**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 2*x* 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 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.

**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 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 . 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 ” 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.

It’s far too quiet here so I’ll kick things off with some general comments on the questions in Section A:

Q1 – Q2: Simple Methods Unit 1 questions.

Q3: Press some buttons on a CAS. Very simple for Specialist students who would just use DSolve (in Mathematica) or similar on a CAS calculator.

Q4: Button pushing.

Q5: Methods Unit 1.

Q6: Two turning points at x < 0 so only one viable option. Very obvious.

Q7: Something that requires intelligence at last.

Q8: Simple binomial with button pushing.

Q9: Advantages Specialist students. Nevertheless simple if you choose f(x) = 5/4 without loss of generality.

Q10: Trivial if you test each option.

Q11: Trivial if you simplify to Pr(X < 259) < Pr(Z < 1.5) and solve (259 – 250)/sd = 259. Can also easily be done without intelligence using Mathematica and one line of generic code.

Q12: Wordy but simple Methods Unit 2.

Q13: Simple to narrow it down to E using only the translation.

Q14: Trivial using Mathematica.

Q15: Trivial to get the equation of each line, apply the definition and press some buttons.

Q16: Simple Methods Unit 1 max-min problem.

Q17: Tricky but obvious if you draw a graph of y = f(x). Nice.

Q18: Simple Methods Unit 1.

Q19: A bit tricky. The graph is irrelevant.

Q20: Tricky but obvious if you see f(x) = 1 is required. Nice.

So the way I see it, Section A can easily be finished in 30 minutes and there should only be three questions that cause a reasonable student any difficulty (Q17, Q19, Q20).

Verdict: Benign.

I haven't checked carefully for errors.

Thanks, John. I mostly agree with you on the MCQ, although I think you might be underestimating the trickiness of some questions: the fact that there’s an easy method doesn’t mean that it’s necessarily quick or easy to find the easy method. I also found more irritants than you, but of course it’s my hobby to be irritated. I’ll post my thoughts shortly.

Re: Q20: * Period = 1 not f(x) = 1. (Must have been tired that night).

I was wondering about that although, coincidentally, f(x) =1 is relevant.

Are you sure the period is 1?

No, the period *might* be 1/2 or 1/3 or … (in fact, anything of the form 1/n where n is a positive integer). But 1/1 is the simplest possible period that gets an answer.

Yes, but …

The period must be an integer… as f(x)=f(x+h) and h is an integer…

No, I think JF is correct.

True… I didn’t look at the question again, was going from memory.

It has to be 1/n where n E Z+

h = 1: If the period is 1/2 then 2 periods will take you from f(x) to f(x+1). If the period is 1/3 then 3 periods will take you to f(x+1) etc.

h = 2: If the period is 1/2 then 4 periods will take you from f(x) to f(x+2). If the period is 1/3 then 6 periods will take you to f(x+2) etc.

h = etc.

Since there doesn’t seem to be any err love for this exam, I suppose I’ll start by saying that greater presence of explicit CAS questions (i.e questions that asked for a numerical question) was a bit unusual. I believe it could be to compensate for the probability section which is primarily CAS-active but it leads to the magic question of “did using a particular CAS, i.e Mathematica over a TI-nspire help students?”. Maybe its my inexperience with the TI-nspire since I tried using one to do this years exam with both calculators, but for various parts of SA (Q1e-f, Q2c, Q4, Q5a-e) there felt like a lot of CAS was in play. I did have a listen to the radio and it really just seems like a mishmash of “the format was unexpected” among other not so specific comments. Maybe anyone who has more expertise with these calculators can chime in.

Hmpph. This whole friggin *year* was unexpected but we all just had to suck it up.

This mishmash of “the format was unexpected”. Cry me a friggin river. Didn’t they see the Cover pages and Amended Formula Sheet? If they didn’t, then all the mewling needs to be directed elsewhere, NOT at the exam and its so-called “unexpected format”. And maybe some tough questions need to be aimed in the same direction …

Thanks, Sai. I assume you mean Section B. Yes, it seemed to be swimming in CAS. Of course many students will do plenty of computations with CAS even if they can readily be done by hand. But there were lots of questions in Section B, like (most of) the questions you note, that can only be reasonably done with CAS.

