31 Replies to “Secret 2024 Specialist Business: Exam 1 Discussion”
The study design has no mention of skew lines nor the distance between two skew lines whatsoever yet the question 10 asked to find the values of m such that the distance between the two skew lines is 14/root(35). Whilst it is covered in textbooks, the formula isn’t on the formula sheet and neither is a bound reference permitted. Is this even assessable?
Was it necessary to know what a skew line was in order to solve the question? If not I think it would be reasonable for a spesh student to derive the equation on the spot if they had not memorised it previously.
Thanks, Chris. Was the term “skew” semi–foreign to students? What about the substance? Would most students have practised, or even seen, any L-L distances? Is it in the texts? (I’m asking the World, not just you.)
If L-L distance was unseen by most students then I do not think it reasonable to expect that derivation/computation in the exam.
My memory is that “distance” is not in the new SD or on the formula sheet, but was in the sample materials VCAA posted for the new SD. My memory is also that I hammered this very point on the blog, although I cannot locate the hammering right now.
Having said that, I think it is reasonable to interpret VCAA’s mish-mosh to imply that “distance” generally is part of the SD: if other distances are examinable, then why not line-line, skew or otherwise?
Having said that, that L-L distance is examinable does not mean it was smart or empathetic for VCAA to do so. It could well be neither.
I think distances are fine since usually they can be constructed using knowledge of scalar resolute which is part of the course, however there is no mention of whether the knowledge of skew lines is required (lines that do not intersect and are not parallel), and really I think the terminology should be avoided if its not particularly mentioned in the study design. But as Chris said, it is possible to derive the equation and most students would be aware of its meaning since it is covered in textbooks (including the formula).
The term “skew” it self would have been familiar to students (including me), and finding the distance between two skew lines is part of the textbook exercises since the texts have included it even thought it isn’t explicitly mentioned in the course. It just is that VCAA should avoid terminology that isn’t mentioned in the study design it self.
I think they made this exam too easy, very standard and routine questions making it difficult to separate students who just did textbook excerises versus students who went beyond that. I’m scared the grade boundaries are going to be like 2022 where you need 38/40 to get an A+ for Exam 1.
Additionally, the word “skew”, although not technically in the SD, is only used to reinforce the idea that the lines do not intersect (which we already given that because the shortest distance wasn’t 0) and not parallel (which we can also see pretty clearly) so I don’t think the word “skew” disadvantaged students. (but perhaps they should have omitted the word “skew” all together, but I am not sure if that messes up the question because I am not a math expert)
Thanks, Everyone, so far. I haven’t seen the exam and I’ll have to look over my thoughts/writings on “distance”.
There is obviously a systemic issue, that the Study Design is a basket case of unclarity (and madness). Accepting that is the Wonderland world we have, the “skew distance” thing doesn’t sound like a big deal, but I’ll take a look.
I also thought it was interesting that they didn’t do much to alter the style of question 1, a question that VCAA had leaked in the exam covers it released early October before re-uploading them all late October.
Highlight the invisible text on page 2 of the link I attached, and you get this. Exact same format, even the exact same question (question 1 on the real exam).
Question 1 (4 marks)
Consider the function with rule f (z) = 2z
4 − iz3 − 16z + 8i, where z ∈ C.
a. Verify that 2z − i is a factor of f (z). 1 mark
b. Hence, or otherwise, solve the equation f (z) = 0.
Give your answers in Cartesian form.
Hi Legionnaire. I’ve now read the paper (quickly). I agree it is generally worded clearly, although I think it can still be improved. Short sentences are good.
Overall, I liked the exam. I felt it was mostly fair (in that good students will do well and only good students should perform well). A few questions slowed me down a bit but that is also more than fair on a Specialist paper; students who were not prepared I suspect will struggle to finish this paper; also not a problem.
Some questions (Q7) were the standard trick where a lot of marks will be lost due to a missing negative sign in the final answer (I’m only guessing, but it seems to happen a lot in SM papers).
Cross product of vectors appearing multiple times was interesting, but not unexpected.
The proof question (Q2) seemed a bit easy. Easier than previous years. Was this deliberate? I guess we will never know.
In question 5, the question states that a solid is formed when the curve is rotated about the x-axis, when what they really mean to be rotated is the region bounded by the curve and the x-axis over the given interval. This probably wouldn’t cause much confusion but it is still frustrating for this to appear year after year.
I see VCAA has finally fixed their spacing on units. In the previous study design, they forgot to include the space between ‘metres’ and ‘per second’ for velocity/speed causing the cursed “ms^-1” which is ‘per millisecond’. Similarly, VCAA used to write “ms^-2” for acceleration, which is totally absurd.
