32 Replies to “Secret 2025 Methods Business: Exam 2 Discussion”
Last question, last page – classic vcaa asking to find derivative at endpoint. as a student familiar with their negligence to this though it probably doesn’t make much difference to anyone.
At this stage, VCAA must always permit derivatives at endpoints. God knows why they chose such a silent manner of going with this, but they’ve gone with it.
Q6 – interesting way of asking about concavity, a decent question in some ways.
Q7 – OK, I guess they had to have something like this somewhere.
Q9 – this was actually a good question I thought.
Q13 – also a decent/good question.
Q17 – hmmm… nice enough, if a bit too obvious that 3 of the 4 options can be eliminated reasonably quickly.
Q18 – a probability mass function??? Not seen that in a while… well written though.
I found it quite interesting that they reverted to a four-question extended response format. There were also no three or four mark questions (aside from a single 3 mark allocation for a sequence of three transformations).
Better than all 1 and 2 mark questions as became standard.
Still nothing like the 10 mark question about the stone thrown at a bird from 1979, but times have changed and undoing these changes therefore will take time.
Oh yeah, sorry. Missed the other 3-marker. Pretty unusual that they have a ‘Show, using algebra’ question in an Exam 2 – but I do like it.
I don’t think 3 marks should’ve been allocated to a sequence of transformations.
Yeah, no way that 3-mark transformation thing is worth three marks.
And, yeah, I also noticed the weird “show that” wording. I think it is probably an attempt to shore up VCAA’s idiotic use of “show that”. The attempt fails: in any sane world, plugging in the given values is “using algebra” to “show that” the values solve the equations. But of course VCAA is insane, so anybody trusting in sanity for the grading of this question will undoubtedly be screwed.
A bit too much of the statistics, normal distribution (AKA button pushing on CAS) and not enough Binomial or discrete probability (I did like the way a binomial was introduced at the end of Q1 but also know a lot of people will find it tokenistic, which it may well be).
A bit too much on transformations.
Newton’s method was highly likely to be seen given the last few rounds have been bisection method – no tangents on Paper 1 just added to the likelihood of this; so no surprises.
A lot too much spelling out and stepping out the method to be used (I get that this makes marking easier, but geez… fill-in-the-blank exams are not fun anymore). Probably never were.
Complete the gradient table to show that there exists a stationary point of inflection.
Except all filling that table will do is show that there is a stationary point. Point of inflection requires there to be second derivative sign changes
There were SO MANY ridiculous questions like “f(x) = sin(x) + 1. Evaluate f(2pi/3)”. What is this meant to assess on a tech active exam???
The only challenging MCQ was Q19. This question will demolish students who aren’t aware that the shortest line segment between a line and a curve is always perpendicular to both the line and the tangent to the curve at the point of contact. In my experience many students never learn this, as usually this type of question can be solved by just solving the derivative of a distance function = 0. That method alone won’t cut it this time, though.
Q2 e) asks for the points of intersection of g-1(x) and y=2(x-7). Some students won’t have recognised that 2(x-7) is actually the inverse of f, and thus the points of intersection are the inverse of the original points labelled on the graph. However, these students will be at no disadvantage, as they’ll get the points anyway by just equating the two equations and solving. So what is the point of this question? If it doesn’t require any understanding of inverses or reflections in y=x, then why are we solving the inverses instead of just any two random equations?
Q 4 g) iii) (the last question) was conceptually interesting, but as far as I’m aware you just plugged in two simultaneous equations, pressed enter, and hopefully recognised the approximate answer given by the cas was pi.
It is difficult for me to evaluate MM2, because it is so damn ugly, and because so much is killed by CAS. I will look carefully at what you have pointed out.
Last question, last page – classic vcaa asking to find derivative at endpoint. as a student familiar with their negligence to this though it probably doesn’t make much difference to anyone.
At this stage, VCAA must always permit derivatives at endpoints. God knows why they chose such a silent manner of going with this, but they’ve gone with it.
Some thoughts on the multiple choice section:
Q6 – interesting way of asking about concavity, a decent question in some ways.
Q7 – OK, I guess they had to have something like this somewhere.
Q9 – this was actually a good question I thought.
Q13 – also a decent/good question.
Q17 – hmmm… nice enough, if a bit too obvious that 3 of the 4 options can be eliminated reasonably quickly.
Q18 – a probability mass function??? Not seen that in a while… well written though.
The rest were a bit “meh – seen this before”.
“meh” is fine, as long as the exam is sufficiently testing, contains no nutty explorations or howlers, and circumvents CAS enough.
In terms of circumventing CAS, this paper did better than a lot of previous years.
Whether the quality of the paper vs number of questions explicitly requiring CAS to solve is a causation or just a correlation…
Wouldn’t MCQ13 be destroyed by CAS?