One thing I will say as someone who teaches at a TI school but uses Wolfram products for my computational needs (including playing around with ideas for SACs…) – a computer keyboard and interface (be it Mathematica or the TI emulator) is ALWAYS easier to use than the hand-held.

The new TI calculators (the blue ones that have a new file format, so are pretty much incompatible with the older black model, including rendering the old docking stations useless except as charging stations…) have more memory and are a bit quicker to process things, but all the shortcomings relative to a larger screen device (computer) remain.

Indeed. Far too quiet. No-one even nibbled the (unintended) bait at Q13. Simple to narrow it down to the WRONG answer of E using only the translation.

Simpler to narrow it down to the correct answer (of A) by starting with x = 2x’ + 4. No knowledge of transformations required. Trivial with Mathematica.

A pointless question foisted on students because of the pointless inclusion of transformation matrices.

(Stupid in fact because:

1) matrices are not on the course and yet they are required.

2) it’s another disconnected piece of mathematics welded onto the course).

Yes, it’s an awful question, worse than usual.

Re Q7:

Intelligence should one try, or to the CAS (Mathematica and the TI-nspire can just evaluate this as is).

On the other questions, Q19 is a good question, although the graph is pointless as you said. Q17 in my opinion is just another optimisation problem the same way Q16, and one could use the fMax function (TI-nspire) or the Maximize function (Mathematica) to hammer the question without further thought. Of course, getting there could be a step of its own…

I also had a look at a walk through of the extended response solutions courtesy of a friendly neighborhood Worm and had seen that the CASIO classpad does not capture all the solutions for an inequality (Q5dii). Now, one may argue that you could (and should) use the previous results to determine that the casio classpad was not functioning properly (in my opinion) whereas both the TI-nspire and Mathematica will return the complete inequality…. While any student would sketch a graph of this, they would have to go to the graph menu, type in the graph along with the two lines… all for one mark. From what I can see as well, it has no implication on the following questions either.

The topic of matrices in the context of transformations annoys me a lot, since those questions feel disconnected from the other topics. Linear algebra is such an interesting topic, and the watering down of it into transformations of functions is a real injustice to the field. I would also say Further does similar things with topics such as least squares (a good use of motivating inner products) but of course all of it is button mashing.

Sorry… LOL I missed your comment proceeding mine!

That Worm guys seems like a jerk! 😉

Thanks, Sai. Quick replies:

I would assume Q7 is quicker by brain than CAS.

Re Q19, it’s true the graph is redundant, but I assume that is the examiners being nice, and I’m fine with it. The question is sufficiently unusual that the graph could help orient students.

Q17 is strange. I *think* I like it, just as John Friend indicated he did, but I’m not sure. I’ll indicate the nature of the problem when I update the post, so people can comment.

I’ll think about your Section B comments once I’ve worked through it. As for transformations in VCE, it’s way beyond/beneath “injustice to the field”.

Hi, Sai. I’m still digesting QB5. Do you have any sense of why the Casio screws up (d)(ii)? I didn’t test any machines, but the question doesn’t look like it’d cause such trouble.

Q.19 I think the graph was to possibly spark symmetry in the heads of students?

ER Q5dii… solving the inequality…

TI inspire gives the correct intervals… CASIO Classpad is missing one of the intervals…

How can they have this on the exam? Surely it should be tested beforehand… 98% of students using a CASIO will not pick up on this given the previous question… Very unfair… and how will it be marked?

There are on-going issues with the non-level playing field of technology.

