Secret 2021 Methods Business: Exam 1 Discussion

November 3, 2021

11:18 am

89 Comments on Secret 2021 Methods Business: Exam 1 Discussion

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.

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UPDATE (22/04/22)

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.

UPDATE (22/04/22)

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?

UPDATE (20/04/22)

The exam report is now available, here.

UPDATE (24/11/21)

The exam is now available, here.

UPDATE (09/11/21)

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 $\boldsymbol{y = -\frac{x}{\sqrt3} + \frac2{\sqrt3}}$ is tangent to the circle $\boldsymbol{x^2 + y^2 = 1}$ . 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.

Yes …

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.

89 Replies to “Secret 2021 Methods Business: Exam 1 Discussion”

John Friend says:

November 3, 2021 at 11:49 am

Well, since giving thoughts is free, here are some quick ones ….

Questions 1 – 8: Benign.
But the eyes of some students will $\displaystyle glaze$ over at Question 6(b).
The more convenient choices in Q8(b) were to test the sign of $\displaystyle odd$ values of x on either side of 3.

Question 9:
(a) Unfair. Very unfair. Through its Examination Reports, VCAA have told students for many years to “show” something by finding it. There are numerous examples from Examination Reports where students were penalised for substituting the given result to get a desirable conclusion. And yet here we have a question where the only straight-forward way of answering it (it’s worth 2 marks, not 4 marks …) is to substitute the given equation into $\displaystyle x^2 + y^2 = 1$ and then find there’s only 1 intersection point (at $x = \frac{1}{2}$ ).

Otherwise (for 2 marks) students might to do the following (boneheaded calculation):

$\displaystyle m = \frac{dy}{dx} = -\frac{x}{\sqrt{1 - x^2}}$ …. 1 mark

Let $x = b$ at P. Then:

$\displaystyle m = -\frac{b}{\sqrt{1 - b^2}}$ …. (1)

$\displaystyle m = -\frac{\sqrt{1 - b^2}{(2 - b)}}$ …. (2) (gradient joining the points A and P)

Solve equations (1) and (2) simultaneously:

$\displaystyle -{\frac{b}{\sqrt{1 - b^2}} = -\frac{\sqrt{1 - b^2}}{2 - b}$ …. 1 mark

$\displaystyle \Rightarrow b(2 - b) = 1 - b^2$

$\displaystyle \Rightarrow b = \frac{1}{2}$ …. 1 mark

$\displaystyle b = \frac{1}{2} \Rightarrow m = -\frac{1}{\sqrt{3}}$ …. 1 mark

$\displaystyle y - y_{1} = m(x - x_{1})$

$\displaystyle \Rightarrow y - 0 = -\frac{1}{\sqrt{3}} (x - 2)$ …. 1 mark

$\displaystyle \Rightarrow y = -\frac{x}{\sqrt{3}} + \frac{2}{\sqrt{3}}$ .

And there aren’t even enough writing lines for “Showing” in this way!!
This change-of-heart by VCAA is very unfair and dishonest in the face of past advice given by VCAA through its Examination reports. Then again, I suppose students could simply use the right-triangle AOP to get the angle at A and then take the tan of the angle to get the gradient … (That would have saved on latex code!!) OK, I take it all back! Nice “Show” question, VCAA. Good “Show” question, VCAA. Now sit!

(b)(i) Nice understanding of the effect of a vertical dilation on a line is required. But 1 mark …? Sheesh. It’s easily worth 2 marks:

$\displaystyle y = -\frac{q}{\sqrt{3}} x + \frac{2q}{\sqrt{3}}$ …. 1/2 mark

Required inequalities for the gradient:

$\displaystyle \frac{1}{\sqrt{3}} \leq -\frac{q}{\sqrt{3}} \leq -\frac{1}{\sqrt3}}$ …. 1 mark

$\displaystyle -1 \leq q \leq 1$ 1/2 mark

(b)(ii) Seriously …? Only 1 mark?

Required inequalities for the gradient (the left inequality is worth 1 mark all by itself):

$\displaystyle -\frac{1}{2} \leq -\frac{q}{\sqrt{3}} < -\frac{1}{\sqrt{3}}$ 1 mark

(gradient OP)(-1/Sqrt[3]) = -1
=> gradient OP = Sqrt[3]
=> tan(theta) = Sqrt[3]
=> theta = Pi/3
=> Max area = sin(Pi/3) = Sqrt[3]/2.

And I wonder how many students who get (c)(i) will say 1 for c(ii) …?

Reply
1. A methods student says:
  
  November 3, 2021 at 12:04 pm
  
  Yep, I said 1 for 9c(ii), I’m so annoyed at myself…
  
  For 9a, I said $\cos\angle POA = \frac{1}{2}$ (using the right-angled triangle) $\implies \angle POA = \frac{\pi}{3}$ to find the coordinates of P, and then used that to calculate the line. Is this right?
  
