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Which do you think is the hardest 4u question from like '90-now? I think it's definately Q8 b) iii) from the '00 paper. I've got no idea how to do it... Can anyone think of a harder one?
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Harimau
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I thought Q8b from 1989 paper was hard...
underthesun
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e irrationality? I still haven't looked at it yet..
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Actually i didn't think those were too bad (compared to the '00 one).
Harimau
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Stop making me cry...
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Heheh nah you misunderstood me, the irrationality ones were obviously difficult compared to most 4u questions, but i meant that the '00 one was much harder (IMO). I had a look at the '89 one, and yeh that looks pretty damn hard too (haven't had a go at it yet though).
turtle_2468
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1998? Whatever the polynomials one was... lol, I got that in a tutoring session (meaning I was tutoring someone else), that got me... lol.. I reckon even 2000 is more approachable than that. But hey, just me... I have a stuffed up sense of relative difficulty a lot of the time 
freaking_out
Saddam's new life
do u reckon they'll ask another one on the irrationality of "e" again?
SoFTuaRiaL
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BLEH! THEY'RE ALL EASY
freaking_out
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i wonder what u got 4 your hsc.Originally posted by SoFTuaRiaL
BLEH! THEY'RE ALL EASY
underthesun
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Dont' know, maybe this time pi irrationality. I think it's in the parabola magazine, after there was a hoax that the value of pi terminates after 3 billion places (UNSW maths magazine), not that I read it
Rahul
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maybe there should be a list of these possibilities....
freaking_out
Saddam's new life
hey, so where can i find the proof of pi irrationality and e irrationality (besides the past hsc paper).Originally posted by underthesun
Dont' know, maybe this time pi irrationality. I think it's in the parabola magazine, after there was a hoax that the value of pi terminates after 3 billion places (UNSW maths magazine), not that I read it
underthesun
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Dr Buchanan's website got the e irrationality proofOriginally posted by freaking_out
hey, so where can i find the proof of pi irrationality and e irrationality (besides the past hsc paper).
Fosweb
I could be your Doctor...
I think i remember seeing something on both of these in that Harder 3U thing on Dr Buchanans site. (The Bill Pender thing. Along with lots of other possible Q8 stuff.)Originally posted by freaking_out
hey, so where can i find the proof of pi irrationality and e irrationality (besides the past hsc paper).
Q8 is usually harder 3U right?
freaking_out
Saddam's new life
yeah it is....thanx, i'll go and download.
freaking_out
Saddam's new life
thanx.
btw, in how many years of the hsc, has these proofs appeared.
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There was no polynomial one in '98 (well there was one in q7, but there's no way you'd have a problem with it). The only really hard polynomial was in the last part of Q8b) in '94, where they had a diagram of a region in the AB plane (where A and B were coefficients of a polynomial) for values that the polynomial had no real roots, and you had to find the line/curve making the region. Is that the one you're referring to?Originally posted by turtle_2468
1998? Whatever the polynomials one was... lol, I got that in a tutoring session (meaning I was tutoring someone else), that got me... lol.. I reckon even 2000 is more approachable than that. But hey, just me... I have a stuffed up sense of relative difficulty a lot of the time
That shouldn't have been too bad for him - he hates geometry, not polynomials.
(Anyone feeling curious about the solution, the trick is to observe that there are two sets of conditions:
- when no real values of u exist (gives the parabolic side)
- when you get real values of u, but then can't solve for x (gives the straight line)
In both cases, set the determinant to a value less than 0 and then solve the equation[1].
Coincidentally, a lucky guess gave me the point T as (6,8) before I'd started, but that was a pure fluke...)
[1] Any uni student curious as to why b^2 - 4ac is called the determinant can do second year linear algebra at UNSW (I don't know which year it's done in in other unis) to find out. It is related to the determinant of a 2 x 2 matrix with entries [a b/2 b/2 c], although some fiddling obviously occurs to get the easier form...
(Anyone feeling curious about the solution, the trick is to observe that there are two sets of conditions:
- when no real values of u exist (gives the parabolic side)
- when you get real values of u, but then can't solve for x (gives the straight line)
In both cases, set the determinant to a value less than 0 and then solve the equation[1].
Coincidentally, a lucky guess gave me the point T as (6,8) before I'd started, but that was a pure fluke...)
[1] Any uni student curious as to why b^2 - 4ac is called the determinant can do second year linear algebra at UNSW (I don't know which year it's done in in other unis) to find out. It is related to the determinant of a 2 x 2 matrix with entries [a b/2 b/2 c], although some fiddling obviously occurs to get the easier form...