VCAA has gives assurances that all exam questions are tested with all three CAS calculators (the TI-Insipid, the Crapio, and the Spewlett Hackard) for ‘equity’. This is obvious bullshit (https://atarnotes.com/forum/index.php?topic=34681.0) and your comment is the latest evidence. Furthermore, Mathematica leaves the calculators for dead (https://mathematicalcrap.com/2020/07/16/guest-post-mathematica-and-the-potential-gaming-of-vce/), but VCAA does not care (for obvious reasons – it wants Mathematica Methods not Mathematical Methods).

Imagine getting those teachers who already can’t teach methods or spesh, to then learn mathematica! They shy away from the basics of a CAS calculator… and would never consider writing a small program….

Some schools have a mini orgasm when they find out that you can use both the TI Inspire… and CASIO and…. mathematica…

I figure that if they force it on you, you may as well become competent in it!

I would love to have a two hour exam on both that was harder, but they have more time to work on the paper…

I dont know if you guys know of a student called Alex Gunning? He got a perfect score in Mathematics in the international olympiad, yet he could never finish a paper in specialist or methods… and got about ~40 in both subjects….

He’s currently studying mathematics (Masters) at Trinity College, Cambridge. Probably because of his Olympiad success, no thanks to the VCAA exams.

More proof of how stupid the VCAA exams really are (although getting 40’s in Methods and Specialist indicates something, I suppose). Answering a bunch of questions within *unrealistic* time constraints is just plain dumb. But *apparently* the exams are subjected to a blind review, which among other things is meant to check that the exam is of an appropriate length for a reasonable student. Either more bullshit from VCAA or the blind reviewer gets ignored. It’s my experience (given the number of errors in the exams each year) that the VCAA vettors have been asleep at the wheel for many years.

What I’d like is the VCAA exam writers, vettors and DuLL to all sit one of *my* exams under normal examination conditions.

The Methods exams were not overly-difficult, the format was not the big surprise many are alleging, and there were no questions outside the scope of the Adjusted 2020 Study Design. But Exam 1 was undoubtedly too long (by my estimate, about 6 marks = 10 minutes more time was needed) – I blame the VCAA vettors.

I haven’t worked through Exam 2 Section B but I think Section A could easily be done within 30 minutes by a reasonable student (therefore not too long).

I completely agree…

There was a new head of the panel in Methods this year… I would suggest that they probably thought they knew best…

So you mean a ‘knew head’ …

A tough year to be new (whether it be teacher, HoD or exam setting panel), although I’m sure work had started on the 2020 exam before the pandemic struck. If exam 1 had been shorter (by deleting a couple of the 1 mark questions and distributing those marks to other questions), I’d say that the ‘knew head’ had done pretty well.

https://www.heraldsun.com.au/news/victoria/answers-just-didnt-add-up-on-year-12-maths-methods-exam/news-story/fcdf73d3cb1f17e82978573a6208b116?sv=644530f908f30c274e59b2ec6adaf9af

Thanks, John. I haven’t yet worked through the comments on this post, and the article is weirdly vague, but I gather this is the issue Worm raised? I’ll post the link above as well.

The newspaper report is related (I remember this – there was a big uproar). The report was evidence that that VCAA aren’t doing the technology checks it claims to be doing – the Crapio seems to fall short relative to the TI-nsipid on some VCAA exam questions. Worm has raised ER Q5dii from the 2020 exam – it adds to this evidence.

And we certainly know that VCAA have no clue (or don’t care) about the huge advantage Mathematica-using students have relative to CAS-calculator using students.

Ah, I see. Stupid me, and I’ve corrected the update. I’ll check out the 2020 issue, and the whole exam, in the next day or so.

Hi, Worm. Same question as for Sai: do you have any sense of why Casio screws up 5(d)(ii)?

Hey Marty,

I’m pretty sure it’s just the algorithms and accuracy of the iterative methods in the CAS…

It may only go to 1 or 2 decimal places which isn’t sufficient in this case.

After using the TI-Inspire and CASIO, it’s clear that generally the algorithms handling inequalities on the CASIO are far inferior to those on the TI…

I knew this when doing the exam, hence, I knew there was every chance that it would give the wrong solutions…

Geez. Next question: how is it possible, if at all, for the VCAA to not catch this? If they claim that they checked the question on all three standard paltforms, would that claim be a provable lie?

