Thanks, John. I hammered the 2017 question here. The issue in 2017 was much more than the one-sided derivative. I haven’t looked at this year’s exam, to compare.
Definitely open circles required ai 2 end points and the original function is only defined over [-pi, pi]. But again, it is interesting to see the marking scheme here if only labelling 2 end points is good enough.
OK, the question is clumsy but it is not nearly as bad as the 2017 question to which John referred.
As I discuss in the post I linked to above, whether you consider a function to be “differentiable” at the endpoints of a closed domain is a matter of convention. It is easy enough and natural enough to include “one-sided derivatives” at the endpoints, but it is also natural enough to leave the endpoints out. And, in VCE, best is probably to duck the issue entirely. To my knowledge, VCAA hasn’t clarified their stance on endpoint derivatives, and of course they should (and definitely should have in 2017, when the exam question was *really* stuffed up).
For the question on the 2024 exam, I would interpret “the domain [-π,π]” to be referring to the domain of f’, and so VCAA would want the filled-in dots. But, I don’t think it’s cut and dried. And, given the general lack of clarity on the issue, I definitely think VCAA should accept either open or closed dots. And and, new to 2024, I would be surprised if VCAA did not accept both.
Even if they do end up accepting both, sticking points like these can be big time-wasters in what was ultimately quite a time-constrained exam. It starts to feel like VCAA punishing those who are actually aware that derivatives aren’t defined at endpoints by throwing in this confusing curveball while those with no knowledge of the idea can sail past without even noticing it.
I think you are over-stating “big time-wasters” in this case. The 2024 question is not remotely as bad in this regard as the 2017 question. In this case, you either colour the dots or you don’t. Not a lot of time.
But, I agree. For a smarter kid it could well be disorienting, and could momentarily knock you off your stride. The issue should have and could have been been avoided, most properly by VCAA declaring once and for all whether one-sided derivatives are or are not a thing.
Hi Marty, just adding to this. I have recently got back the Statement of Marks for the Methods and the Specialist exams. I received full marks for the graph despite using open circles for the endpoints. I have also heard from friends that closed circles was also accepted. Looks like VCAA recognised the ambiguity and awarded both.
Aren’t double derivatives in the Spec study design? How do VCAA expect Methods students to find the range of the derivative function (double derivatives are quite intuitive, but that’s not really an excuse)
On a different note, I’m really curious whether VCAA will penalise students for writing “dilation by x-axis” instead of “dilation by t-axis”. I think most students made that mistake
Most people at my school wrote x-axis instead of t-axis, but I would assume that only the latter would be accepted. It seems like a mark that VCAA would like to use to help differentiate the top end of the distribution.
I think vcaa expects students just to evaluate each endpoint and graphically consider how the function of the derivative may look (sin(x) decreases and xcos(X) decrease (cos X decreases and is negative, so the X increasing will also decreasw xcos(X)). From that you can infer it’s just decreasing over the provided domain and use the endpoints. Still a pretty terrible question for methods knowledge, but doable
Hi, Jay. I don’t think you need f” for 7(b), and I doubt it was expected. But the question is tricky and, although I like the principle of the question, I’m not sure I like it here, or at least so given the way the question was executed.
On 5(b), one would hope “x-axis” didn’t result in students losing a mark. But, it’s the kind of thing VCAA traditionally loves to do.
VCAA has said on frequent occasions in “meet the examiners” and also in the occasional examiners’ report that candidates must use the variables given in the question.
Whether or not you consider an axis the same as a variable is of course debatable (why is saying “horizontal axis” OK but saying “-axis” not OK…?)
But yes, VCAA does have a track record as a bit of a pedant with some things.
The at the end of an integral comes to mind as well…
Right, since you could just use the endpoints and it would work
I skipped that question* because I assumed it required a double derivative and I didn’t have time to solve that. Only afterwards did I find out that double derivatives are actually only part of the spec curriculum. I imagine there’s a reasonably large crossover between Spec and Methods students, and I feel that that exam question would have very much disadvantaged Spec students. Then again, I guess there’s other questions that would have benefited spec students, so maybe it “levels the playing field”, I guess
It was a hard question and, in principle a good question, although debatable whether it was kosher. i think so, but there is an argument there.
But in general VCAA has way way undertested the hard end, so doing MM and SM has been like Olympic rifle shooting: a couple stupid misses and you’re screwed. More and harder questions would be much fairer.