Thanks, Daniel. I haven’t seen the exam yet, but if Q5 does what you say, I’ll definitely have something to say about it, beyond “frustrating”.
I don’t care about units, but if the convention is to write m s-2 rather than ms-2 then it’s good that VCAA fixed it. But it just seems to be a convention, right? For example, ab-1 doesn’t mean (ab)-1, unless there’s some stupid BODMAS convention of which I am unaware.
OK, I’ve seen the paper now and Q5 is really annoying. I agree that it won’t likely cause confusion – the psychometrician defence – but it is blatantly wrong and needlessly wrong. And I’ve repeatedly hammered this point: see here and here and here and here. Just really stupid.
It demonstrates that the VCAA writers either do not read this blog, which they damn well should, or they still don’t know what the hell they are doing.
Algebraically, of course (ab)^-1 and ab^-1 are different for non-zero pronumerals a and b. However, the ‘m’ in “ms^-1” is a prefix, so the entire unit “ms” (millisecond) is being raised to the power -1, and just so happens to require multiple letters to write. Just very unfortunate that “m” is used for both ‘metres’ (unit of length) and for ‘milli’ (×10^-3 prefix).
For another cursed fact, the units for the variance of the cost of a weed trimmer in question 6 is measured in square dollars ($^2).
1. Paper was easier than we have seen in a long time, not just because there were no complicated irrational solutions (which I think is artificial difficulty anyway, but the people at MAV may feel a little let down), but the skills required were a bit boring.
2. In Q1, why bother to ask students to represent such basic complex numbers on the plane? Is this just checking if they recognise 2/3<1?
3. Repeated testing of cross products in a 1 hour paper seems to be waste of opportunity to assess other knowledge – very little circular function work.
Thanks, EM. So a little unbalanced and a little easy? I’m not sure why you are against irrational tinkering (or why the lack of it might annoy the MAV.)
I don’t mind arithmetic processes having some challenge embedded in them (there was none in this exam), but MAV trial papers seem to be a little obsessed by it. I don’t like it when this gets too heavily in the way of students being able to demonstrate their knowledge of the content.
Something I find interesting with hindsight: in the past, questions that have been done badly in one year get repeated the following year (more or less). But in 2023 the examiners’ report said that cross-products, lines and planes were done well, yet they appeared twice in the 2024 paper.
OK, I looked at the “skew line” thing. There is no question that this is a screw-up. As people have suggested, however, it may have been a screw-up that teachers and students had already factored in, and so may not have had much effect on exam scores: the psychometrician defence, once again. But it is a screw-up nonetheless. Here are my thoughts.
To begin, as vce maths student pointed out in the first comment, the Study Design, which works more like a Rorschach test than a curriculum, makes no mention of distances between lines and/or planes and/or points, or of “skew” things. (See our hammering, here, here and here. ) Ditto the formula sheet. Nonetheless, the VCAA sample materials contain some distance questions, and last year’s Exam 2 contained a couple distance questions. So, Study Design silence notwithstanding, it must have been common knowledge that geometry distances were examinable. However, there are howevers:
*) Yes, we’re stuck with Leigh-Lancaster’s execrable SD for at least another couple years, but why the hell are the distance formulas still not on the formula sheet? Can VCAA’s nitwits really not recognise that this is a serious flaw, particularly given the idiotically silent SD? They really seem to just not give a shit.
*) The VCAA sample materials and 2023 Exam 2 contain distance questions, including parallel line-line distance, but no skew line-line distance questions.
*) I’m now guessing here, but I think this is probably the reason for the rather clumsy insertion of “skew” in the 2024 exam question. It feels as if the purpose was to flag to the students that it was not a parallel line-line question, so that students would not autopilot with the more familiar scenario.
*) It is still not exactly clear to me where or why students would have seen skew line distance, although commenters here do not seem that fussed.
Thanks, WW. The general feeling seems to be that Exam 1 was too easy. Was that made up for in Exam 2, and did Exam 2 have an integration by parts question (although parts is still better as an Exam 1 question)?
The study design has no mention of skew lines nor the distance between two skew lines whatsoever yet the question 10 asked to find the values of m such that the distance between the two skew lines is 14/root(35). Whilst it is covered in textbooks, the formula isn’t on the formula sheet and neither is a bound reference permitted. Is this even assessable?
Was it necessary to know what a skew line was in order to solve the question? If not I think it would be reasonable for a spesh student to derive the equation on the spot if they had not memorised it previously.
Thanks, Chris. Was the term “skew” semi–foreign to students? What about the substance? Would most students have practised, or even seen, any L-L distances? Is it in the texts? (I’m asking the World, not just you.)
If L-L distance was unseen by most students then I do not think it reasonable to expect that derivation/computation in the exam.