Question 4eiii

For the TI-nspire CX CAS when equating areas and solving for n without inserting a domain the calculator returns 1.087 to 3 decimal places, but when inserting the domain 1<n<3, it returns 1.088. Will both answers be accepted?

Who knows. VCAA probably tossed a coin last Sunday (assessor training day). It seems to be how it does most things.

Ryan, what happens if you set the TI to return, say, five or six decimal places? To how many places do the two answers (with or without domain) agree?

Re: Q5 part e.

The values of a are found from the equation .

We’re told in the preamble to part (a) that so it would follow that .

But the positive solution for makes no sense in the context of the graph given in the preamble to part (e) … Is it my imagination or are we meant to now *assume* that for part (e)?

And here's a question about part (f):

Does the word "Find" mean that an answer with some working is required? As opposed to "State", where clearly only an answer is wanted? So will a student who simply writes w < 0 (maybe as a hopeful guess) get the 1 mark or is some working required to justify this answer. We know VCAA says

"In questions where more than 1 mark is available, appropriate working must be shown."

But does this mean that NO working is required in a question worth 1 mark where students are asked to "Find" …?

In a 1 mark question, is there a difference between "State" and "Find" in terms of what VCAA expects??

And if anyone would like to opine on Q5 part (h) …

My interpretation (and that of some others) is that the tangent at x = t is parallel to the tangent at x = -t and therefore there *can* be vertical translation of p.

However, I’ve seen arguments for the interpretation that the tangent at t cuts the x-axis at -t and therefore there *cannot* be vertical translation of p.

I’m curious what others think and if the question might be ambiguous.

And … it’s a 1 mark “State …” rather than a 1 mark “Find …” question. I’m still curious whether others think VCAA might attach a different meaning to each word (in the way discussed in my previous comment). (If VCAA does, my blood will boil).

Not sufficiently drunk for (h) just yet …

OK, drunk enough now. John, I don’t think the question is ambiguous, and that clearly vertical translations will also work. Part (e) is maybe leading people to look at the question in the other way, but I think (h) is worded clearly, give or take the ridiculous matrix formulation.

Yes, I thought the same.

It will be very interesting to see the MAV solutions for this exam. Since 2019 all MAV exam solutions have been written through the cracked VCAA lens of an assessor – I have found their clarity and mathematical rigour very poor (based on last years solutions I wouldn’t use them if you paid me to). It’s an interesting insight into the mind of VCAA.

On the topic of written solutions – I thought some of the free solutions currently available were not nearly as good as they’ve been in the past. I’ve found errors and a very noticeable lack of clarity this year (particularly for some of the MCQ and many of the 1 mark questions in Part B). I find this very interesting because if the people who write these solutions are struggling to present clear and accurate solutions, I can only wonder what the solutions written by the exam candidates look like. Maybe that’s why some of these parts are only worth 1 mark – too hard to explain and justify answers …?

Which brings me back to how very interesting it will be to see the MAV solutions for this exam.

I’m still pondering on whether VCAA sees a difference in the meanings of “Find” and “State” in 1 mark questions … Does “State” mean an answer requires no justification but “Find” means a justification is required? If there’s no difference, why are two different words used to mean the same thing??

Because as we have seen countless times, VCAA likes to give its own special meaning to words … Can anyone shed any light on whether VCAA might or might not attach a different special meaning to ‘Find’ versus ‘State’ in a 1 mark question?

Thanks, JF. I don’t see the graph as misleading for part (e). Perhaps graphing the case where subliminally suggests this is to be assumed or concluded, but I don’t know what one can do about it.

I assume your other query is about (g)? Yeah, the word “find” for that 1-marker made no sense to me. Even ignoring the single mark, I haven’t convinced myself there’s an easy way to see always works, other than by traditional Methods logic: “It’s a 1-marker, and so …”.