[Live POV] 2023 Extension 2 Maths Paper except you are the teacher seeing it for the first time. (1 Viewer)

[epicmaths]

Hi all, first post here!

I've been working in education for a bit over a decade a have taught cohorts in the previous Ext2 HSC course. Have not yet taught a class for this new syllabus but have some cursory knowledge of the new NESA syllabus.

Decided on a whim to spend the next 3 hours and 10 minutes attempting this under exam conditions.

Will this be a massive flop? Find out together at:

youtube user: epicmaths

I might later on correct the attempt and have a link of improved solutions.

PS. Don't dox me and I won't dox myself
PS. Don't be distracted by this if you are studying for another exam!

 

[epicmaths]

Can anyone confirm if Q15a ii) was a typo or just my poor algebra? Cheers!

 

[scaryshark09]

Can anyone confirm if Q15a ii) was a typo or just my poor algebra? Cheers!

The question is correct, there is no typo

 

[epicmaths]

Nuts just saw Mok's solution, certainly a question worthy of 4 marks! I did think of doing x=2\theta but promptly wrote x=\pi /2 and gave up, video evidence!

 

[shywa]

What were your thoughts on the exam?

 

[epicmaths]

It was quite time pressured, with an equal amount of insightful, standard, tedious and quirky questions. Certainly harder than what I was used to in the old syllabus. The unscaffold Q16b was as difficult as any of the previous syllabus's final questions.

I would say the new syllabus favours naturally bright students, there are less things you can just coach students up for.

 

[scaryshark09]

What were your thoughts on the exam?

Yeah, do you know what the difficulty was @epicmaths?
How would it compare to previous HSCs?

 

[epicmaths]

@scaryshark09 I certainly felt less prepared....I've only briefly looked at the 2020-2022 papers, and the vectors, proofs and newer mechanics concepts are big unknowns that are stressful. The 10minutes of reading time was not reassuring at all.

In comparison to things like Conics, Circle Geometry, and Further Complex (applied to polynomials), those old topics were far more self contained.

 

[hehe43]

@epicmaths not to invalidate your opinion but every teacher I've talked to who has taught both new and old syllabus ext 2 agrees that the new syllabus is less strenuous and less broad. A lot of stuff from the old syllabus in topics that remained had also been removed. A lot of students also didn't see this exam to be much more difficult than a typical ext 2 paper.

 

[epicmaths]

Re 16a) iii)
I've since had a look at the other solutions - pardon my ignorance but I felt uncomfortable just multiplying the two cases =0 which I can see is what the question is intending. Here is my solution which I am more comfy with.

Can anyone give a non-tertiary rationale for the solutions from the other forum post where they multiply ii) and iii)? I thought you can't have the two orientations occurring simultaneously...

 

[Sam14113]

Re 16a) iii)
I've since had a look at the other solutions - pardon my ignorance but I felt uncomfortable just multiplying the two cases =0 which I can see is what the question is intending. Here is my solution which I am more comfy with.

Can anyone give a non-tertiary rationale for the solutions from the other forum post where they multiply ii) and iii)? I thought you can't have the two orientations occurring simultaneously...

I much prefer your solution but I'll explain why their solution is valid (at least as I understand it):
In short, the triangle is either clockwise or anticlockwise.
If the triangle is anticlockwise, then
Similarly, if the triangle is clockwise, then

So either way, the product evaluates to 0

Okay now time for a personal rant (feel free to ignore):
It's still a weird solution in my opinion - like when you're given two different cases (for instance 2020 HSC 15 (a) (iii) ) you don't blindly hope that the one case happens to be the missing puzzle piece for the other case - you treat the two cases separately. Especially here where the result is symmetric in a,b,c so a result for just an anticlockwise triangle will automatically apply to both triangles, there's no mathematical reason (at least as I can see) to actually keep the second case alive -- except that the question subtly hinted at it and it happens to work if you try. Anyway that's just one question, still think the rest of the paper was super well-written

 

[epicmaths]

Ooooh yea when only one of them need to be 0 at any one time so in either case noway! I'm so rusty.

I vibe with your rant though - I try to read into the intention of the question and work backwards from it, so the whole point of introducing the clockwise triangle is not that there is anything mathematically significant about the 2nd case that we need to separately consider, but an excuse to not-so-subtly funnel us into using a symmetrical expression to help simplify.

I will have a further think about 16c and the spiral when I get a spare moment from performing my day job as classroom management.

 

[Sam14113]

I made a pdf of screenshots from last night's youtube solutions. It will only take a minute to look through it instead of 3 hours!

Note there are some wrong like 16c not the whole quadrant etc.

There are probably a few too many pages because there is some insert which sometimes covered stuff up and you can't see it. If that insert wasn't there there would be fewer pages.

I'd probably relabel to 'attempt' rather than 'sols' as epicmaths made it clear that he was just trying to complete the paper under exam-style conditions.

 

[epicmaths]

Thanks Tywebb and Sam14113, that Q5 was embarrassing!

After considering 16c and arriving at the same answer - I can appreciate the open-ended format of the last question to really differentiate the top students.

I'm starting to form the belief that this recent trend of hard multi-choice that makes you consider four theoretical statements to not be a great use of the format. YMMV.