Thanks, vce.m.s.
My memory is that “distance” is not in the new SD or on the formula sheet, but was in the sample materials VCAA posted for the new SD. My memory is also that I hammered this very point on the blog, although I cannot locate the hammering right now.
Having said that, I think it is reasonable to interpret VCAA’s mish-mosh to imply that “distance” generally is part of the SD: if other distances are examinable, then why not line-line, skew or otherwise?
Having said that, that L-L distance is examinable does not mean it was smart or empathetic for VCAA to do so. It could well be neither.
I think distances are fine since usually they can be constructed using knowledge of scalar resolute which is part of the course, however there is no mention of whether the knowledge of skew lines is required (lines that do not intersect and are not parallel), and really I think the terminology should be avoided if its not particularly mentioned in the study design. But as Chris said, it is possible to derive the equation and most students would be aware of its meaning since it is covered in textbooks (including the formula).
So, the term “skew” was unknown to you, and puzzled you a bit?
What about (skew) L-L distance? Had you ever done one previously? Is it in the text(s)?
The term “skew” it self would have been familiar to students (including me), and finding the distance between two skew lines is part of the textbook exercises since the texts have included it even thought it isn’t explicitly mentioned in the course. It just is that VCAA should avoid terminology that isn’t mentioned in the study design it self.
I think they made this exam too easy, very standard and routine questions making it difficult to separate students who just did textbook excerises versus students who went beyond that. I’m scared the grade boundaries are going to be like 2022 where you need 38/40 to get an A+ for Exam 1.
Additionally, the word “skew”, although not technically in the SD, is only used to reinforce the idea that the lines do not intersect (which we already given that because the shortest distance wasn’t 0) and not parallel (which we can also see pretty clearly) so I don’t think the word “skew” disadvantaged students. (but perhaps they should have omitted the word “skew” all together, but I am not sure if that messes up the question because I am not a math expert)
Thanks, Everyone, so far. I haven’t seen the exam and I’ll have to look over my thoughts/writings on “distance”.
There is obviously a systemic issue, that the Study Design is a basket case of unclarity (and madness). Accepting that is the Wonderland world we have, the “skew distance” thing doesn’t sound like a big deal, but I’ll take a look.
Really like this paper, which is very straight-forward.
No mathematical error spotted.
The formatting and phrasing is MUCH better.
Thanks, Legionnaire. There was a suggestion that it may have been to easy. Any thoughts on that?
I also thought it was interesting that they didn’t do much to alter the style of question 1, a question that VCAA had leaked in the exam covers it released early October before re-uploading them all late October.
Click to access specmath1-cov.pdf
Highlight the invisible text on page 2 of the link I attached, and you get this. Exact same format, even the exact same question (question 1 on the real exam).
Question 1 (4 marks)
Consider the function with rule f (z) = 2z
4 − iz3 − 16z + 8i, where z ∈ C.
a. Verify that 2z − i is a factor of f (z). 1 mark
b. Hence, or otherwise, solve the equation f (z) = 0.
Give your answers in Cartesian form.
I didn’t even know about this until it was brought to my attention on reddit https://www.reddit.com/r/vce/comments/1ghsa2s/exam_leaks_why_the_exams_are_strange_this_year/ … interesting behaviour from an “assessment authority”.
Whoops.
Hi Legionnaire. I’ve now read the paper (quickly). I agree it is generally worded clearly, although I think it can still be improved. Short sentences are good.
Overall, I liked the exam. I felt it was mostly fair (in that good students will do well and only good students should perform well). A few questions slowed me down a bit but that is also more than fair on a Specialist paper; students who were not prepared I suspect will struggle to finish this paper; also not a problem.
Some questions (Q7) were the standard trick where a lot of marks will be lost due to a missing negative sign in the final answer (I’m only guessing, but it seems to happen a lot in SM papers).
Cross product of vectors appearing multiple times was interesting, but not unexpected.
The proof question (Q2) seemed a bit easy. Easier than previous years. Was this deliberate? I guess we will never know.
In question 5, the question states that a solid is formed when the curve is rotated about the x-axis, when what they really mean to be rotated is the region bounded by the curve and the x-axis over the given interval. This probably wouldn’t cause much confusion but it is still frustrating for this to appear year after year.
I see VCAA has finally fixed their spacing on units. In the previous study design, they forgot to include the space between ‘metres’ and ‘per second’ for velocity/speed causing the cursed “ms^-1” which is ‘per millisecond’. Similarly, VCAA used to write “ms^-2” for acceleration, which is totally absurd.
Thanks, Daniel. I haven’t seen the exam yet, but if Q5 does what you say, I’ll definitely have something to say about it, beyond “frustrating”.
