Nah. I’m not excusing VCAA’s silence on this point, and I have already made that clear when commenting on the Exam 1 question. But the 2(a) confusion would be there anyway. If anything, MCQ10 clarifies 2(a), albeit that’s a weird method by which to clarify.
Sorry, RF. I was reading on my phone, which didn’t include the “≤” in your question. (Which left your question comprehensible but very strange.)
I am predicting that VCAA will expect endpoint derivatives, although I wouldn’t bet the house on it. I am also predicting that VCAA will accept “both answers” on the relevant questions, but I definitely wouldn’t bet the house on that one. (In any previous year, I would have bet the house against it.) VCAA is exhibiting genuine signs of sense and good faith, so this kind of thing is likely to be handled better.
Whatever VCAA decides, they will also have to decide if and how to address the issue in the exam reports.
Yes, I stand corrected
EDIT: oh yeah, I forgot about the endpoints issue that Red Five mentioned below. I LOLed so hard when I saw that
I walked out of that exam quite pleased. No bizarre function intercepting with its inverse on the last question, no particularly cumbersome CAS slogs. The Q5 was actually quite interesting. The increased focus on transformations instead of inverses was notable, though they weren’t hugely challenging. The difficulty of the exam is ultimately a problem though, as they clearly overcompensated for the extremely low scores seen last year.
I don’t want to jinx myself, but I found today far easier than every previous VCAA exam I have sat. Among boys at my school who were getting at least Bs on the SACS (top 30%), the perception was that it was very easy, which seems to be reflected online. I would be shocked if the A+ boundary was below 70/80 (for context, it was 61/80 last year). I think that last year was definitely too hard, so there is probably a sweet spot between the two that VCAA should be aiming for.
It seems to me like the problem was the lack of diversity in the difficulty of questions. The easier questions were fine, but it felt like it was missing a ramp in difficulty. I think most of that could’ve been fixed by adding a 5ish mark challenge question near the end
From a quick glance, I noticed some nice new formatting with the “use the following information to answer parts c and d of this question” and some weird modelling questions which felt more SAC-like than what you usually expect from a Methods exam.
The stronger students I spoke found it accessible yet reasonably set. The weaker students I spoke to found it fairly equivalently challenging to other papers.
I must say, if they’re going to do such odd transformations questions I’m going to need to get better at them. Q1dii was not my favourite, despite being able to identify what needed to happen I struggled to get it working.
Thanks, Samantha. You mean the framing of the questions was clearer than you’re used to?
I don’t know what to do with transformations (if I were the VCE God). In principle, it should be a good topic, but in practice it is fiddly and annoying and pointless. It needs fixing, or jettisoning, but I’m not sure how.
MCQ10 raises a few questions. If and both have domain does this imply that VCAA thinks functions on restricted domains are differentiable at their end-points…?
Because the wording of this question seems to imply that.
Overall, a bit too much CAS-bashing for my liking but overall an OK paper by VCAA standards.
I quite literally threw my hands up in frustration mid-exam when I saw the [0,5], as it reinforces this stupid ambiguity that VCAA should have put to bed long ago. However, it ultimately doesn’t have any bearing on the answer itself, so I can live with it.
What an intrinsic dissection of the question – such ambiguity failed to spark for me in the examination! Though, I do believe the 2024 examinations were crafted poorly offering no substantive material to separate the cohort. It is simply preposterous how VCAA resorts to manipulative and contrived pitfalls to stratify students. It is also patently clear the inchoate writing panel hastily produced the questions under duress of the widespread leaks.
Is this the first Methods exam 2 with only four multi choice answers A-D instead of five A-E?
I’m kind of happy that we have three instances across yesterday and today of a derivative function being defined at the endpoints of the original function, because it means we might finally get a clear statement on what VCAA expects for this.
Do you know why 4 is considered preferable to 5? I personally didn’t feel much of a difference, and it feels odd to improve the chances of guessing correctly.
It also feels odd to me, for the same reason. In fact the research, or at least the “research”, supports 4 over 5, although I’m not sure I believe it. It’s on my (long) list to investigate.