Absolutely! It is absurd that after a year of Methods you only get tested on applying it tech-free for a total of 1 hour (excluding SACs). Nearly everyone at my school said they didn’t finish the exam during that time. Would be so much better if it was a 2 hour tech-free exam (perhaps with double as many questions, although I personally prefer if the exam is completeable and not a time management challenge)
(As for the tech-active exam, may as well just make that 1 hour, and then it will actually test your ability to ~~type quickly on a non-qwerty keyboard~~ quickly and efficiently use technology to solve mathematical problems)
I totally agree with this. This exam turned into something of a race to write out algebra as quickly as possible instead of an actual test of knowledge.
The exam is shallow, and too short. A test should be testing. But Methods has so little content and such an ingrained culture of triviality, it leaves the examiners with little option but to test speed.
I’m not really defending this, but I think attacking this exam is misguided, and ignores much deeper and more systemic issues.
I will say that the last question wasn’t too bad. Although it could still be essentially brute-forced algebraically, it was made much easier by having knowledge of odd functions and how the cube root graph had been transformed. It’s on the easier side for a final question, but it was ultimately fair and not too similar to things we’ve seen in recent years.
Perhaps only some students; I know Jacaranda uses this notation in their textbook but Cambridge doesn’t. I wonder if students will be confused by X∼N(μ,σ^2) for the normal distribution given the CAS takes σ and not σ^2.
Hi, Pippa. Given that the question also provides the turning point information, i think it’s within the SD, and a reasonable question, and maybe a good question. But teachers would be a better judge of the legitimacy and the merits.
I think this question was fair. The SD can be deliberately vague on these matters, but as others have said, the way the question was stepped out I think kept in well within the scope of Methods.
If anything, questions like this fit better inside the Methods SD than the Specialist SD.
That does not make them good questions, but I think it was fair.
1. Q5b. Can this not be done in ONE transformation? OK, you can do it in two, but why not allow two different correct answers?
2. Q6. Interesting. Three answers, two of which need to be rejected. A fair question, maybe, I liked it. Others will not. I do wonder why the question didn’t say to give the answer in a specific form (as has been the case in previous years).
Q7biii. Interesting use of the IVT by stealth? Again, probably fair. Others may disagree.
Q8. Didn’t really get the point of this question. Part d was nice(ish) in that it could be done geometrically ( is an odd function so…) or by brute force.
Like the rest of the exam, question 6 looks deceptively easy. I think the rejection part is fair (even though I forgot to do that), but I didn’t like that it required long-division, since it made the question take much longer than expected and hence messed up my time management
I think the long division was fair game and especially since was such an obvious factor (the sort of thing I would hope was drilled in Methods 1&2 but accept that this may not have been the case).
The first few questions seemed very typical of past exams.
Hi, Emma. It is obviously not the worst issue one might find with an exam, but you are definitely not being pedantic. The formatting is very clumsy. (I wouldn’t think it is likely to cause confusion in practice, but you’re probably a better judge.)
I agree it isn’t likely to cause confusion, but definitely is clumsy. Once the PDF is out then we’ll be able to see what in the world VCAA typed to get that formatting
Q6 – it has been typical of VCAA to say “give your answer in the form “.
Q7 – I think it is fair given the bisection method is now in the curriculum, but geez…
Q8 – again, fair but I’m really not sure what the point of the question was and Methods questions in the past have all had a point (usually a really poorly engineered point, but still…)
I think VCAA messed up by requesting it be sketched over a closed interval. I doubt that’s an intentional trick question, and I doubt they’ll penalise students based on it.
Also, if you follow that rule then question 7biii arguably becomes impossible to solve (since you’re required to use the answer for 7bii for it)
The idea is to use the fact that f'(x) contains a zero value within the interval [pi/2,2pi/3] to prove that f(x) contains a stationary point within that interval.
But the f(x) only necessarily contains a stationary point within that interval if f'(x) contains a zero value within the interval (pi/2,2pi/3). Otherwise it could just be an endpoint (I guess it’s up for debate whether a stationary point at x=pi/2 would could as a “stationary point for x∈[pi/2,2pi/3], but I would argue it wouldn’t)
Hi Banacek. If I understand your question I don’t think (b)(ii) is too observational. But I don’t expect students to do well on the question. (Which doesn’t necessarily mean that it’s a bad question.)
Yes, but hopping over the issue pleases me not.
Mathematical art is suffering.
Worth a separate mark,and so i think the logical gap was left.