  Reply
  1. John Friend says:
    
    November 3, 2021 at 12:33 pm
    
    Yep. But note that this blog is not typically to tell students whether their exam answers are right or wrong. So this comment is a one-off freebie.
    
    A free plug to the free solutions at itute: They’ll probably be published in the next 24 hours. Students can do post mortems until their heart is content using them.
    
    Reply
    1. marty says:
      
      November 3, 2021 at 12:35 pm
      
      I have no problem with students asking such questions, although I probably won’t work so hard myself to answer them. Not at least today. If other commenters want to answer or ignore, or something in between, it’s up to them.
      
      Reply
  2. Riley says:
    
    November 3, 2021 at 12:51 pm
    
    Ah same. Annoying, considering the model does work for pi/2>theta>0 but the domain is restricted. Better make sure to read things more carefully tomorrow.
    
    Hopefully marks are awarded for finding the correct derivative in the next part either way.
    
    Reply
2. Damien says:
  
  November 3, 2021 at 12:13 pm
  
  And for 9bi you are missing that 0 must also be excluded as per definition in pre amble to part b.
  
  Reply
  1. John Friend says:
    
    November 3, 2021 at 12:33 pm
    
    Yep, post in haste, repent in leisure.
    
    Reply
  2. MyCool says:
    
    November 3, 2021 at 3:24 pm
    
    I just send Marty a message about this rather than read what was already here (woops!)
    
    Am I missing something, why can’t q be zero? q can be zero. I think it’s great if q is zero! Maybe I’m wrong. I’d love to be convinced that I am.
    
    Reply
  3. MyCool says:
    
    November 3, 2021 at 3:28 pm
    
    Here’s my thinking on the matter:
    
    I thought question 9bi from today’s methods exam might be WITCH worthy. I feel that there is no need to make q non-zero, as this transformation would map the linear line onto the x-axis (which satisfies the condition of the question). I.e. -1<= q <= 1 is a good way to think about the question/transformation, but students will be punished for not remembering VCAAs weird q =/= 0 restriction.
    
    Reply
    1. John (No) Friend (of VCAA) says:
      
      November 3, 2021 at 3:59 pm
      
      Hi MyCool.
      
      I agree with $\displaystyle q = 0$ . But you have to remember that Pedant is VCAA’s middle name. VCAA likes to do things like this, to trip people up to try to make themselves look clever. (It tripped me up, no hard thing to do). Wait for the sanctimonious comment in the Examination Report (some time in 2025).
      
      VCAA is the Frank Burns of Victorian Education – Pedantic, incompetent, sanctimonious, arrogant, “infallible” …
      
      Reply
      1. MyCool says:
        
        November 4, 2021 at 8:07 am
        
        Yep, it tripped me up too…maybe that’s why I’m bitter. I think I quite like the essence of the question, but I feel bad for the kids who have a good grasp on transformations, but won’t get to separate themselves from the pack here because of that silly trap. There aren’t that many opportunities to shine on this paper, hopefully there’s some good opportunities today.
        
        Reply
        
        marty says:
        
        November 4, 2021 at 8:16 am
        
        Good luck today, MC, and everyone. I’ll be interested to hear how you go, and what people think. (I’ll put up a companion Methods 2 post soon after the exam finishes.)
        
        Reply
3. Damien says:
  
  November 3, 2021 at 12:23 pm
  
  Also, do you think they will want a piecewise function for 9ci to properly account for always using the furthest left intercept for p’ as theta goes past pi/3
  Edit: realised restricting to 0<theta<=pi/3 covers all required q values so no piecewise needed
  
  Reply
4. John Friend says:
  
  November 3, 2021 at 12:24 pm
  
  Whoops, I timed out …
  
  (b) (ii) continued:
  
  1 (gradient OP)(-1/Sqrt[3]) = -1
  => gradient OP = Sqrt[3]
  => tan(theta) = Sqrt[3]
  => theta = Pi/3
  => Max area = sin(Pi/3) = Sqrt[3]/2.
  
  I wonder how many students who get (c)(i) will say 1 for c(ii) …?
  
  Reply
5. Simon says:
  
  November 3, 2021 at 5:02 pm
  
  I agree about 6b – it was quite a setup to parse… but once a probability tree diagram was drawn it was straight forward. [I’m out of practice on those sorts of questions – and missed the solution the first time through]
  
  Q9a) I think you’ve gone overboard. Just use the triangle to find the angle and/or slope of the tangent line and go from there. The only fact you need is that the tangent is perpendicular to the radius – and that is given in the diagram for you.
  Q9bi) 1 mark is a bit stingy – but I think they just expected a quick drawing and some thought – no working, so hard to allocate another mark fairly – or maybe not.
  Q9bii) Maybe one mark for setup up and one for answer? But again, it would be a mess to mark…
  Q9c) I’m not sure why ci was worth two marks and bi / bii only one.
  Looking at the teacher facebook group, quite a few teachers said 1 for part ii 🤷🏽‍♀️
  
  Reply
  1. Simon says:
    
    November 3, 2021 at 5:48 pm
    
    Oops – I must have misread or missed your edit. You gave the triangle method for 9a!
    
