Maths Extension 2 Thoughts and Feelings (1 Viewer)

[youssseeefffff-wahbbbaaa]

q16d was a neat q.
You need to recognise that it was somewhat a polynomial question.

u get |z1| = |z2| = |z3| = 1.
z1+z2+z3 = 1, z1z2z3 = 1.
1/(z2z3) + 1/(z1z3) + 1/(z1z2) = 1.
=> z2z3 + z1z3 + z1z2 = 1 (noticing mod = 1, 1/z = z_conj, and then noticing rhs is real)
Notice that you get sum, product, sum of two roots formulas. Then you can make a cubic polynomial and solve that for the three complex numbers.

if this is not the correct method, well oops lol

Yo sorry i never read this, i just posted my solution to this (though i didnt actually have enough time to complete in the test) and coincidentally it was the exact same as urs. Congrats on solving it, just wanna make it clear that i didnt mean to plagiarise lol

 

[okkk]

This is because v is defined as velocity in the solution (with upwards defined as positive) instead of speed (which is what most people do). When you define v as speed then you tend to define the direction of motion as positive. This usually makes adding/subtracting the vectors more intuitive as you can define the signs yourself using the magnitudes given - i.e. you don’t need to think about the sign of v.

Once you define v as velocity (which is a vector quantity), you have to take a bit more care on the signs because the vector can change direction.

Technically speaking though the question defined v as speed…

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

 

[notme123]

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

conservation of energy is violated if the time going up and down is the same. should take longer to go down. that's why assuming impact speed is v0 is also completely wrong.

It's impossible to construct unit vectors that add together to get one if one of the is not one. For example, construct the first one anywhere you want, then consider the second vector as one, if it shifts up or down, the distance between its tip and 1 would change and it no longer 1, so the third vector cannot get to one if the second vector is not 1. I think at least, I can't visualise a counter example

ye i cant think of a good counter example but the method isn't rigorous or rather there isn't some established way to reach that conclusion

 

[okkk]

conservation of energy is violated if the time going up and down is the same. should take longer to go down. that's why assuming impact speed is v0 is also completely wrong.


ye i cant think of a good counter example but the method isn't rigorous or rather there isn't some established way to reach that conclusion

Ah I can say that cos our four vectors are z_1, z_2, z_3 and 1, and they all have modulus one, i.e 4 sides are equal, it has to be a rhombus which has parallel sides. so therefore one of them also has to be 1. That works right (hopefully lmao my yr 9 geometry is rusty)?

 

[notme123]

Ah I can say that cos our four vectors are z_1, z_2, z_3 and 1, and they all have modulus one, i.e 4 sides are equal, it has to be a rhombus which has parallel sides. so therefore one of them also has to be 1. That works right (hopefully lmao my yr 9 geometry is rusty)?

maybe if you had a diagram to explain it it would be easier but idk how you get a rhombus. did you do this in the actual exam?

 

[okkk]

maybe if you had a diagram to explain it it would be easier but idk how you get a rhombus. did you do this in the actual exam?

Yeah I did , it's a rhombus cos a rhombus is (well can be) defined as a four sided shape with equal side lengths and it's the only one with the definition (square is a rhombus) so that's the conclusion right?

 

[idkkdi]

It's impossible to construct unit vectors that add together to get one if one of the is not one. For example, construct the first one anywhere you want, then consider the second vector as one, if it shifts up or down, the distance between its tip and 1 would change and it no longer 1, so the third vector cannot get to one if the second vector is not 1. I think at least, I can't visualise a counter example

On second thought, your way works.

|z1|=|z2|=|z3|=1 and z1+z2+z3 = 1 does imply a rhombus with vectors z1,z2,z3, and (1,0).
Since a rhombus has parallel sides, one of z1/z2/z3 has to be the vector (1,0).
Not completely sure if you'll get the marks since it's HSC marking, but this method does work fine imo.

 

[Vall]

idk why smh articles make me cringe a little inside.

some friends and I were saying this on our discord. It feels like they have a bunch of template articles to release around HSC time.

 

[maths4dayz]

I probs got between 85 and 90 but pretty annoyed at how hard that was. I reckon an extra 20 or 30 minutes would've gone a long way. I got most of the vector, mechanics and proof questions but the complex number ones were random and I had a wtf moment. It was weird how they put in some easy questions though.

 

[ExtremelyBoredUser]

I probs got between 85 and 90 but pretty annoyed at how hard that was. I reckon an extra 20 or 30 minutes would've gone a long way. I got most of the vector, mechanics and proof questions but the complex number ones were random and I had a wtf moment. It was weird how they put in some easy questions though.

yep same assuming the solutions made are accurate, the paper felt inconsistent. MC was half hard, half easy. Q11-13 was really standard. Q14-15 was extremely slow pacing. Q16 was hard given the time crunch.

 

[tgone]

Id say the most ridiculous mcq were 7, and 9.

7. Idk if they expect us to prove the converse or something, but I said it was true with the few examples I could find, which is not a proof.
9. This question involved a little bit of circle geo theorem which would fly over many students' heads perhaps. I haven't done vector proofs on a circle since hsc so it took me a few minutes to remember so maybe it would've been easier for youse idk.

the converse was very straightforward if you take the contrapositive

edit: didn't see that solutions were already posted... oops

 

[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.

 

[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)

 

[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)?

 

[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