I would change the question to:
“Explain why SP must be between … ”
With the intension of finding the opposite signs of derivatives there and the consequence.
The actual range is irrelevant
Hopping over what issue? I agree the question is muddy, and may be worth more marks (which would hurt most students), but I don’t think the issue is one of hopping or being “observational”.
Hi All,
I actually really liked this exam! On first read through I thought the questions felt very accessible, which is always encouraging for students, and the first 5 questions pretty straight forward to do.
I enjoyed question 6 thoroughly, and I think it fits squarely within the Methods curriculum. I love that the students were tested in one question on log laws, polynomial long division, the long lost quadratic formula (at least I reckon a lot of students will forget it as its not on formula sheet) and then a sneaky domain restriction at the end. I agree formatting was sloppy for the base, and that it is typical in the past to give the format of an answer, but I think it would just give too much away here.
Q7 was tricky with the wording – I feel like verify isn’t a key word we encounter often and I don’t expect students to know that sqrt(3)/2 – pi/3 is negative to realise 0 is included in the interval, but otherwise fine enough depending on what VCAA accept.
Endpoints will be a very interesting discussion for assessors I am sure.
Q8 I liked; confusing at times to know exactly what was going on, but if you lean into the maths then it all falls out pretty nicely.
I finished in the 60 mins but would have liked another 5 to go back and check over some answers (I initially missed the restriction to eliminate 2 answers for Q6)
Re “verify”, I’m not sure in practice that will cause much of an issue, if only because I don’t expect many students to obtain this mark (or the previous one). But also because there’s really only one thing to do/say. I’m curious you think the question might have been worded better.
One thing that occurred to me, but which no one has noted, is that the writing generally seemed straight-forward and clean. There was little or no excess verbiage. (The real test for this will be tomorrow’s Exam 2.)
I agree Marty, the laguage was very easy to interpret.
Except for 7bii and iii – tbh I think they could have just left both of these out. It is obvious visually that there is a turning point in the original graph, and if x-ints of the derivative function are not required to be labelled in 7C then who really cares the exact position of that TP? I think they were just trying to trick students into saying range was [0,1].
Maybe they just needed 2 more marks to get them to 40 for the paper?
Figuring out if the value in Q7 is less than 0 is ultimately pretty trivial, as it turns into (3sqrt(3)-2pi)/6 and since sqrt(3) is obviously less than 2 and pi is greater than 3 one can surmise that it is negative. These estimation skills are pretty important for figuring out if things fall within a domain (especially if the CAS can’t just convert it to a decimal for you), so I think testing them is fair game.
Thanks, Parkie. I agree that aspect was good, although I am guessing very few students will score the marks for (iii), or (ii). (Not necessarily a bad thing. Again, a test should be testing.)
There are more subtle reasons why I’m less thrilled with the question, probably along the lines of Banacek’s concerns, but I don’t think these subtleties would have had too much effect.
Just finished up, seemed fairly good, nothing major error wise, 2nd to last question is going to bite quite a lot of the state.
How can a function’s derivative be defined on the function’s endpoints?
Not the first time this has happened.
See 2017 Methods Exam 1 Q9 (in particular part c).
https://www.vcaa.vic.edu.au/sites/default/files/Documents/exams/mathematics/2017/2017MM1-w.pdf#page=12
Thanks, John. I hammered the 2017 question here. The issue in 2017 was much more than the one-sided derivative. I haven’t looked at this year’s exam, to compare.
I treated it as a different function with the rule of the derivative of f(x) and the stated domain, as this avoided the endpoint issue.
Which question is this? (And general advice to commenters: try to be specific and clear.)
Question 7 I think, though I’d have to see the paper to remind myself of the specific sub-question.
Definitely open circles required ai 2 end points and the original function is only defined over [-pi, pi]. But again, it is interesting to see the marking scheme here if only labelling 2 end points is good enough.
Question 7c.
In the question, they defined f(x) to be xsin(x) defined in the domain [-pi,pi], then asked students to sketch f'(x) across the same domain in part c.
Thanks, VS. I’ll look.
OK, the question is clumsy but it is not nearly as bad as the 2017 question to which John referred.
As I discuss in the post I linked to above, whether you consider a function to be “differentiable” at the endpoints of a closed domain is a matter of convention. It is easy enough and natural enough to include “one-sided derivatives” at the endpoints, but it is also natural enough to leave the endpoints out. And, in VCE, best is probably to duck the issue entirely. To my knowledge, VCAA hasn’t clarified their stance on endpoint derivatives, and of course they should (and definitely should have in 2017, when the exam question was *really* stuffed up).