    Also, you must be using quite a bit of Mathematica recently – the Sqrt[3] notation!
    
    Reply
Glen says:

November 3, 2021 at 11:58 am

I’m out of the loop. What are we commenting on?

Reply
1. Red Five says:
  
  November 3, 2021 at 1:55 pm
  
  send me an email to remind me and I’ll send you scans of the papers.
  
  Methods today and tomorrow, Specialist Friday and Monday.
  
  Reply
  1. Steve R says:
    
    November 3, 2021 at 2:05 pm
    
    RF,
    
    How about sending scans to Marti to upload for non Method Bloggers before itute gets its act together?
    
    Steve R
    
    Reply
    1. marty says:
      
      November 3, 2021 at 2:36 pm
      
      Sorry I don’t want this kind of discussion on the blog. If someone hints a reddit link or whatnot, that’s fine. But I’m enough of a target for VCAA without becoming a file-sharing site.
      
      Reply
      1. Glen says:
        
        November 3, 2021 at 4:30 pm
        
        Alright, I can’t participate in this one then.
        
        Reply
        
        marty says:
        
        November 3, 2021 at 4:42 pm
        
        See the video that Riley posted.
        
        Reply
    2. John (No) Friend (of VCAA) says:
      
      November 3, 2021 at 2:39 pm
      
      Speaking for Marty, unfortunately he can’t do this because of copyright. He can post links but not the exams themselves (not even old pre-VCAA exams). A bit petty of VCAA, I think, given that it would be for educational purposes.
      
      Reply
      1. Steve R says:
        
        November 3, 2021 at 5:05 pm
        
        Guys,
        
        Sorry for potentially causing trouble … I can wait
        
        I hope todays exams were fair and well vetted even if they were uninteresting
        
        Steve R
        
        Reply
        
        marty says:
        
        November 3, 2021 at 5:11 pm
        
        No problem, Steve. It was fine for people to ask.
        
        Reply
        
        John Friend says:
        
        November 3, 2021 at 10:24 pm
        
        Hi Steve.
        
        You haven’t missed much. The allocated marks in Q9 were not what I’d have used, and there were some odd restrictions for no good reason (that I could see). But in fairness to VCAA, the exam was dull, uninteresting and benign. And I mean that in a nice way. ‘Safe’ would be a fair assessment. (But others might see things more noteworthy of discussion than I did)
        
        And yes, I am seeing a doctor tomorrow about the concussion I suffered today just before the exam became available.
        
        Reply
  2. Boarder Soapbox says:
    
    November 3, 2021 at 2:09 pm
    
    What is your email address?
    
    Reply
    1. John Friend says:
      
      November 3, 2021 at 2:41 pm
      
      Email addresses are not shared at these blogs. Some of us know email addresses through other channels.
      
      A tip: No-one should be disclosing an email address in a public domain, even if its a one-use-only address.
      
      I’m certain bootleg copies of the exam will appear in the coming days on the internet. And most teachers who visit here should be able to borrow a copy from their school’s VCE Coordinator. (And some non-teachers will know teachers …)
      
      Reply
Boarder Soapbox says:

November 3, 2021 at 12:09 pm

Was definitely one of the easiest Methods exams for a while; most likely a reaction to the response last year. Much less computation required. The last question did require some thinking but that’s about it.

Reply
Tungsten says:

November 3, 2021 at 12:28 pm

I thought that it was a good exam overall to be honest, question 9 was challenging but nice, although I would have preferred more generous mark allocations there.

Thank goodness VCAA killed the petition (https://www.change.org/studentvoicevic) to change the exam formats, imagine if it had to be rewritten. The whole thing would have been a complete trainwreck.

Reply
1. Lemon says:
  
  November 3, 2021 at 12:51 pm
  
  VCAA killing the petition would imply that they engaged with it. I don’t think anyone ever took it seriously.
  
  Reply
  1. Tungsten says:
    
    November 3, 2021 at 1:02 pm
    
    Actually, the Victorian SRC managed to secure a proper meeting with VCAA and DET in which they successfully lobbied for the recommendation 2, the staggered return to school. Over 5000 signed the petition, it is quite clear that it was and had to be taken seriously.
    
    Reply
    1. Lemon says:
      
      November 3, 2021 at 1:07 pm
      
      Wow – I don’t know if I should be amazed or disappointed. Thanks for the correction.
      
      Reply
2. John Friend says:
  
  November 3, 2021 at 3:21 pm
  
  The “student voice”. Spare me.
  Proposals (1) and (2) were lobbied by several professional organisations (including schools). I don’t think the ‘VicSRC’ gets sole credit for (2) being successful, but I acknowledge that its input wouldn’t have hurt.
  As for proposal (3) …. Spare me. This is the hair-brained sort of thing that triggers the “Spare me” eye-roll.
  
