Maths Extension 2 Thoughts and Feelings (1 Viewer)

[Allan Mekisic]

 

[Daedalus13]

It's just I graphed the curve she got for x on desmos, and it's symmetrical about the turning point implying that the time it takes to reach max height is the same as it takes to fall to the ground and that's not right right? It should take longer to fall down is my understanding of mechanics, I'm still struggling to understand how v is a vector resolves this asymmetry

I graphed the x function and the axis of symmetry is around 3.3 (using v_0 = 39.1), not quite 3.5. So the solution is valid, with the time to fall longer than the time to go up.

 

[tywebb]

For 16b, with resistive force acting in the same direction as when it goes up as it goes down you get 39.1 as has previously been demonstrated. However if you assume the direction of resistance changes when it goes down you would expect the value will have to increase slightly in order for it to reach the ground again in the same time of 7 seconds. A number of perhaps 41.9 for example.

 

[Daedalus13]

For 16b, with resistive force acting in the same direction as when it goes up as it goes down you get 39.1 as has previously been demonstrated. However if you assume the direction of resistance changes when it goes down you would expect the value will have to increase slightly in order for it to reach the ground again in the same time of 7 seconds. A number of perhaps 41.9 for example. See the attached solution with this change in mind - but it is a little harder to do. Sorry if there are typos. If so I'll fix it later.

On the way down, the velocity is negative (as you define upwards as positive). In this case, an 'resistive force' of 0.1v is still negative i.e. in the same direction as the velocity. So your resistive force is pushing the mass down when it should be pushing it up. You should have a = -g - 0.1v as your equation on the way down to ensure the -0.1v is pointing up. Note this is the exact same as the equation on the way up, so you don't need to separate. (Even if you do, the answer is the same, 39.1)

 

[tywebb]

On the way down, the velocity is negative (as you define upwards as positive). In this case, an 'resistive force' of 0.1v is still negative i.e. in the same direction as the velocity. So your resistive force is pushing the mass down when it should be pushing it up. You should have a = -g - 0.1v as your equation on the way down to ensure the -0.1v is pointing up. Note this is the exact same as the equation on the way up, so you don't need to separate. (Even if you do, the answer is the same, 39.1)

Oh yes so v changes direction and hence so too does -0.1v. So I think we can concur now that 39.1 is the correct answer.

 

[Life'sHard]

2022 looks like a fun exam. From the brief skim I had, I am seeing quite a few "show" qs (which I prefer). Is it just me or does this paper look a lot longer than normal lol. Weird linear independence q on no. 14 (uni stuff??). Q15 just looks like a physics q. Also a lot more integration which is always nice to see. With the vector qs, I feel like you've just got to have the vibes when doing them lmao. And Q16 is well, question 16. Multiple choice looks chills for the most part. Oh well, now that the hell that is math ext 2 is done, ext 1 should be a breeze.

 

[dgns]

Typeset solutions. Hopefully not too many mistakes : )

Shouldn't the answer to Q8 be (b)?

 

[tywebb]

Shouldn't the answer to Q8 be (b)?

Well if you look back at Lkc36's solutions from a previous post it is explained why it is indeed B

 

[ExtremelyBoredUser]

2022 looks like a fun exam. From the brief skim I had, I am seeing quite a few "show" qs (which I prefer). Is it just me or does this paper look a lot longer than normal lol. Weird linear independence q on no. 14 (uni stuff??). Q15 just looks like a physics q. Also a lot more integration which is always nice to see. With the vector qs, I feel like you've just got to have the vibes when doing them lmao. And Q16 is well, question 16. Multiple choice looks chills for the most part. Oh well, now that the hell that is math ext 2 is done, ext 1 should be a breeze.

Enjoyed 90% of the time, hell the last 10% of the time. Really long exam IMO, bogged down in algebra by 16b) because i split the motion into 2 parts . This is more of a test of how quick are you able to solve the decent qs in q11-15 and have enough time to think abt q16.

I'm sure the 2023 cohort's going to enjoy doing this as a practice exam.

 

[dansk1er]

What's everyone's predictions on the e4 cut-off for this year? Sounds like many of you here are going well above it, but it's gonna be tight for me.