For the question on the 2024 exam, I would interpret “the domain [-π,π]” to be referring to the domain of f’, and so VCAA would want the filled-in dots. But, I don’t think it’s cut and dried. And, given the general lack of clarity on the issue, I definitely think VCAA should accept either open or closed dots. And and, new to 2024, I would be surprised if VCAA did not accept both.
Even if they do end up accepting both, sticking points like these can be big time-wasters in what was ultimately quite a time-constrained exam. It starts to feel like VCAA punishing those who are actually aware that derivatives aren’t defined at endpoints by throwing in this confusing curveball while those with no knowledge of the idea can sail past without even noticing it.
I think you are over-stating “big time-wasters” in this case. The 2024 question is not remotely as bad in this regard as the 2017 question. In this case, you either colour the dots or you don’t. Not a lot of time.
But, I agree. For a smarter kid it could well be disorienting, and could momentarily knock you off your stride. The issue should have and could have been been avoided, most properly by VCAA declaring once and for all whether one-sided derivatives are or are not a thing.
Hi Marty, just adding to this. I have recently got back the Statement of Marks for the Methods and the Specialist exams. I received full marks for the graph despite using open circles for the endpoints. I have also heard from friends that closed circles was also accepted. Looks like VCAA recognised the ambiguity and awarded both.
Thank you, VS. Good to hear.
Aren’t double derivatives in the Spec study design? How do VCAA expect Methods students to find the range of the derivative function (double derivatives are quite intuitive, but that’s not really an excuse)
On a different note, I’m really curious whether VCAA will penalise students for writing “dilation by x-axis” instead of “dilation by t-axis”. I think most students made that mistake
Most people at my school wrote x-axis instead of t-axis, but I would assume that only the latter would be accepted. It seems like a mark that VCAA would like to use to help differentiate the top end of the distribution.
“top end of the distribution”. FFS.
I think vcaa expects students just to evaluate each endpoint and graphically consider how the function of the derivative may look (sin(x) decreases and xcos(X) decrease (cos X decreases and is negative, so the X increasing will also decreasw xcos(X)). From that you can infer it’s just decreasing over the provided domain and use the endpoints. Still a pretty terrible question for methods knowledge, but doable
Hi, Jay. I don’t think you need f” for 7(b), and I doubt it was expected. But the question is tricky and, although I like the principle of the question, I’m not sure I like it here, or at least so given the way the question was executed.
On 5(b), one would hope “x-axis” didn’t result in students losing a mark. But, it’s the kind of thing VCAA traditionally loves to do.
VCAA has said on frequent occasions in “meet the examiners” and also in the occasional examiners’ report that candidates must use the variables given in the question.
Whether or not you consider an axis the same as a variable is of course debatable (why is saying “horizontal axis” OK but saying “
-axis” not OK…?)
But yes, VCAA does have a track record as a bit of a pedant with some things.
The
at the end of an integral comes to mind as well…
Right, since you could just use the endpoints and it would work
I skipped that question* because I assumed it required a double derivative and I didn’t have time to solve that. Only afterwards did I find out that double derivatives are actually only part of the spec curriculum. I imagine there’s a reasonably large crossover between Spec and Methods students, and I feel that that exam question would have very much disadvantaged Spec students. Then again, I guess there’s other questions that would have benefited spec students, so maybe it “levels the playing field”, I guess
It was a hard question and, in principle a good question, although debatable whether it was kosher. i think so, but there is an argument there.
But in general VCAA has way way undertested the hard end, so doing MM and SM has been like Olympic rifle shooting: a couple stupid misses and you’re screwed. More and harder questions would be much fairer.
Absolutely! It is absurd that after a year of Methods you only get tested on applying it tech-free for a total of 1 hour (excluding SACs). Nearly everyone at my school said they didn’t finish the exam during that time. Would be so much better if it was a 2 hour tech-free exam (perhaps with double as many questions, although I personally prefer if the exam is completeable and not a time management challenge)
(As for the tech-active exam, may as well just make that 1 hour, and then it will actually test your ability to ~~type quickly on a non-qwerty keyboard~~ quickly and efficiently use technology to solve mathematical problems)
Make the tech-active exam one minute, not one hour.
I totally agree with this. This exam turned into something of a race to write out algebra as quickly as possible instead of an actual test of knowledge.