  5,247/(50,000 plus*) is approx 10% of all Yr 12 students sitting exams, at best.
  Yr 11’s sitting a Unit 3&4 subject are not included in the 50,00 plus (but are possible included in the 5,247).
  * https://vcaa.vic.edu.au/news-and-events/latest-news/Pages/VCEExams.aspx
  
  Who vouches for the authenticity of the signatures? Did Yr 11’s sign? How do we know mum and dad didn’t sign too?
  I’m not familiar with this stuff, is 10% (at best) a good result? Something to be taken seriously? Seriously enough for proper meetings with VCAA and DET?
  
  Where’s the VicSRC petition for better quality VCE Mathematics exams?? Would a signature proportion of 10% (at best) secure a proper meeting with VCAA and DET?? I would have thought better quality exams was an important issue for student (and teacher) well-being. Maybe we should all align with the VicSRC and get some real action started.
  
  Reply
  1. Tungsten says:
    
    November 3, 2021 at 3:54 pm
    
    Personally, I feel that the number is an incredibly good result, even considering that many non-students would have signed. Even apart from that, the Victorian SRC is surprisingly influential in lobbying, they are involved with the senior secondary reform and the merging of VCE and VCAL, which they had previously advocated for. This influence is what made the petition so dangerous.
    
    Getting the Victorian SRC onto VCAA’s incompetence would be great, only problem is that they are 80% funded by the Victorian government and usually tend to avoid rocking the boat too harshly. Doubt Marty’s rhetoric would appeal to them.
    
    Reply
    1. marty says:
      
      November 3, 2021 at 3:59 pm
      
      I have zero time for an organisation that avoids rocking boats.
      
      Reply
    2. John (No) Friend (of VCAA) says:
      
      November 3, 2021 at 4:22 pm
      
      Aha. A conflict of interest, due to funding. Well then, it looks like the VicSRC does/(can do) nothing more than lobby for vanilla ice-cream. Rather than being a true agent for meaningful, positive change.
      
      Any change that doesn’t require rocking the boat is either superficial or trivial.
      
      Rhetoric? Marty’s blogs don’t contain rhetoric. Their content is based on cold, hard, incontrovertible facts. These facts are in almost every VCAA exam.
      
      Facts that are no doubt very inconvenient for some people and organisations.
      
      Reply
      1. marty says:
        
        November 3, 2021 at 4:40 pm
        
        Well, to be fair, the blog also contains plenty of rhetoric.
        
        Reply
        
        John Friend says:
        
        November 3, 2021 at 10:28 pm
        
        Yeah, the cold hard facts can really get the blood boiling.
        
        Reply
  2. Anonymous says:
    
    November 3, 2021 at 3:54 pm
    
    “Where’s the VicSRC petition for better quality VCE Mathematics exams??”
    
    Unfortunately it appears most teachers are unaware of the pitiful quality of VCE Mathematics exams, let alone students. In fact, as a student that is doing methods and spesh this year at a reasonably decent private school, the SACs we have done make the VCE exams look like flawless gifts from the heavens. It’s probably better at the top schools in the state (e.g. Scotch, Haileybury, Melbourne Grammar etc.) but it’d probably be much worse at a typical underfunded public school.
    
    Reply
    1. John (No) Friend (of VCAA) says:
      
      November 3, 2021 at 4:26 pm
      
      “Unfortunately it appears most teachers are unaware of the pitiful quality of VCE Mathematics exams,”
      
      Yes, and that’s nearly the whole problem. Add apathy and the problem is complete. As well as the fact that some of those teachers end up writing and vetting VCAA exams.
      
      Reply
3. marty says:
  
  November 3, 2021 at 3:43 pm
  
  Huh! why doesn’t anybody ever tell me anything? I didn’t know anything about this.
  
  Of course VCAA has been a Morrisonian screw-up, but I agree with John: (3) was a pretty stupid idea.
  
  Reply
Riley says:

November 3, 2021 at 1:34 pm

From a methods student..

Q1 – Just standard differentiation stuff, comparatively easy to other years’ Q1

Q2 – Simple antidifferentiation, again pretty easy but I feel it clashes with later question

Q3 – Pet peeve, let ‘find the range and period of g(x)’ be one question like it usually is in exam 2. Interesting that they made us find general solutions instead of a restricted domain, imagine this would trip people up.

Q4 – Fine again, just graphing. I imagine b will confuse some people as y2 but they will only solve y>=3 and leave it as x>=1… Like myself…

Q5 – a is easy, surprised they didn’t use a matrix for b

Q6 – a&c are fine, b is interesting and I think it would trip some people, despite it not being too hard, by merit of g not fitting directly into the conditional probability formula.

Q7 – Easy integration, definitely worth only one and two marks.

Q8 – A was probably the worst question in my opinion. Not difficult but the fractions demand more time than they’re worth. What’s more is this question tests the same concept as Q2, except for the antidifferentiation of the square root. B is nice though, maybe not worth 2 marks though. In my opinion, replace Q2.