Notably, it mainly talks about the lack of benefit associated with having 5 options. I think the sentence “Moreover, writing an additional option for each multiple-choice item uses valuable test development time” is quite telling: VCAA don’t see much benefit to having a 5th option, and having only 4 options is cheaper and allows more funding to be allocated into other parts of exam writing
If the time previously spent on the fifth option is now spent catching mistakes and improving clarity, then this must be a good thing. But the report itself acknowledges that there are some (albeit small) negative impacts on exam accuracy, so I hope this isn’t just a cost-cutting measure that won’t lead to improvements elsewhere.
To be honest it might actually be an improvement. When there’s too many options it sometimes becomes obvious which one is correct, for example:
Which is the answer:
a. 5,8,7
b. 4,7,1
c. 10,5,42
d. 5,7,42
e. 1,2,3
that’s an obviously exhaggerated example, but it demonstrates that exam writers will usually include multiple correct options for each key detail, so that you can’t solve them just by solving one key detail. A real life example is questions 1 and 2 of last year’s methods exam. Both have 2 key details, and option c can be eliminated from both on the basis that no other answer includes those key details. And from today’s exam, question 1 option b can easily be eliminated, as can 6a (although in fairness I believe this strategy does fail for question 13). And question 15 options c and d can be eliminated on the basis that they’re identical, and then b can be eliminated on the basis that it doesn’t share key details with options c and d
Another notable aspect of the exam – pseudocode only made up 1 mark on multi choice qns. The question didn’t involve any of the algorithms in the study design or require technology, but was a pretty simple algorithm to grasp and just made sure students could follow the basic flow of code. It felt like the examiners just ticking a box for the sake of it
That was a bit of a surprise, we had been led to believe by our teachers that pseudocode and Newton’s Method would play a greater role in their second year on the study design. I’m not complaining though, in fact, I thought the pseudocode question was a smart one. You couldn’t just plug it into the CAS; you actually had to follow the code in a logical manner.
Also interesting that there was no Newton’s Method on either exam – made up quite a big chunk of the E2 last year.
Overall, exam felt like VCAA was trying to ‘play it safe’. There weren’t any ‘seperator’ questions that truly challenged or distinguished between more capable students. This will probably be a year where one mark dropped = one study score dropped.
A very interesting MM exam 2. Makes me wonder what we will see on SM next week.
Some observations: brand new approach adapted by the panel.
The reading is a lot – in some good way. One really needs strong stamina, acute observations, attentiveness, and quite good handle of CAS to do well in this exam.
Good to see there’s no particularly challenging MCQ, nor could we see MCQs that require 4-5 stages working.
I like ERQ5 as a whole. In ERQ5ai, TI encountered a bit issue when solving one equation, whereas Classpad was OK with it (students could still draw the graph though, locating an approximate value for x).
I like the probability question – the luggage scenario and a mixture of tree diagram and binomial random variable. Reminded me of some good and classic exercises from this book back in Uni:
“Dimitri P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, Athena Scientific, 2002.”
The circular function graphing question – a decent 2 marker.
I don’t see many such examples in Cambridge MM textbooks, but I notice some older textbooks (MathQuest, Heinamann Pearson did have these type of graphs “linear + circular”). I must check my bookshelf.
Overall ERQ3 is a clever choice.
Critique: the transformation skills is overly assessed, even if it was assessed based on different contexts/models/graphs.
Here is a tally of questions/parts obviously involving transformations (altogether at least 9 marks out of 80…)
MCQ12, MCQ13, MCQ15, MCQ20 (total 4 marks)
ERQ1di+dii (1 + 2 = 3 marks)
ERQ3aii (2 marks)
On the fence: I like Q2, especially the Power-Time-Energy relations.
But I think many teachers and students dislike it. These parts (although clearly introduced and explained in stem using ‘area under the curve’) are leaning towards Physics students, strictly speaking, not leaning towards specialist students anymore…
I think this paper serves the purpose of separating the top-end students. But the kids in the middle may suffer a bit.
Thanks, everyone, for your comments. All very interesting. I only gave the exam a brief read but, allowing for the crappy Study Design and the crappier CAS, it seemed to me to be pretty good. Plenty of the extended response seemed silly, as always, but it was merely silly rather than Drug Trip Weird, which has typically been the case. I only read very quickly but I didn’t notice any errors or ambiguities (other than the endpoint derivative thing).
