In the physical copy of yesterday's Sydney Morning Herald they included a photo of Xu's solution to 16c. But stupidly it's cropped and you can't see a lot of it.
Here is a better photo uncropped.
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[Live POV] 2023 Extension 2 Maths Paper except you are the teacher seeing it for the first time. (2 Viewers)
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Here is a better photo uncropped.
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
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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.
itute solutions, but I think their 16c is wrong: https://www.itute.com/wp-content/uploads/2023-NSW-ESA-Mathematics-Extension-2-Solutions.pdf
Here are my solutions. https://4unitmaths.com/hsc2023e2-tywebb.pdf
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.
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.
Something very eldritch happened in my latexed solutions and those with esoteric knowledge of latex may know how to fix it but I don't.
The eagle-eyed may have noticed it but you have to look very closely to see it.
I call it the latex triple dot weirdness
There are 2 instances of using triple dot here. Comparing the size of the dots in the second instance in the numerator the second and third dots are larger than the first.
1st instance (normal)
2nd instance (weird)
So the question is why and how to fix it?
This is the latex code I used
Code:
$\ddot x=-16\sin4t-16\cos2t$ and $\dddot x=-64\cos4t+32\sin2t$
\
If it were simple harmonic we would have $\ddot x=-n^2(x-c)$ for some positive number $n$ and a real number $c$ in which case $\frac{d\ddot x}{dx}$ would be the negative constant $-n^2$.
\
But $\frac{d\ddot x}{dx}=\frac{\dddot x}{\dot x}=\frac{-64\cos4t+32\sin2t}{4\cos4t-8\sin2t}$ which is not constant and so it is not simple harmonic in which case the answer is $B$I also tried \dddot x\over\dot x but that also has the triple dot weirdness.
I also tried
Code:
$\frac{d\ddot x}{dx}=\ $\scalebox{0.67}{$\dfrac{\dddot x}{\dot x}$}$\ =$
but that created new problems
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Hey I fixed it using 2 vertical phantom characters but the code is ugly
Surely there's a more elegant way to fix the latex triple dot weirdness!
Any ideas?
Code:
$\frac{d\ddot x}{dx}=\frac{\hskip0.012in\dot{\hskip-0.03in\vphantom x}\dot x\dot{\hskip-0.018in\vphantom x}}{\dot x}=$Surely there's a more elegant way to fix the latex triple dot weirdness!
Any ideas?
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harrowed2
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I think that the author of the itute solutions is saying that the ray in the 3rd quadrant could rotate within the 3rd quadrant, depending on the position of z/w. So if arg(z/w) is very close to pi/2, then the resultant ray could be very close to the negative y axis.
But look at their answer
This is my answer:
Mine also agrees with Xu's, fizzysoda's, Mok's and Mind Your Decisions'
A wild guess but \overset maybe?
\frac{d\overset{.}{x}}{dx} = \frac{d\overset{..}{x}}{dx} = \frac{d\overset{\ldots}{x}}{dx}
I've been using \underset and \overset as a crutch ever since vector notation crept into the new syllabus.
In nesa's mg https://educationstandards.nsw.edu....-a2d37b93-72bb-4a62-b907-63aca804dc39-oL-IGGs they put this for 16c:
It is wrong. Can you see why wrong?
It is wrong. Can you see why wrong?
Exclude negative x-axis and (0,0):
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scaryshark09
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bruh nesa made this question so hard, that even they couldn't answer it
was anyone actually able to do this in the exam?
Yeah. If you look at post #21 you can see Vivian Xu did it.
Even more worrying is nesa encouraging students to use an inefficient method for 15bii resulting in a hopelessly laborious solution, painfully lexically dense, very unpleasing to the eyes, not at all appealing to the mind's eye - so much so any reputable publisher would reject it for publication
and although the question encouraged using vectors it didn't actually say that you had to, and if you don't you can do it this way instead which is much better:
and a version of this method was actually published in the American Mathematical Monthly.
We use vectors to make things easier, not harder, as is the case in many proofs of geometrical theorems. But that is not so in this case.
So one skill with vectors is knowing not just when to use it, but also when NOT to use it!
This skill seems to have eluded nesa in this exam.
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nesa had been informed of the error so we will see if they fix it.
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