Q9 – Definitely the ‘hard’ question of the exam. A was nice, finding the angle then gradient requires knowledge of trig and perpendicular lines. Spesh people might fall into a trap, trying to use inappropriate strategies. Bi is nice too, though one mark is a bit cruel it can be solved just from looking at the graph. Bii should absolutely be two marks, as it requires a bit of working to find sqrt(3)/2. Ci, triangles are God. Restricting q is the hardest part of this question as many students may simply fail to consider it (For transparency – I did.). Cii is pretty fine, not having any local maximum sit in the domain is interesting but anyone who got this far would be able to notice the area is increasing for the domain and will solve for the correct value.

Overall, pretty standard in my opinion.

Reply
1. Simon says:
  
  November 3, 2021 at 10:41 pm
  
  Hi Riley – you gave a really good breakdown of the questions!
  
  I especially like the observation that Q8a and Q2 test the same knowledge and Q2 could have been better used testing a different skill.
  
  Reply
2. Glen says:
  
  November 5, 2021 at 10:07 pm
  
  Not sure if Q6 is awful, but it didn’t sit well with me. Especially part (b).
  
  Reply
marty says:

November 3, 2021 at 2:59 pm

No public sharing of emails!

Reply
marty says:

November 3, 2021 at 3:02 pm

I’m sorry for you guys that don’t have access to the exams. It’s idiotic, since there’s no reason for the paper to be public within 24 hours of the exam. But I’m not going to be the sharing guy.

Sooner or later, here or elsewhere, someone will post a social media link of some type.

Reply
1. Riley says:
  
  November 3, 2021 at 3:35 pm
  
  Not sure if this was the invitation to share a link but here, if it’s inappropriate I apologise and feel free to delete it.
  
  It’s tied to a video, not ideal but it’s all I could find.
  
  ALSO some of the dude’s solutions are wrong in the video so beware.
  
  Reply
  1. marty says:
    
    November 3, 2021 at 3:48 pm
    
    Yep, Riley, it was an invitation, and thanks very much. I also wouldn’t be too harsh on the guy: it was obviously designed to get rough solutions out as quickly as possible, and the video is labelled as such.
    
    Reply
    1. Riley says:
      
      November 3, 2021 at 4:22 pm
      
      Of course, and they corrected their errors in the captions so their video is greatly helpful.
      
      Reply
    2. John (No) Friend (of VCAA) says:
      
      November 3, 2021 at 4:28 pm
      
      More importantly, it gets the exam out as quickly as possible!!
      
      Reply
    3. Worm says:
      
      November 5, 2021 at 8:52 am
      
      Haha… Marty your interpretation was correct…
      
      28 mins to get it done and explain it a bit… Thought it was likely that I fucked stuff up! I hadn’t even glossed over it… Just jumped straight into it… I have created an updated video for future students.
      
      I have approval from VCAA to post the worked solutions… (After I received an angry phone call from he who shall not be named a few years ago 🙂 ) and I was trying to get them out for people to see the paper. I like to help students understand what VCAA wants… not what is always the correct thinking and/or correct answer!
      
      Reply
      1. marty says:
        
        November 5, 2021 at 9:04 am
        
        Thanks, Worm (and watch your language, please). I and plenty of others appreciate your hot takes. Feel free to link videos to the other exams, if you do them.
        
        Reply
        
        Worm says:
        
        November 5, 2021 at 9:25 am
        
        Will do…
        
        Reply
      2. John Friend says:
        
        November 5, 2021 at 3:43 pm
        
        I’m very curious about the VCAA approval – did it come from the Acting Mathematics Manager or from higher up? Email or phone?
        
        Reply
2. John (No) Friend (of VCAA) says:
  
  November 3, 2021 at 3:44 pm
  
  Apparently, and I’m only reporting what VCAA said, the exams don’t get published until after ‘Legal’ has signed off on them. Copyright issues etc. The sorts of things I would have thought had been sorted out $\displaystyle before$ students sat the exam (except for English Exams: https://www.smh.com.au/education/sloppy-copy-in-exam-raises-ire-20111109-1n7eo.html#:~:text=By%20Jewel%20Topsfield&text=THE%20VCE%20exam%20body%20has,acknowledging%20she%20was%20the%20author)
  
  But apparently not and apparently it takes months.
  As Robert Ripley said about VCAA’s explanations, “Believe It or Not!”.
  
  Maybe VCAA should hire NESA’s legal team – the NSW HSC exams get published within days of students sitting them. And the $\displaystyle Marking$ $\displaystyle Scheme$ shortly after. Believe It or Not!
  
  Reply
  1. Simon says:
    
    November 3, 2021 at 5:22 pm
    
    And the NESA (like most examining bodies around the world) publish a *marking scheme* as well as *marking feedback*, not just a *examiners report*. See eg https://educationstandards.nsw.edu.au/wps/portal/nesa/resource-finder/hsc-exam-papers/2020/mathematics-extension-1-2020-hsc-exam-pack
    
    Reply
marty says:

November 3, 2021 at 3:50 pm

Thanks very much to everyone who has commented. I’m not looking at the exam today, but will try to go through it reasonably thoroughly tomorrow.

