Sorry, no energy for a joke title. The reports are here (Word, idiots):

Specialist Exam 1 report (and exam)

Specialist Exam 2 report (and exam)

Methods Exam 1 report (and exam)

Methods Exam 2 Report (and exam)

For background, readers may wish to go to the following blog posts:

Specialist Error List (and see here, here, here, here, here and here)

Methods Error List (and see here and here)

We’ll update the various posts soon(ish).

Initial Methods gripes:

Exam 1:

4b, c: ‘A significant number of students treated the situation as a conditional probability, which was acceptable, although unnecessary’. shut up

5a: typo (should say 10^10 instead of 1010; this was confusing and i was puzzling for a little over what it was meant to say).

7ai. Only 2/3 of students could find the area of the square! And Methods is one of the harder maths…that’s just scary. VCAA only writes ‘This question was well done’.

7b. I can only imagine how many students lost marks after the whole integral process, for not specifying that 200 is half the area of the tile.

7c. ‘ Students need to have an appreciation of the meaning of terms in mathematics.’ from the VCAA that brought us the maximum of a logistic graph. This sentence is about students who tried to prove that the ‘continuous pattern’ had smooth joins.

Exam 2:

MCQ: I hate how they don’t provide an explanation for most of the MCQ.

Extended response:

1a: they didn’t accept ‘y-axis’ for the axis of symmetry of a parabola that’s symmetric about the, um, y-axis. Only x=0 was accepted.

1c. ‘Others did not use their technology and often algebraic errors were seen in responses.’ What idiot students, doing maths in their maths exam.

1d. ‘As in Question 1c., those who did not use their technology tended to make algebraic errors.’ How can VCAA not see how damning this line is? It’s just admitting that no students can find a tangent to a parabola on their own…

3ai. Ughhhh why do VCAA expect the use of technology to find the chance of flipping 5 heads in a row? (fair coin). ‘Some students… had their technology on the wrong float’ this error is so meaningless! There’s no test of the students’ maths, so it’s just their calculator settings now?

3biii. Only 6% of the state got the mark, so you’d think VCAA would provide an explanation, wouldn’t you? Nup — just state the values and go. Same in 3ciii and 4ei (and like half the MCQ)

4d. ‘The tanh function is not part of the study design but the output on some students’ technology gave this function and it is correct.’ Ah yes the educational value of technology, now students can give answers that they do not understand. (The word ‘some’ downplays how common the tanh answer would have been; most of the students I talked to after the exam answered tanh).

5b. ‘Some students did not show enough working’. It’s one bloody mark! Did they lose the singular mark for this?

And that’s all for now on Methods; might do a Specialist gripe list later.

Very helpful, and painful. Thanks, aps.

From the Methods Paper 1 Report: “Students need to have an appreciation of the meaning of terms in mathematics.”

Is this irony, considering VCAA’s questionable use of terms such as “median”, “PDF”, “show that”…?

EDIT: Just read APS comments where this point is raised also. Suspect a third of students didn’t write their units for the area of the square…

Oh yeah, the units– that’ll be it. The culmination of VCAA making up for their easier and easier questions with pettier and pettier nitpicks.

Initial Specialist gripes:

Exam 1:

3b) Aside from the (non)-ambiguous wording that’s already been WitCHed here, apparently you could use z=1.96 or z=2. It’s not at all obvious that you can use z=2. I remember using 1.96, as I wasn’t sure z=2 would be accepted; they should have made it clear that you can use z=2. I guess the answers end up being the same because of rounding. So it’s not really wrong, just messy.

6bii. They should teach students that the dot product being 0 doesn’t NECESSARILY mean the vectors are perpendicular; it’s also possible that one of the vectors is 0. Might be a bit of a nitpick, but combined with their f(x)=f^{-1}(x) –> f(x)=x nonsense, there’s an issue with students not learning the limitations of their methods. I worry that students won’t be taught the limitations of Newton’s method either, when that’s introduced to Methods.

But for the most part, and to be fair to VCAA, I thought the exam 1 was a decent exam. The answers on the exam report show a decent amount of working. Students scored decently on the exam (mean score 48.19/80). There were a couple of questions with more than 1 step required to find the answer. I think the Specialist exam 1 is the best of all the VCE maths exams (not much of an accomplishment, but still)– hopefully the new study design doesn’t butcher it.

Exam 2:

MCQ: I counted this time. They explained the answer for 7 questions out of 20. Answers to MCQ4 and MCQ19 are given without comment. And, I have a question:

MCQ10: ‘The tangent at the point (1, m) will have a negative gradient when:’. 21% of students chose the accepted answer E. But, given the wording, aren’t A and C also technically correct, since the two individual solutions lie in these ranges of values?

Extended Response: (more CAS bs)

1b. ‘Setting the calculator screen to match the grid provided will help students sketch graphs correctly’. Ughhhhhh

2ai. These ‘show that’ questions are intended as a foil to CAS, and it’s not enough. ‘A number of students apparently used a CAS to solve the given equation… again using CAS to verify the given result’. You reap what you sow, VCAA.