As with MM1, I thought the writing was notably better than in previous years. It was still a little fussy in places, and for the life of me I cannot see the purpose of the phrase “the value of”. What is the difference between “Find X” and “Find the value of X”? But it was generally very good.
I’m not sure I can forgive VCAA the bad brackets in MCQ5, but other than that, and failing someone discovering a hidden clanger, the exam seems to me to be a distinct improvement over previous years’.
Question 3biv assesses maximum rate of change which was on the previous study design but isn’t on the current study design. VCAA explicitly stated it as being no longer present in their implementation of the new study design presentation.
The specific sentence from the previous study that was removed is “identification of
the maximum rate of increase or decrease in a given application context (consideration of the second derivative is not required)”.
Is assessing content not on the study design not an issue with the exam? Sure, it could come under the general “identification of local maximum/minimum values over an interval” but VCAA made a point of saying it was removed.
Question 2fiii asks for when 1 kWh of energy is consumed, and whilst it is correct, it would have been better if the question had asked to find the value of x such that after x seconds 1 kWh of energy is consumed. The reason for this is, many students, including me would have simply defined p(t) as a piecewise function on a CAS calculator, and would have solved
instead of something like
However, this has an issue the upper terminal is the variable we integrating w.r.t. and whilst the above equation will yield the right answer, it is unclear whether VCAA will accept this as working out. This is more of a specialist mathematics thing where you would introduce something like a dummy variable with differential equations and would be unfair if VCAA were to penalise.
I think that the working on the left is simply incorrect and should be penalised, as it is perfectly simple to introduce a new variable to denote the amount of time that needs to pass for 1kWh to be expended. Could you explain why you think this is a “specialist mathematics thing”, as to me it seems well within the bounds of Methods calculus?
I feel like this is a specialist maths thing since, in order to solve for a particular solution of a differential equation involving an initial condition of the form y=f(x) and you know the condition f(a)=b
You could either find the antiderivative of f(x) and include + c then solve for it. Or, alternatively you could use a definite integral:
This it self would get the right answer.
However, mathematically you would need to introduce a dummy variable
Here is a comment from the 2022 specialist mathematics exam 1 external assessment report:
“Quite a few students set up the differential equations in Questions 2 and 9 as definite integrals. While the method is sound, students need to use a ‘dummy’ variable in such problems. The majority of students who successfully solved these problems approached them using a more traditional method.”
I agree the question it self is valid, however I think it would have been better if the question introduced a new variable to denote the time it takes to consume 1 kWh in order to prevent students losing marks since the issue of having the same variable in a terminal as the variable that is being integrated w.r.t. would seem strange to someone who isn’t doing specialist maths.
Can a function with a stationary point of inflection have an inverse function? If yes, MCQ 10 is likely fundamentally flawed
Thanks, Jay. Haven’t looked yet but others can comment. I’ll look later.
Question stated sign change of f'(x). A function with a stationary point of inflection has f'(x) = 0 but no sign change.
Meaning MCQ 10 is ok?
Yes, I think that it was fine. Clearly there was at least one local min within the given range so it couldn’t be one-to-one.
I agree that MCQ10 has an answer and that there must be a turning point somewhere in the domain because of the sign change of the derivative.
I do not, however, agree that MCQ10 is “fine”.
See comment below.
I think MCQ10 is fine, if a little nervously over-worded. Having derivatives at the endpoints is notable but it plays no role in the question.
Except that it raises questions about whether to include endpoints in derivatives later in the paper such as Q2a.
Nah. I’m not excusing VCAA’s silence on this point, and I have already made that clear when commenting on the Exam 1 question. But the 2(a) confusion would be there anyway. If anything, MCQ10 clarifies 2(a), albeit that’s a weird method by which to clarify.
So, are you predicting that the solutions will use
symbols for the derivative?
Huh?
Sorry, RF. I was reading on my phone, which didn’t include the “≤” in your question. (Which left your question comprehensible but very strange.)