Reply
1. Worm says:
  
  November 5, 2021 at 4:05 pm
  
  Actually. Neither of them… VCAA…
  
  Had nothing to do with the Head of Mathematics… that was who the original phone call came from to tell me to remove them unless I get approval.
  
  I emailed someone at VCAA who gives you the ok to use them. I couldn’t tell you her name?
  
  Reply
  1. steve r says:
    
    November 5, 2021 at 4:48 pm
    
    Worm,
    
    From one of those who don’t have direct access to the papers… many thanks for sharing your thoughts “legally”
    
    I liked your method of directly writing on the paper and thinking aloud on how best to use the Casio
    
    Steve R
    
    Reply
  2. John (No) Friend (of VCAA) says:
    
    November 5, 2021 at 10:31 pm
    
    By Acting Mathematics Manager I meant the person currently acting as the Mathematics Manager at VCAA, not a school head of maths. I like to keep a score card of who does what at VCAA, but it’s no biggie.
    
    Reply
    1. Worm says:
      
      November 6, 2021 at 6:45 am
      
      Yes that’s who I was referring to… I meant mathematics manager… head of maths at VCAA…
      
      I don’t work in a school.
      
      Reply
      1. John (No) Friend (of VCAA) says:
        
        November 6, 2021 at 11:30 am
        
        I see. How typical and unsurprising. No doubt some favour currying goon referred your Youtube to him. Good riddance to him, hopefully a new broom sweeps clean and can earn back the trust that has been totally lost over many years.
        
        @Marty: I’ve really bitten my tongue in this comment.
        
        Reply
marty says:

November 9, 2021 at 10:35 am

Thanks again to everyone who has commented. It was very interesting to follow, and it made my job much easier.

I know everybody has moved on to pondering Specialist, or to getting drunk, or whatever, but I’ve posted my thoughts above. In the normal scheme of things, Q9 would definitely be a WitCH, but commenters have already hammered the question sufficiently hard. On to Specialist 1 …

Reply
John (No) Friend (of VCAA) says:

April 22, 2022 at 7:36 pm

Re: Update 22/04/2022.

Not just an error but an extremely conspicuous error (in the comment on Question 1(b) – the answer was given as $\displaystyle \frac{1}{4 x^4} + \frac{1}{x^2}$ ). This is what happens when the publication of a Report is rushed (published after only 5 months), no-one has enough time to vet it properly.
I heard from a reliable source that it was a clerical error that occurred in the final version of the report. Apparently a VCAA clerk writes the final report, which explains a lot.
I saw that that the error was fixed today and acknowledged in the usual way.

Reply
1. John Friend says:
  
  September 30, 2022 at 4:15 pm
  
  And amended 22 April 2022.
  
  So VCAA can fix errors in a timely manner – when the error is so obvious that it’s an embarrassment that cannot be evaded. Copies of the original report would be quite valuable, except anyone can reconstruct the original report using the word file (*).
  
  * The word files are not VCAA’s fault. In fact, the State Govt apparently requires all Govt departments to provide documents in the public domain in word format. So the idiocy (as is usually the case) lies with Govt bureaucracy.
  
  Reply
  1. marty says:
    
    September 30, 2022 at 5:41 pm
    
    Thanks, John. I’ll update the Methods error list. Also, I don’t care which idiot is responsible for the Word files. As long as organisations such as VCAA and ACARA publish Word documents, I’ll announce the idiocy.
    
    Reply
John (No) Friend (of VCAA) says:

April 23, 2022 at 9:29 am

Re: 22/02/22 update on Question 5 Part (a).

“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”

Marty, I totally agree. It is deplorable. VCAA, you are a total disgrace and deserve to be hammered with the full force of every mathematics teacher in Victoria (but how many will overcome their apathy/fear/toadying to do so?)

I am very surprised that my suggested proof was not mentioned in the Report. A missed opportunity by VCAA to gloat and pontificate about how you must not use the given result to “show”.

I understand $\displaystyle why$ VCAA uses show questions – it gives students access to later parts of a question if the result is needed. BUT VCAA’s use of the word show is appalling. Given that such a question has at least two intents:
1) To give students access to later parts of a question that require the result, and
2) To see if students could get the answer had it not been given (this intent is implicit)

is it really too hard to use wording such as:
“By calculating the equation of the line passing through points A and P, show that its equation is …”

I decided long ago that my advice to students for answering a “Show …” question is to mentally change it into a “Find …” question. And then, once the (hopefully correct) answer was found, to sign off with “Which was to be shown.”

Joseph de Maistre said that “Every nation gets the government it deserves.” I’ll paraphrase de Maistre and say that as a group, teachers gets the VCAA it deserves. It’s way past time that teachers actively demand better, because we certainly deserve a much, much better VCAA.