 

[Run hard@thehsc]

What's everyone's predictions on the e4 cut-off for this year? Sounds like many of you here are going well above it, but it's gonna be tight for me.

idk but last year a 65 went to 88. And judging by the overall consensus that the test was as difficult if not more than last year, I would guess around 65, maybe 66 to be the cut off. But honestly, we do not have control over this, and this alone will make us stressed thinking about this. ig better to move on to other subs

 

[tgone]

What's everyone's predictions on the e4 cut-off for this year? Sounds like many of you here are going well above it, but it's gonna be tight for me.

yeah, thinking around 63-65 based on previous years' scaling and difficulties

 

[Allan Mekisic]

I have a slightly different view about the extension 2 exam to others. I am a mature age self tuition student who sat extension 2 last year and this year for fun because I enjoy maths. I found both exams difficult for different reasons. I was much better prepared this year but I agree this years exam was more difficult. The main difference between the two exams is question 14. Last year, question 14 was a gift. This year, it was long , extremely difficult and poorly rewarded. Only 2 marks for the induction question (b) part (iv). This question was far too long and I’m not sure the vectors question is within the scope of the syllabus. Question 15 was also very long and poorly rewarded. I spent a long time drawing a force diagram and eventually was able to resolve the vertical and horizontal components and solve part (i). Could not do part (ii). In retrospect, I think question 16 part (c) and (d) were relatively straight forward however most of us by this stage were exhausted and my brain was like mush. In hindsight, I would like to have done question 16 first.

 

[rickonda]

I have a slightly different view about the extension 2 exam to others. I am a mature age self tuition student who sat extension 2 last year and this year for fun because I enjoy maths. I found both exams difficult for different reasons. I was much better prepared this year but I agree this years exam was more difficult. The main difference between the two exams is question 14. Last year, question 14 was a gift. This year, it was long , extremely difficult and poorly rewarded. Only 2 marks for the induction question (b) part (iv). This question was far too long and I’m not sure the vectors question is within the scope of the syllabus. Question 15 was also very long and poorly rewarded. I spent a long time drawing a force diagram and eventually was able to resolve the vertical and horizontal components and solve part (i). Could not do part (ii). In retrospect, I think question 16 part (c) and (d) were relatively straight forward however most of us by this stage were exhausted and my brain was like mush. In hindsight, I would like to have done question 16 first.

It was interesting to see linear independence tested in Q14a

 

[notme123]

I’m not sure the vectors question is within the scope of the syllabus.

If you're talking about 14a, all of it was in scope including the linear independence part, but it provided a little taste of the abstract world of uni linear algebra.

The current 4u syllabus IMO has too much physics and mechanics in it and not enough of that abstract maths. If they were ever to reform the syllabus the top priorities I suggest are (extreme and uniformed opinion incoming):
1. Truth tables in proofs. I did this in my discrete maths uni course in a topic called 'Logic' and proof tables was actually really neat to learn since they're so relevant and really helpfil. I guess logic proofs could also be added since they use all the concepts like contrapositive and converse already.
2. Delete SHM and some other mechanics. They're not maths idk why they're here. Physics should take these topics. Ik IB phys has them, why not HSC Phys. In phys these concepts can get the proper depth they deserve, using concepts like work, which isn't covered in maths.
3. Add Further Work on Functions. In uni, many students struggle with concepts like the formal definition of limits, continuity, and differentiability, and doing this in 4u would've been helpful.
4. Expand 3d vectors. Cross-product should get added too. And if they really wanted to be demanding sure linear independence is welcome.
If anyone thinks this is too much to ask (which it kinda is) all these things I mentioned are taught within the span of 3-4 weeks in uni. They're really not that deep.

The point of the new syllabus in 2020 was to get rid of that obsolete archaic high school math (e.g. conics and volumes) and introduce more relevant content that will be expanded in the future should people choose maths in tertiary study. I don't know why they half-assed it with this new syllabus.

EDIT: AND another thing. Get rid of one-to-one, many-to-one etc all those function types from advanced. this will never be used again ever again. instead just use injective, surjective, bijective (along side formal definitions of functions like f: R->R). much easier for everyone.

 

[Life'sHard]

3. Add Further Work on Functions. In uni, many students struggle with concepts like the formal definition of limits, continuity, and differentiability, and doing this in 4u would've been helpful.

I second this. Limits, continuity, and differentiability are quite interesting and intuitive topics if learnt correctly and by far way better topics than mechanics.

 

[idkkdi]

I second this. Limits, continuity, and differentiability are quite interesting and intuitive topics if learnt correctly and by far way better topics than mechanics.

that shit is boring as.

ok tbf, epsilon delta's pretty neat. otherwise mech much more fun topic

 

[notme123]

bro what are you on. that shit is boring as.

ok tbf, epsilon delta's pretty neat. otherwise mech much more fun topic

ik they're boring as shit but imagine learning them properly and structured like in high school. I'm sure nesa can spice them up.

its just i don't want people learning this stuff in uni when lecturers start overusing the word 'trivial' for not so straight forward things

 

[idkkdi]

ik they're boring as shit but imagine learning them properly and structured like in high school. I'm sure nesa can spice them up.

then ur lowkey learning nothing in t1 uni tho lol.

 

[notme123]

then ur lowkey learning nothing in t1 uni tho lol.

true. there's still all those limit things like lohpitals, squeeze, and theorems like minmax, mean value, intermediate value. all these should stay in uni.