I don’t care about units, but if the convention is to write m s-2 rather than ms-2 then it’s good that VCAA fixed it. But it just seems to be a convention, right? For example, ab-1 doesn’t mean (ab)-1, unless there’s some stupid BODMAS convention of which I am unaware.
OK, I’ve seen the paper now and Q5 is really annoying. I agree that it won’t likely cause confusion – the psychometrician defence – but it is blatantly wrong and needlessly wrong. And I’ve repeatedly hammered this point: see here and here and here and here. Just really stupid.
It demonstrates that the VCAA writers either do not read this blog, which they damn well should, or they still don’t know what the hell they are doing.
Algebraically, of course (ab)^-1 and ab^-1 are different for non-zero pronumerals a and b. However, the ‘m’ in “ms^-1” is a prefix, so the entire unit “ms” (millisecond) is being raised to the power -1, and just so happens to require multiple letters to write. Just very unfortunate that “m” is used for both ‘metres’ (unit of length) and for ‘milli’ (×10^-3 prefix).
For another cursed fact, the units for the variance of the cost of a weed trimmer in question 6 is measured in square dollars ($^2).
Ah, thanks, Daniel. So “ms” is ambiguous without the space (or brackets). Fair enough. I still don’t care about units, but I see what you’re saying.
What is wrong with the units for variance being $2? (I still don’t care.)
My thoughts:
1. Paper was easier than we have seen in a long time, not just because there were no complicated irrational solutions (which I think is artificial difficulty anyway, but the people at MAV may feel a little let down), but the skills required were a bit boring.
2. In Q1, why bother to ask students to represent such basic complex numbers on the plane? Is this just checking if they recognise 2/3<1?
3. Repeated testing of cross products in a 1 hour paper seems to be waste of opportunity to assess other knowledge – very little circular function work.
So overall a bit meh.
Thanks, EM. So a little unbalanced and a little easy? I’m not sure why you are against irrational tinkering (or why the lack of it might annoy the MAV.)
I don’t mind arithmetic processes having some challenge embedded in them (there was none in this exam), but MAV trial papers seem to be a little obsessed by it. I don’t like it when this gets too heavily in the way of students being able to demonstrate their knowledge of the content.
I see. Thanks, EM. The MAV is, of course, a basket case, so it’s hardly a surprise if their exams are more fussiness than depth.
Something I find interesting with hindsight: in the past, questions that have been done badly in one year get repeated the following year (more or less). But in 2023 the examiners’ report said that cross-products, lines and planes were done well, yet they appeared twice in the 2024 paper.
Not sure what this means (if anything).
OK, I looked at the “skew line” thing. There is no question that this is a screw-up. As people have suggested, however, it may have been a screw-up that teachers and students had already factored in, and so may not have had much effect on exam scores: the psychometrician defence, once again. But it is a screw-up nonetheless. Here are my thoughts.
To begin, as vce maths student pointed out in the first comment, the Study Design, which works more like a Rorschach test than a curriculum, makes no mention of distances between lines and/or planes and/or points, or of “skew” things. (See our hammering, here, here and here. ) Ditto the formula sheet. Nonetheless, the VCAA sample materials contain some distance questions, and last year’s Exam 2 contained a couple distance questions. So, Study Design silence notwithstanding, it must have been common knowledge that geometry distances were examinable. However, there are howevers:
*) Yes, we’re stuck with Leigh-Lancaster’s execrable SD for at least another couple years, but why the hell are the distance formulas still not on the formula sheet? Can VCAA’s nitwits really not recognise that this is a serious flaw, particularly given the idiotically silent SD? They really seem to just not give a shit.
*) The VCAA sample materials and 2023 Exam 2 contain distance questions, including parallel line-line distance, but no skew line-line distance questions.
*) I’m now guessing here, but I think this is probably the reason for the rather clumsy insertion of “skew” in the 2024 exam question. It feels as if the purpose was to flag to the students that it was not a parallel line-line question, so that students would not autopilot with the more familiar scenario.
*) It is still not exactly clear to me where or why students would have seen skew line distance, although commenters here do not seem that fussed.
This is no question on Intergration by part, it was new last year for VCAA and was on the exam 1. Overall, the exam 1 is too easy.
Thanks, WW. The general feeling seems to be that Exam 1 was too easy. Was that made up for in Exam 2, and did Exam 2 have an integration by parts question (although parts is still better as an Exam 1 question)?
Why would a CAS exam test integration by parts.
Or, perhaps a better question is HOW?
I dunno. I don’t think about what CAS may or may not test, since it’s all garbage.
Yeah, I really need to remember to add the sarcasm tag at the start of some of my comments…