Reply
1. John (No) Friend (of VCAA) says:
  
  April 23, 2022 at 9:37 am
  
  And now that a major impediment to having a better VCAA is gone, and as a consequence VCAA will undoubtedly embark on a ‘good will tour’, there will never be a better time to demand better and be listened to.
  
  Reply
  1. marty says:
    
    April 23, 2022 at 11:00 am
    
    Well, that is a very good question. As the new Curriculum Manager, Michael MacNeill has an opportunity to change the culture of VCE Mathematics, or at least to attempt to change it. Will he do so? I cannot see any good reason to believe he will, but I’ll wait to see what he does before hammering him.
    
    Reply
2. marty says:
  
  April 23, 2022 at 10:52 am
  
  Thanks, John. I have decided that this “show that” perversion is much worse that I had initially considered. I will try to post just on this issue very soon.
  
  Reply
SRK says:

April 23, 2022 at 11:12 am

Notwithstanding the other justified complaints, I commend the examiners report for including the second derivative test as a suggested solution to 8b. This should finally clarify this issue to teachers / students.

Reply
1. marty says:
  
  April 23, 2022 at 11:13 am
  
  Ah, yes. Thanks, SRK. I noted that to myself but then forgot to note it above. I’ll add it now.
  
  Reply
2. John (No) Friend (of VCAA) says:
  
  April 23, 2022 at 1:40 pm
  
  Let’s not be too quick and generous with our commendations ….
  $\displaystyle Some$ teachers probably needed the security of a clarification that content outside the scope of the course can be used (when the question does not prescribe a method).
  
  HOWEVER, the fact is that the second derivative test is NOT part of the Maths Methods curriculum … With this in mind, the Report does not state whether students who made a mistake using this test (eg. drew the wrong conclusion from the value of f”(x)) received zero marks (*) or received a method mark.
  
  * For making a mistake in the usage of content outside the scope of the course – I have a vague memory of VCAA stating this somewhere.
  
  The statement
  
  “Those who tried a second derivative approach met with mixed success.”
  
  sheds no light on this. To me, the Report has muddied the waters (rather than provided clarification) by not clarifying this.
  
  And it is, of course, absurd that the double derivative test is NOT part of the Maths Methods syllabus (according to both old and new Stupid Designs). Which raises the question – does the sanctioning in the Examination Report of something not in the Stupid Design make it (an implicit part) part of the Stupid Design and therefore something that must/should be taught …??
  
  Reply
  1. marty says:
    
    April 23, 2022 at 1:47 pm
    
    That’s too conspiratorial. The clear implication is that SDT is permitted.
    
    Reply
    1. John (No) Friend (of VCAA) says:
      
      April 23, 2022 at 2:34 pm
      
      I’m unconvinced. What happens in 4 years time when half the Maths Methods teachers are new, the exam writers are new etc. The 2021 Report will be long forgotten.
      
      It’s not stated in the Stupid Design. So what happens if it’s used incorrectly in the future (or even in 2021 …) – partial credit (because an examination report sanctioned its use) or no credit (because its outside of the Maths Methods part of the Stupid Design).
      
      The simple fact is that the SDT, and plenty of other things (*), should have been explicitly stated in the new Stupid Design. But that was far too sensible a thing for VCAA to do. Instead, we get a Stupid Design with STD.
      
      * This is part of a much broader and very troubling problem – there is a Stupid Design and then there is random stuff scattered throughout decades of exams and Examination Reports (and secret marking schemes) and therefore ‘sanctioned’ as part of the course. But there’s no central repository (which should be the Stupid Design) of this random stuff.
      
      Reply
      1. marty says:
        
        April 23, 2022 at 2:40 pm
        
        Ugh! Tone it down. John, you don’t always have to have the volume at eleven.
        
        I’m not defending the new (or old) study design. But there will always be edges of a curriculum, where stated topics and techniques end, but where natural extensions will often be taught to some extent by some teachers. Then, how the curriculum managers deal with that can be tricky.
        
        Should there be a clear statement from VCAA that SDT is permitted? Yes, of course. But don’t blame the exam report for being something it isn’t. The report implies clearly enough that SDT was considered an acceptable technique on Q8.
        
        Reply
        
        John (No) Friend (of VCAA) says:
        
        April 23, 2022 at 3:09 pm
        
        for the 2021 Exam 1 …
        
        “but where natural extensions will often be taught to some extent by some teachers. Then, how the curriculum managers deal with that can be tricky.”
        
        No, Marty. It’s not tricky. It’s very simple.
        The advice I’d offer the new Mathematics Manager is to create a link to a repository of these “natural extensions”. It would:
        1) be called the Stupid Design Supplement.
        2) be updated each year with relevant curriculum and assessment content arising from the Examination Reports.
        3) include assessment advice such as:
        a) when an equation of a line is asked for, unless otherwise stated the equation should be given in the form y = mx + c.
        b) answers involving a fraction must be given in a form where the numerator and denominator are co-prime integers.
        c) Formal VCAA definitions of “Show”, “Rule” and other terms.
        d) *
        etc.
        