If I get some time later this term I will tidy up the iPad document and post a corrected version. But certainly not a state ranking worthy attempt from me - maybe in a later year when I've taught the course with a cohort and get more comfortable with the new topics!

 

[Sam14113]

Thanks Tywebb and Sam14113, that Q5 was embarrassing!

After considering 16c and arriving at the same answer - I can appreciate the open-ended format of the last question to really differentiate the top students.

I'm starting to form the belief that this recent trend of hard multi-choice that makes you consider four theoretical statements to not be a great use of the format. YMMV.

If I get some time later this term I will tidy up the iPad document and post a corrected versiion. But certainly not a state ranking worthy attempt from me - maybe in a later year when I've taught the thing and get more comfortable with the new topics!

Lol all good - everyone's done a 3-2=0 before!

I completely understand your view on the multiple choice questions but I personally do actually like it - I think that it tests for your understanding in a way that written questions can't, and doesn't just make you perform a 3-4 mark calculation question for 1 mark multiple choice. The ones this year were alright, but I particularly like the ones from mx1 last year (especially Q9 -- tests if you really understand what's going on with inverse functions intersecting the original, to eliminate option (a)). I do see your point though that it can take more time as you have to consider all of the options carefully to pick the right one.

Just thought I'd share my opinion - again completely understand where you're coming from and think you have a legitimate point of view.

 

[Luukas.2]

I'm starting to form the belief that this recent trend of hard multi-choice that makes you consider four theoretical statements to not be a great use of the format. YMMV.

I think that many of these difficult MCQs are more easily approached by eliminating incorrect answers rather than identifying the correct one. This can be a case of applying examination technique strategically, which can be of questionable educational value... but it can also be an application of valuable skills of reflection, by supposing that your working produced each answer in turn and reflecting on whether that answer is reasonable / plausible. Many silly / careless mistakes in SA questions can be identified as wrong by reflecting on whether the answer is reasonable, and so this is a skill that students should be developing and using routinely, in my opinion. If these harder MCQ help foster that skill then they can have educational value.

Related to this point, I have posted a thread in the Extension 1 forum about a multiple choice question where reflection on the solutions provided shows that the method leads to two solutions, one of which is invalid. I think that questions that require this sought of awareness are good tests of understanding that can be included as part of more challenging multiple choice questions.

 

[ExtremelyBoredUser]

I think that many of these difficult MCQs are more easily approached by eliminating incorrect answers rather than identifying the correct one.

Did this when I did the HSC. This is the strat for any MCQ tbh, just saves so much time when you can narrow your options down rather than just hunting for the solution.

 

[011235]

I'm starting to form the belief that this recent trend of hard multi-choice that makes you consider four theoretical statements to not be a great use of the format. YMMV.

Imo, this depends - what is the purpose of the question? Is it to test mathematical intuition and ability for deduction? In which case I think it is a good use. Or, is it to test direct knowledge of the course content, and the ability to form evidence-based conclusions with rational logic? If so I don't think it is a good use.

I feel the MC in recent years has been more on the side of the first, given that short answers do not give much room for that.

 

[Luukas.2]

Imo, this depends - what is the purpose of the question? Is it to test mathematical intuition and ability for deduction? In which case I think it is a good use. Or, is it to test direct knowledge of the course content, and the ability to form evidence-based conclusions with rational logic? If so I don't think it is a good use.

I feel the MC in recent years has been more on the side of the first, given that short answers do not give much room for that.

People like to see exams as a test of knowledge / understanding, but the true purpose is to produce a ranking order of candidates from first to last. If that order happens to correlate at least moderately well with knowledge or understanding, that's a bonus.

The mark someone achieves on an exam is an excellent measure of how they performed on that exam... it is not necessarily a good measure of knowledge of a subject, understanding, mathematical insight (in the case of a Maths exam), potential for achievement in a future university course, general intelligence, worth as an individual, future worthy, desirability as a partner, likely life span, nor average length of nostril hairs at age 60.

HSC results and ATAR will have a substantial impact on people's short-term future, but results below what is sought can merely slow progress towards a goal. They become less important as they disappear into the past.

Exam results are for ranking / filtering to fit the systems we have, but remember that they are (at best) an imperfect and incomplete snapshot. Every single person is far more than their ATAR and exam results.

 

[011235]

People like to see exams as a test of knowledge / understanding, but the true purpose is to produce a ranking order of candidates from first to last. If that order happens to correlate at least moderately well with knowledge or understanding, that's a bonus.

The mark someone achieves on an exam is an excellent measure of how they performed on that exam... it is not necessarily a good measure of knowledge of a subject, understanding, mathematical insight (in the case of a Maths exam), potential for achievement in a future university course, general intelligence, worth as an individual, future worthy, desirability as a partner, likely life span, nor average length of nostril hairs at age 60.

HSC results and ATAR will have a substantial impact on people's short-term future, but results below what is sought can merely slow progress towards a goal. They become less important as they disappear into the past.

Exam results are for ranking / filtering to fit the systems we have, but remember that they are (at best) an imperfect and incomplete snapshot. Every single person is far more than their ATAR and exam results.

I absolutely agree with every single part of this.

Particularly in that exams are an incomplete snapshot of a person's ability -- even their ability in that field of study.