The exam is shallow, and too short. A test should be testing. But Methods has so little content and such an ingrained culture of triviality, it leaves the examiners with little option but to test speed.
I’m not really defending this, but I think attacking this exam is misguided, and ignores much deeper and more systemic issues.
I will say that the last question wasn’t too bad. Although it could still be essentially brute-forced algebraically, it was made much easier by having knowledge of odd functions and how the cube root graph had been transformed. It’s on the easier side for a final question, but it was ultimately fair and not too similar to things we’ve seen in recent years.
The derivative function was a one:one over that interval, so could just sub in endpoints.
Q4. I think this is the first time VCAA has used X~Bi(n,p) notation on an exam.
Thanks, Chris. It seems odd phrasing, rather than simply “n = …, p = …”, or whatever. Do you think it will have actively confused students?
Perhaps only some students; I know Jacaranda uses this notation in their textbook but Cambridge doesn’t. I wonder if students will be confused by X∼N(μ,σ^2) for the normal distribution given the CAS takes σ and not σ^2.
Question 7 – x cos(x) + sin(x)
Is this in the study design in tech free?
Or is it spec maths?
Hi, Pippa. Given that the question also provides the turning point information, i think it’s within the SD, and a reasonable question, and maybe a good question. But teachers would be a better judge of the legitimacy and the merits.
I think this question was fair. The SD can be deliberately vague on these matters, but as others have said, the way the question was stepped out I think kept in well within the scope of Methods.
If anything, questions like this fit better inside the Methods SD than the Specialist SD.
That does not make them good questions, but I think it was fair.
Not a great paper. Some random thoughts:
1. Q5b. Can this not be done in ONE transformation? OK, you can do it in two, but why not allow two different correct answers?
2. Q6. Interesting. Three answers, two of which need to be rejected. A fair question, maybe, I liked it. Others will not. I do wonder why the question didn’t say to give the answer in a specific form (as has been the case in previous years).
Q7biii. Interesting use of the IVT by stealth? Again, probably fair. Others may disagree.
Q8. Didn’t really get the point of this question. Part d was nice(ish) in that it could be done geometrically (
is an odd function so…) or by brute force.
Like the rest of the exam, question 6 looks deceptively easy. I think the rejection part is fair (even though I forgot to do that), but I didn’t like that it required long-division, since it made the question take much longer than expected and hence messed up my time management
I think the long division was fair game and especially since
was such an obvious factor (the sort of thing I would hope was drilled in Methods 1&2 but accept that this may not have been the case).
The first few questions seemed very typical of past exams.
Then it all seemed to finish rather abruptly.
Not sure what was going on really…
No one, in practice, should ever do long division. Just do boxes.
Pedantic I know – but I find the formatting of the log base 3 terms very annoying, especially when compared to the log base e in question 1.
Given that the examiners often given feedback about students needing to unambiguously show the base, I find this an even more egregious oversight.
Hi, Emma. It is obviously not the worst issue one might find with an exam, but you are definitely not being pedantic. The formatting is very clumsy. (I wouldn’t think it is likely to cause confusion in practice, but you’re probably a better judge.)
I agree it isn’t likely to cause confusion, but definitely is clumsy. Once the PDF is out then we’ll be able to see what in the world VCAA typed to get that formatting
Thanks, RF. Why “not a great paper”? I’m not necessarily disagreeing, but curious as to your thought. On the specific questions you note:
Q5. Mighty weird population models. Maybe I’m being dumb, but how do you do the question with one transformation?
Q6. Why might people not like the question? (I cannot see any reason to ask for a specific form, but then I never do.)
Q7. Yes, a peculiar inclusion, and I’m not sure it’s fair.
Q8. It seems OK to me. I guess no particular “point” to the question, but typically when a Methods question has a point, I hate it.
Q5 – what happens if you dilate horizontally…?
Q6 – it has been typical of VCAA to say “give your answer in the form
“.
Q7 – I think it is fair given the bisection method is now in the curriculum, but geez…
Q8 – again, fair but I’m really not sure what the point of the question was and Methods questions in the past have all had a point (usually a really poorly engineered point, but still…)
Will students be expected to label the derivative graph with hollow endpoints?
I think VCAA messed up by requesting it be sketched over a closed interval. I doubt that’s an intentional trick question, and I doubt they’ll penalise students based on it.
Also, if you follow that rule then question 7biii arguably becomes impossible to solve (since you’re required to use the answer for 7bii for it)
Thanks, Jay. I agree with your first point, but don’t understand the second.
