument.
The answer is given and students are required to provide a detailed progression to the answer.
And no. This second sentence is meaningless, since “answer” is meaningless: a clear proposition – perhaps “conclusion” – is required, rather than a noun. And no, this is not nitpicking
But, simply, nothing like the second sentence follows from the first. “Show that” only has such a perverted, and perverting, sense in VCE because VCAA does not know the proper meaning of mathematical expressions, and because VCAA has no proper conception of mathematical proof. Which, poisonously, they then inflict upon students.
Commenting on the question directly, the report repeats this idiocy:
It is important to remember that for ‘show that’ questions, the working needs to be clear and logically structured, with a well-defined progression from start to finish.
Only because you pointlessly demand it, you cretins. This idiocy has to stop. We shall wage full on war on this anti-mathematical idiocy in the very near future.
The wording of Part (b)(i) is atrocious, but in effect asks students for which vertical dilations the line from (a) will still intersect the circle. The easy answer is -1 ≤ q ≤ 1, where q is the stretch factor, and that answer is wrong; as commenter Damien noted, the trap is that q = 0 is not permitted. Presumably, then, students who answer -1 ≤ q ≤ 1 will score 0/1 on this question. But note that students don’t have to score 0/1 for this obvious answer; since q = 0 has been excluded in the preamble to the question, this exclusion can then be considered to apply to any answer as well. So, if the Methods assessors decided, for once, to not be assholes, …
(22/04/22) Guess what? Yep, they’re assholes.
This is just a 1-mark question, but it is the kind of completely avoidable crap that makes VCAA so loved by so many. OK, sure, even though q = 0 makes perfect sense as a transformation, projections are not part of Methods and so you exclude it. But why not just exclude it by restricting q to be positive? You’d lose absolutely nothing of value in the question, and you’d stop kids stressing whether VCAA is, once again, going to be dicks.
Part (b)(ii) requires students to find for which vertical dilations the line from (a) will intersect the circle twice at points with positive coordinates. The question is ok, but it is over-egged, and it is way too much work for 1 mark.
Part (c) involves the determination and maximisation of the area of an associated triangle. The question is ok, although the not-obviously restricted domain will probably trick many students. In any case, we doubt students will do well on (c), since many will have been flustered by the earlier parts of the question.