Potentially but I thought it easier to do by hand.
I found it quite interesting that they reverted to a four-question extended response format. There were also no three or four mark questions (aside from a single 3 mark allocation for a sequence of three transformations).
One pseudo-3-mark question and no 4-mark questions?
EDIT: Two 3-mark questions, which of course doesn’t remotely save it. That’s beyond scaffolding: it’s elevatoring.
Better than all 1 and 2 mark questions as became standard.
Still nothing like the 10 mark question about the stone thrown at a bird from 1979, but times have changed and undoing these changes therefore will take time.
It’s gonna take more than time. It’s gonna take a new VCAA.
The past is a foreign country…
It’s time to move.
Can you remind us of the bird stone problem please?
This one.
The examiners’ report (not online) simply said “this question was not done well”.
I’ve seen this question appear in textbooks from the 1980s, with a few minor changes, still an excellent problem and a glimpse of what once was…
The answer (that I got, no idea if it is correct as solutions were never published publicly) is
m/s
As I said in the talk, I don’t know how to solve the problem. I know what to do to go about solving it, but I don’t know what happens.
In those days, a raw 35%-ish was a pass. The top end was well and truly differentiated.
I’d be happy to share my working, but maybe that problem deserves a post of its own some day.
Yeah, let’s leave it. Maybe I’l try to restart TGIF in some form.
Oh yeah, sorry. Missed the other 3-marker. Pretty unusual that they have a ‘Show, using algebra’ question in an Exam 2 – but I do like it.
I don’t think 3 marks should’ve been allocated to a sequence of transformations.
Yeah, no way that 3-mark transformation thing is worth three marks.
And, yeah, I also noticed the weird “show that” wording. I think it is probably an attempt to shore up VCAA’s idiotic use of “show that”. The attempt fails: in any sane world, plugging in the given values is “using algebra” to “show that” the values solve the equations. But of course VCAA is insane, so anybody trusting in sanity for the grading of this question will undoubtedly be screwed.
Extended response section general comments:
A bit too much of the statistics, normal distribution (AKA button pushing on CAS) and not enough Binomial or discrete probability (I did like the way a binomial was introduced at the end of Q1 but also know a lot of people will find it tokenistic, which it may well be).
A bit too much on transformations.
Newton’s method was highly likely to be seen given the last few rounds have been bisection method – no tangents on Paper 1 just added to the likelihood of this; so no surprises.
A lot too much spelling out and stepping out the method to be used (I get that this makes marking easier, but geez… fill-in-the-blank exams are not fun anymore). Probably never were.
Heavy on the stats and the transformations. I’m gonna love it …
There are some *nice-ish* questions, but yeah, a lot of crap too.
An improvement on pre-2023 exams, but that is not a high bar.
Some of the MCQs could be decent non-CAS Paper 1 questions with a minimum of tweaking which is always nice to think about. Briefly.
Pre-2023 is not a bar: it’s a trench.
Indeed. But pre-1967 had a few significantly higher peaks, too.
Back when graduating with honours meant something significant.
Question 1 Part C:
Complete the gradient table to show that there exists a stationary point of inflection.
Except all filling that table will do is show that there is a stationary point. Point of inflection requires there to be second derivative sign changes
Oh, dear. Has that nonsense returned? I’ll look.
Never mind I think in this case it is valid
Yes, I think the question is ok, although the examiners are on thin ice, and I wonder if they are aware of it.
This exam was obscenely easy.
There were SO MANY ridiculous questions like “f(x) = sin(x) + 1. Evaluate f(2pi/3)”. What is this meant to assess on a tech active exam???
The only challenging MCQ was Q19. This question will demolish students who aren’t aware that the shortest line segment between a line and a curve is always perpendicular to both the line and the tangent to the curve at the point of contact. In my experience many students never learn this, as usually this type of question can be solved by just solving the derivative of a distance function = 0. That method alone won’t cut it this time, though.
Q2 e) asks for the points of intersection of g-1(x) and y=2(x-7). Some students won’t have recognised that 2(x-7) is actually the inverse of f, and thus the points of intersection are the inverse of the original points labelled on the graph. However, these students will be at no disadvantage, as they’ll get the points anyway by just equating the two equations and solving. So what is the point of this question? If it doesn’t require any understanding of inverses or reflections in y=x, then why are we solving the inverses instead of just any two random equations?
Q 4 g) iii) (the last question) was conceptually interesting, but as far as I’m aware you just plugged in two simultaneous equations, pressed enter, and hopefully recognised the approximate answer given by the cas was pi.
Thanks, bigM.
It is difficult for me to evaluate MM2, because it is so damn ugly, and because so much is killed by CAS. I will look carefully at what you have pointed out.