I am predicting that VCAA will expect endpoint derivatives, although I wouldn’t bet the house on it. I am also predicting that VCAA will accept “both answers” on the relevant questions, but I definitely wouldn’t bet the house on that one. (In any previous year, I would have bet the house against it.) VCAA is exhibiting genuine signs of sense and good faith, so this kind of thing is likely to be handled better.
Whatever VCAA decides, they will also have to decide if and how to address the issue in the exam reports.
Yes, I stand corrected
EDIT: oh yeah, I forgot about the endpoints issue that Red Five mentioned below. I LOLed so hard when I saw that
I walked out of that exam quite pleased. No bizarre function intercepting with its inverse on the last question, no particularly cumbersome CAS slogs. The Q5 was actually quite interesting. The increased focus on transformations instead of inverses was notable, though they weren’t hugely challenging. The difficulty of the exam is ultimately a problem though, as they clearly overcompensated for the extremely low scores seen last year.
So you found the exam too easy?
I don’t want to jinx myself, but I found today far easier than every previous VCAA exam I have sat. Among boys at my school who were getting at least Bs on the SACS (top 30%), the perception was that it was very easy, which seems to be reflected online. I would be shocked if the A+ boundary was below 70/80 (for context, it was 61/80 last year). I think that last year was definitely too hard, so there is probably a sweet spot between the two that VCAA should be aiming for.
Hmm. “Very easy” is much worse than very hard.
Couldn’t agree more. The curve could get ugly on this one.
It seems to me like the problem was the lack of diversity in the difficulty of questions. The easier questions were fine, but it felt like it was missing a ramp in difficulty. I think most of that could’ve been fixed by adding a 5ish mark challenge question near the end
Unfortunately, the challenging questions in Exam 2 are extremely repetitive, as VCAA seems to struggle to come up with them.
That’s what happens when the subject has such little content, and you have an idiot machine.
Ah. Thanks, Lenny.
From a quick glance, I noticed some nice new formatting with the “use the following information to answer parts c and d of this question” and some weird modelling questions which felt more SAC-like than what you usually expect from a Methods exam.
The stronger students I spoke found it accessible yet reasonably set. The weaker students I spoke to found it fairly equivalently challenging to other papers.
I must say, if they’re going to do such odd transformations questions I’m going to need to get better at them. Q1dii was not my favourite, despite being able to identify what needed to happen I struggled to get it working.
Thanks, Samantha. You mean the framing of the questions was clearer than you’re used to?
I don’t know what to do with transformations (if I were the VCE God). In principle, it should be a good topic, but in practice it is fiddly and annoying and pointless. It needs fixing, or jettisoning, but I’m not sure how.
MCQ10 raises a few questions. If
and 
both have domain ![[0,5]](https://mathematicalcrap.com/wp-content/ql-cache/quicklatex.com-2ab692caa14812024561eda2b8c11590_l3.svg "Rendered by QuickLaTeX.com")
does this imply that VCAA thinks functions on restricted domains are differentiable at their end-points…?
Because the wording of this question seems to imply that.
Overall, a bit too much CAS-bashing for my liking but overall an OK paper by VCAA standards.
(Any CAS-bashing is too much)
I quite literally threw my hands up in frustration mid-exam when I saw the [0,5], as it reinforces this stupid ambiguity that VCAA should have put to bed long ago. However, it ultimately doesn’t have any bearing on the answer itself, so I can live with it.
What an intrinsic dissection of the question – such ambiguity failed to spark for me in the examination! Though, I do believe the 2024 examinations were crafted poorly offering no substantive material to separate the cohort. It is simply preposterous how VCAA resorts to manipulative and contrived pitfalls to stratify students. It is also patently clear the inchoate writing panel hastily produced the questions under duress of the widespread leaks.
kylie, there are minor issues with the exam questions and major issues with administration, but you are ranting.
Is this the first Methods exam 2 with only four multi choice answers A-D instead of five A-E?
I’m kind of happy that we have three instances across yesterday and today of a derivative function being defined at the endpoints of the original function, because it means we might finally get a clear statement on what VCAA expects for this.
Well it’s a clear implication. A clear statement would still be welcome.