        Even the best curriculum document in the world, let alone the miserable piece of chicken vomit VCAA give us, would benefit from such a supplement. Then we all know where we stand by the middle of each year – teachers, students, exam writers, trial exam writers.
        This is not rocket science.
        (btw I’m not even close to 11).
        
        * VCAA might even feel obliged to remark – wrongly – that conjectures based on pictures, graphs etc. are considered acceptable as answers.
        
        Reply
        
        marty says:
        
        April 23, 2022 at 3:11 pm
        
        John, the fact that you have a twelve, and probably a thirteen, doesn’t imply that you’re not close to eleven.
        
        Reply
        
        marty says:
        
        April 23, 2022 at 3:24 pm
        
        If Michael does nothing that would be a dramatic improvement over the previous manager doing anything.
        
        Reply
        
        John (No) Friend (of VCAA) says:
        
        April 23, 2022 at 3:44 pm
        
        I wonder how the school passes its Specialist Maths SAC audits?
        
        As Marty said:
        “As the new Curriculum Manager, Michael MacNeill has an opportunity to change the culture of VCE Mathematics, or at least to attempt to change it. Will he do so? I cannot see any good reason to believe he will, but I’ll wait to see what he does before hammering him.”
        
        I think Marty expresses the view many of us have. Time will tell.
        
        Reply
        
        Red Five says:
        
        April 25, 2022 at 11:28 am
        
        Remember, JF, not all audits are equal…
        
        Reply
        
        Red Five says:
        
        April 25, 2022 at 12:31 pm
        
        “…a one hour test every 4 weeks or so…”
        
        How on earth (or Mars) does that meet the requirements of a SAC in ANY WAY?
        
        One wonders (out loud, but anonymously…) if a tip-off to VCAA would trigger anything here.
        
        Reply
        
        marty says:
        
        April 25, 2022 at 12:40 pm
        
        Of course the whole SAC system is evil and insane. But, talking generally, why do I care if a school does this? Who gets hurt? If the argument is that such a school is somehow luckily or unfairly avoiding audits, I understand the objection and/or jealousy. But other than that, why would anyone care?
        
        If there is no other reason then the real objection appears to be not that some school avoids some garbage, but that other schools do not or cannot. In which case, people should be hammering the assholes and idiots responsible for the garbage, not the fortunate school.
        
        Reply
        
        John (No) Friend (of VCAA) says:
        
        April 25, 2022 at 5:39 pm
        
        Moving completely off-topic, people should care if the Mayor of a local Council who enables dodgy stuff to occur gets elected to State or Federal Govt. And people should care even more if that Mayor has been supported and/or protected by State or Federal Govt. People should care a lot.
        
        Reply
    2. John Friend says:
      
      September 30, 2022 at 4:30 pm
      
      MacNeill had the opportunity in a recent webinar to upgrade use of the SDT from an implication in an Examination Report to a publicly stated fact. But he chose instead to say that “the second derivative is not required” and move on.
      Rather than adding that it was nevertheless acceptable to use the SDT to determine the nature of a stationary point where appropriate. (The fact that he also did not say how a point of inflection could be calculated without using the second derivative is a separate – and vexing – issue).
      
      Reply
Red Five says:

April 24, 2022 at 7:06 pm

I know how much Marty loves brackets*, but I was a bit surprised to see the brackets around the integrand in the Methods Paper 1 Report, page 2 end of paragraph 1. I know they hammer the inclusion of the $dx$ REPEATEDLY, but does a line like this mean students now must put brackets around their integrand?

* I don’t think he does.

Reply
1. marty says:
  
  April 24, 2022 at 7:14 pm
  
  Ugh! That is pretty stupid. However I cannot believe that brackets around the integrand would be mandatory.
  
  Reply
  1. John (No) Friend (of VCAA) says:
    
    April 24, 2022 at 8:25 pm
    
    It’s another example of VCAA idiocy and inconsistency *.
    
    In response to this exact query, VCAA has publicly stated that the integral sign and the ‘dx’ act as $\displaystyle defacto$ brackets and therefore brackets around the integrand are NOT required.
    
    Brackets around an integrand are NOT mandatory. They are, however:
    1) Superfluous.
    2) Typically unsightly and reduce clarity.
    3) Used by pedantic pinheads who think it makes them look smart (look at some of the commercial solutions to the VCAA exams and trial exams). Here’s a (pin)heads-up: It makes you look like a stupid try-hard.
    
    * This is why I’m pushing for a ‘Stupid Design Supplement’ – see my previous comments.
    
    Reply

UPDATE (22/04/22)

UPDATE (22/04/22)

UPDATE (20/04/22)

UPDATE (24/11/21)

UPDATE (09/11/21)

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