The idea is to use the fact that f'(x) contains a zero value within the interval [pi/2,2pi/3] to prove that f(x) contains a stationary point within that interval.
But the f(x) only necessarily contains a stationary point within that interval if f'(x) contains a zero value within the interval (pi/2,2pi/3). Otherwise it could just be an endpoint (I guess it’s up for debate whether a stationary point at x=pi/2 would could as a “stationary point for x∈[pi/2,2pi/3], but I would argue it wouldn’t)
No, I think you’re tying yourself in unnecessary knots.
I think the question is fine, but agree that it is debatable and I can see why some people will not like it.
Marty… I left out the backslashes in my
in the above comment and also forgot a closing bracket… sorry.
No worries. Fixed now.
I would have thought it obvious, but do *not* post the exam here. Links to reddit or facebook or whatever is ok.
Link to Reddit:
Apology accepted.
Is it not too “observational” , q7bii, asking for the range of the values of the derivative ?
Hi Banacek. If I understand your question I don’t think (b)(ii) is too observational. But I don’t expect students to do well on the question. (Which doesn’t necessarily mean that it’s a bad question.)
How do we know it’s past the point of inflection at x=
/2? For the range of f’.
Aren’t both terms of f’ decreasing?
Yes, but hopping over the issue pleases me not.
Mathematical art is suffering.
Worth a separate mark,and so i think the logical gap was left.
I would change the question to:
“Explain why SP must be between … ”
With the intension of finding the opposite signs of derivatives there and the consequence.
The actual range is irrelevant
Hopping over what issue? I agree the question is muddy, and may be worth more marks (which would hurt most students), but I don’t think the issue is one of hopping or being “observational”.
Hi All,
I actually really liked this exam! On first read through I thought the questions felt very accessible, which is always encouraging for students, and the first 5 questions pretty straight forward to do.
I enjoyed question 6 thoroughly, and I think it fits squarely within the Methods curriculum. I love that the students were tested in one question on log laws, polynomial long division, the long lost quadratic formula (at least I reckon a lot of students will forget it as its not on formula sheet) and then a sneaky domain restriction at the end. I agree formatting was sloppy for the base, and that it is typical in the past to give the format of an answer, but I think it would just give too much away here.
Q7 was tricky with the wording – I feel like verify isn’t a key word we encounter often and I don’t expect students to know that sqrt(3)/2 – pi/3 is negative to realise 0 is included in the interval, but otherwise fine enough depending on what VCAA accept.
Endpoints will be a very interesting discussion for assessors I am sure.
Q8 I liked; confusing at times to know exactly what was going on, but if you lean into the maths then it all falls out pretty nicely.
I finished in the 60 mins but would have liked another 5 to go back and check over some answers (I initially missed the restriction to eliminate 2 answers for Q6)
Cheers!
Thanks, LH. I’m glad it went well for you.
Re “verify”, I’m not sure in practice that will cause much of an issue, if only because I don’t expect many students to obtain this mark (or the previous one). But also because there’s really only one thing to do/say. I’m curious you think the question might have been worded better.
One thing that occurred to me, but which no one has noted, is that the writing generally seemed straight-forward and clean. There was little or no excess verbiage. (The real test for this will be tomorrow’s Exam 2.)
I agree Marty, the laguage was very easy to interpret.
Except for 7bii and iii – tbh I think they could have just left both of these out. It is obvious visually that there is a turning point in the original graph, and if x-ints of the derivative function are not required to be labelled in 7C then who really cares the exact position of that TP? I think they were just trying to trick students into saying range was [0,1].
Maybe they just needed 2 more marks to get them to 40 for the paper?
Figuring out if the value in Q7 is less than 0 is ultimately pretty trivial, as it turns into (3sqrt(3)-2pi)/6 and since sqrt(3) is obviously less than 2 and pi is greater than 3 one can surmise that it is negative. These estimation skills are pretty important for figuring out if things fall within a domain (especially if the CAS can’t just convert it to a decimal for you), so I think testing them is fair game.
Thanks, Parkie. I agree that aspect was good, although I am guessing very few students will score the marks for (iii), or (ii). (Not necessarily a bad thing. Again, a test should be testing.)
There are more subtle reasons why I’m less thrilled with the question, probably along the lines of Banacek’s concerns, but I don’t think these subtleties would have had too much effect.
VCAA has posted the exam. Link is in the update.