2c. Once again, VCAA shows no working. Same issue in 3ai, 3bi, 3c, 4bii, 5b, 6b, 6d

3bi. ‘Relatively few students gave a correct response’ 23% of students got the mark, ‘relatively few’, that’s funny.

3e. In the exam I was unsure of whether the ratio should be 2/3 or 3/2, and I can’t have been the only one. The exam report gives 2/3 and doesn’t mention this issue. (Is there a way to tell, from the question? I would like to know.)

4c. Is ‘perpendicularity’ even a word?

4d. ‘A number of incorrect student responses incorrectly found the straight line distance’ sheesh, we get it, the students were incorrect. (Except the wording was ambiguous, so, were they?).

5c. ‘Just as in other ‘show that’ questions, sufficient detail was required’ thanks for the truism. It’d be nice if you could define ‘sufficient detail’ though.

6f. No mention of the independence/dependence issue, though the average score was 0.8/3.

And that’s it. ugh

It would appear that VCAA policy is to only explain answers to MCQs when less than 50% of students answered correctly.

In the case of Q4 (and yes, that question still irks me greatly) I do wonder if the defense will be “well, more than half of all students answered the intended option, so there is no problem.”

Thanks, RF. I’m not doubting it, but what makes you think that is the policy?

I cannot find an example of a VCAA paper 2 where they gave an explanation for a MCQ that had a successful response rate of 51% or more.

Maybe there is one. I can’t find it.

Seems too coincidental otherwise.

Yeah, I think that’s right. For methods and spesh, all the explained questions had less then 50% of students get the right answer (highest percentage of these being 47%) and all the unexplained ones had >= 50% of students getting it right (lowest percentage 50%).

Still stupid though. Up to 50% of students get the question wrong and VCAA won’t explain to them why…

Thanks again, aps. I won’t go to the substance of VCAA’s sins. But a few quick responses to other points you’ve raised.

a) In the real mathematical world, it is standard for the zero vector be parallel and perpendicular to everything. In VCE, this stuff is a mess, and the tip of an entire iceberg of mess. I’ve now put it on my list to post on it, but see the points made about parallel here.

b) I don’t get your point re MCQ10. It’s a bad, nasty question, but I don’t think it’s wrong.

c) I’m fine with “perpendicularity”, but of course i think wordingness is something to which we should all aspire.

Thanks for your responses 🙂

a) Ah, I suppose that makes sense. Yeah, we never learnt that in VCE. And since, as in the WitCH you linked, textbooks/teacher like to specifically exclude the 0 vector when talking about parallelism/‘perpendicularity’, one comes to the conclusion that zero vectors can’t be parallel/perpendicular to anything.

b) The question’s probably fine, but I’ll try to elaborate on what I meant:

Consider the statement:

(*) The tangent at (1, m) has negative gradient when m is in R\[-1,0]

It’s true that m in R\[-1,0] is a necessary condition for the the tangent at (1,m) to have negative gradient. It’s also a sufficient condition if it’s coupled with ‘and the tangent at (1,m) exists’.

So, if either:

1. The ‘when’ in (*) can be interpreted as ‘only if’; or

2. It can be assumed that the tangent at (1, m) exists

then the question is somewhat ambiguous; if (*) is true, then A is a correct answer. (Similar-ish argument for option C).

Maybe I’m just biased though- I picked A since I didn’t notice the extra step required. I do think they intended for this to be obscure, otherwise they could have written something like ‘Find m such that the tangent at (1, m) has a negative gradient’.

Thanks, aps.

On (a), it’s much worse than you think. I’ll try to post on it soon.

On (b), I now get what you mean, but I think it’s a strained reading of the question. I think the intended interpretation is clearly fair enough (even if the question as a whole is not).

My understanding is that it is a convention to say the zero vector is parallel to every other vector. This has consequences in linear dependent sets of vectors and other definitions, but I can’t see why it must be the case. I guess it comes down to how you define parallel vectors. Allowing means that the zero vector is parallel to every other vector, but I’m not sure the world ends if you choose to define parallel vectors in a different way.

Don’t say “convention”. Have some balls and pick a definition.

I say the zero vector is parallel to all other vectors.

If others say this is not true, OK, but you need to define your axioms carefully.

Since VCAA does not pick a side, I can only assume they follow the “convention”.

Thanks, although “define your axioms” doesn’t mean anything.

OK – there are two choices: either the zero vector is parallel to everything or it is parallel to nothing.

I am of the belief that it is parallel to everything. Until a question chooses to define “parallel” otherwise, I would argue that this is the definition. An axiom perhaps (although I’m probably using the word incorrectly).

I’m not 100% sure that my definition MUST be correct, but I also cannot think of any good arguments to the contrary.

RF,

some support for your assertion on zero vectors

https://math.stackexchange.com/questions/1909952/convention-regarding-zero-vector

Steve R

Ugh! Pointless. Don’t look for authority: look for argument.

I will ask, as I did on this post:

Suppose you have two non-zero vectors,

aandb. Can you always splitbinto components parallel and perpendicular toa?