And yes, the four options for MCQs is new. It was an explicit recommendation of the Bennett review.
Do you know why 4 is considered preferable to 5? I personally didn’t feel much of a difference, and it feels odd to improve the chances of guessing correctly.
It also feels odd to me, for the same reason. In fact the research, or at least the “research”, supports 4 over 5, although I’m not sure I believe it. It’s on my (long) list to investigate.
The reasoning can be found at https://www.education.vic.gov.au/Documents/Independent%20Review%20VCAA%20Full%20Report%20Final.pdf (pages 45 and 46)
Notably, it mainly talks about the lack of benefit associated with having 5 options. I think the sentence “Moreover, writing an additional option for each multiple-choice item uses valuable test development time” is quite telling: VCAA don’t see much benefit to having a 5th option, and having only 4 options is cheaper and allows more funding to be allocated into other parts of exam writing
If the time previously spent on the fifth option is now spent catching mistakes and improving clarity, then this must be a good thing. But the report itself acknowledges that there are some (albeit small) negative impacts on exam accuracy, so I hope this isn’t just a cost-cutting measure that won’t lead to improvements elsewhere.
It is definitely not a cost-cutting measure. It is for better or worse, and probably better, implementing a Bennett recommendation.
To be honest it might actually be an improvement. When there’s too many options it sometimes becomes obvious which one is correct, for example:
Which is the answer:
a. 5,8,7
b. 4,7,1
c. 10,5,42
d. 5,7,42
e. 1,2,3
that’s an obviously exhaggerated example, but it demonstrates that exam writers will usually include multiple correct options for each key detail, so that you can’t solve them just by solving one key detail. A real life example is questions 1 and 2 of last year’s methods exam. Both have 2 key details, and option c can be eliminated from both on the basis that no other answer includes those key details. And from today’s exam, question 1 option b can easily be eliminated, as can 6a (although in fairness I believe this strategy does fail for question 13). And question 15 options c and d can be eliminated on the basis that they’re identical, and then b can be eliminated on the basis that it doesn’t share key details with options c and d
Another notable aspect of the exam – pseudocode only made up 1 mark on multi choice qns. The question didn’t involve any of the algorithms in the study design or require technology, but was a pretty simple algorithm to grasp and just made sure students could follow the basic flow of code. It felt like the examiners just ticking a box for the sake of it
Good.
That was a bit of a surprise, we had been led to believe by our teachers that pseudocode and Newton’s Method would play a greater role in their second year on the study design. I’m not complaining though, in fact, I thought the pseudocode question was a smart one. You couldn’t just plug it into the CAS; you actually had to follow the code in a logical manner.
Also interesting that there was no Newton’s Method on either exam – made up quite a big chunk of the E2 last year.
Overall, exam felt like VCAA was trying to ‘play it safe’. There weren’t any ‘seperator’ questions that truly challenged or distinguished between more capable students. This will probably be a year where one mark dropped = one study score dropped.
My above average students found the exam enjoyable and as expected. Below average students did not have a good time. I guess a pretty standard exam.
Thanks, G.
A very interesting MM exam 2. Makes me wonder what we will see on SM next week.
Some observations: brand new approach adapted by the panel.
The reading is a lot – in some good way. One really needs strong stamina, acute observations, attentiveness, and quite good handle of CAS to do well in this exam.
Good to see there’s no particularly challenging MCQ, nor could we see MCQs that require 4-5 stages working.
I like ERQ5 as a whole. In ERQ5ai, TI encountered a bit issue when solving one equation, whereas Classpad was OK with it (students could still draw the graph though, locating an approximate value for x).
I like the probability question – the luggage scenario and a mixture of tree diagram and binomial random variable. Reminded me of some good and classic exercises from this book back in Uni:
“Dimitri P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, Athena Scientific, 2002.”
The circular function graphing question – a decent 2 marker.
I don’t see many such examples in Cambridge MM textbooks, but I notice some older textbooks (MathQuest, Heinamann Pearson did have these type of graphs “linear + circular”). I must check my bookshelf.
Overall ERQ3 is a clever choice.
Critique: the transformation skills is overly assessed, even if it was assessed based on different contexts/models/graphs.
