ExtremelyBoredUser
Bored Uni Student
Pre sure scalings gonna be generous considering how the exam threw most people off
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Maths Extension 2 Thoughts and Feelings (2 Viewers)
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ExtremelyBoredUser
Bored Uni Student
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
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
yanujw
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I'm not convinced this works. If you assume this is true and divide by z1z2z3 for example, you get 1/z1 + 1/z2 + 1/z3 = 1/z1z2z3. RHS has a modulus of 1 while the LHS has 3 terms of modulus 1. Although, maybe that is a hint in solving the equation, so feel free to correct me if I'm wrong.
that's the same as saying z1 + z2 + z3 =/ 1 since lhs has mod 3 lol. ur missing that mod includes imaginary parts
i.e. |1/z1 + 1/z2 + 1/z3| =/ |1/z1| + |1/z2| + |1/z3|
q9. s1 was a sphere. s2 was a plane. they intersect to form a circle. and then u do some simple trig to get the answer. but ye, definitely some imagination involved there.
jamal123999
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yo what was the answer for 16b, for initial velocity, was it 39.1ms^-1?
Jordi El Nino Polla
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Brutal by the reactions here. When I did my HSC in 2021 I thought that paper was way harder than 2020, didn't expect 2022 to be even worse.
Lowkey pretty upset with this exam, Did the 2020 and 2021 exams timed and easily cleared e4 aligned, this year I am hoping for low 60s raw. NESA better make align marks significantly better to make up for just how much harder this test really was. Oh well, hopefully I can make up for it with 3u on monday.
MemeCognoscente
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Yeah surely that's wrong, the person assumed that the impact speed of impact to the ground is the same as the initial velocity unless I'm missing something normally it's different
the assumption is completely wrong lol. violates conservation of energy
But overall, I think this test was good actually. Time would've been your worst enemy. There was less room for silly mistakes compared to last year since this year there were way more 'show' questions. q16 this year i reckon was more challenging than last year but the rest of the test was on the same level. Especially that last sum and product of roots q. if you hadn't seen that q before, you would've been stumped (like I was). 16(a) and (c) were fine tho. 16(b) on the other hand felt illegal lol. Would never think of integrating 0 -> 0, especially when air resistance changes direction during flight.
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(teacher) very difficult paper, harder than sample, 2020, 2021. q11,12,13 good q14,15,16 ridiculous. mult choice also horrible. I reckon I only got 80 in the time frame. Advice - nothing you can do now, everyone is in the same situation. put it from your minds and prep for ext1. and also, this stupid exam doesn't define you.
Actually 1 question id like to comment on is 14 a) i. This is about linear independence which is an algebra concept that comes up in uni. From what I recall, I was not taught this in high school. Sure you could figure it out by saying they're not parallel but throwing students straight into a proof like that is whack.
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.
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I find it interesting that a number of the harder or more unusual questions in Ext2 lately come from topics that existed in the old syllabus. Where were these in the 2010s? In the years before the new syllabus, the HSC exams trended towards being more boring/generic (with a few exceptions) which makes you think the writers got lazier or just ran out of ideas. However, they seem to have gotten a refresh, particularly after 2020 and put in some questions in those old syllabus topics that were a little unexpected (compared to papers in the 2010s) and arguably more challenging than some of the harder trial papers.
Will be interesting to see if this is sustained or whether it will also eventually become more generic over time.
Will be interesting to see if this is sustained or whether it will also eventually become more generic over time.
Question 9 didn't need circle geo right, it was just pythag with hypotenuse as radius of the sphere in the first set, the radius that we're trying to find and 1/4 the length of AB
the dot product = 0 of two points forming a sphere is kinda derived from a circle geo thing, where if A and B are on the same diameter, both lines joining to any point on a circle are perpendicular. idk i feel you need to be a bit creative as someone said earlier. not hard once you got it tho