Here is a tally of questions/parts obviously involving transformations (altogether at least 9 marks out of 80…)
MCQ12, MCQ13, MCQ15, MCQ20 (total 4 marks)
ERQ1di+dii (1 + 2 = 3 marks)
ERQ3aii (2 marks)
On the fence: I like Q2, especially the Power-Time-Energy relations.
But I think many teachers and students dislike it. These parts (although clearly introduced and explained in stem using ‘area under the curve’) are leaning towards Physics students, strictly speaking, not leaning towards specialist students anymore…
I think this paper serves the purpose of separating the top-end students. But the kids in the middle may suffer a bit.
Thanks, Legionnaire. Interesting observations. I disliked Q2 and Q3 and Q4, but of course that’s just me: I prefer mathematics.
The MM exam pdf files are now released officially:
Click to access 2024MM1-w.pdf
Click to access 2024MM2-w.pdf
Great. Thanks, Legionnaire. I’ll update soon.
Done.
Thanks, everyone, for your comments. All very interesting. I only gave the exam a brief read but, allowing for the crappy Study Design and the crappier CAS, it seemed to me to be pretty good. Plenty of the extended response seemed silly, as always, but it was merely silly rather than Drug Trip Weird, which has typically been the case. I only read very quickly but I didn’t notice any errors or ambiguities (other than the endpoint derivative thing).
As with MM1, I thought the writing was notably better than in previous years. It was still a little fussy in places, and for the life of me I cannot see the purpose of the phrase “the value of”. What is the difference between “Find X” and “Find the value of X”? But it was generally very good.
I’m not sure I can forgive VCAA the bad brackets in MCQ5, but other than that, and failing someone discovering a hidden clanger, the exam seems to me to be a distinct improvement over previous years’.
Question 3biv assesses maximum rate of change which was on the previous study design but isn’t on the current study design. VCAA explicitly stated it as being no longer present in their implementation of the new study design presentation.
The specific sentence from the previous study that was removed is “identification of
the maximum rate of increase or decrease in a given application context (consideration of the second derivative is not required)”.
Oh for Christ’s sake. Who cares?
Is assessing content not on the study design not an issue with the exam? Sure, it could come under the general “identification of local maximum/minimum values over an interval” but VCAA made a point of saying it was removed.
Yeah, yeah. I couldn’t give a stuff.
Question 2fiii asks for when 1 kWh of energy is consumed, and whilst it is correct, it would have been better if the question had asked to find the value of x such that after x seconds 1 kWh of energy is consumed. The reason for this is, many students, including me would have simply defined p(t) as a piecewise function on a CAS calculator, and would have solved
However, this has an issue the upper terminal is the variable we integrating w.r.t. and whilst the above equation will yield the right answer, it is unclear whether VCAA will accept this as working out. This is more of a specialist mathematics thing where you would introduce something like a dummy variable with differential equations and would be unfair if VCAA were to penalise.
I think that the working on the left is simply incorrect and should be penalised, as it is perfectly simple to introduce a new variable to denote the amount of time that needs to pass for 1kWh to be expended. Could you explain why you think this is a “specialist mathematics thing”, as to me it seems well within the bounds of Methods calculus?
I feel like this is a specialist maths thing since, in order to solve for a particular solution of a differential equation involving an initial condition of the form y=f(x) and you know the condition f(a)=b
You could either find the antiderivative of f(x) and include + c then solve for it. Or, alternatively you could use a definite integral:
This it self would get the right answer.
However, mathematically you would need to introduce a dummy variable
Here is a comment from the 2022 specialist mathematics exam 1 external assessment report:
“Quite a few students set up the differential equations in Questions 2 and 9 as definite integrals. While the method is sound, students need to use a ‘dummy’ variable in such problems. The majority of students who successfully solved these problems approached them using a more traditional method.”
I agree the question it self is valid, however I think it would have been better if the question introduced a new variable to denote the time it takes to consume 1 kWh in order to prevent students losing marks since the issue of having the same variable in a terminal as the variable that is being integrated w.r.t. would seem strange to someone who isn’t doing specialist maths.
Thanks, vce.m.s. I have no comment except that CAS poisons everything.