# Thread: Hardest Questions In HSC maths?

1. ## Re: Hardest Questions In HSC maths?

Originally Posted by Rathin
What do you think are the hardest questions given in the HSC maths (2u, 3u, 4u) exam?
Post question number and Year below
Well Coroneos said that Q8b in the 1989 4 unit paper was too hard for that course. Try it yourself in the last 2 pages in this pdf: http://4unitmaths.com/hsc1981-1989.pdf

The stats verify what Coroneos said. 1989 had one of the largest candidatures ever for 4 unit and guess how many successfully answered this question? ZERO!

So this might qualify as one of the hardest.

2. ## Re: Hardest Questions In HSC maths?

Originally Posted by DatAtarLyfe
Yeh i never even use quotient rule period, just product rule everything. But i think i might keep it up my sleeve for dem integrations
What lol ok then. (Personally I hate chain rule within product rule)

Well tbh there was also a long route to get to the answer with that integral. But the presence of an e^u would've thrown people off before they attempted an IBP after the substitution

Originally Posted by tywebb
Well Coroneos said that Q8b in the 1989 4 unit paper was too hard for that course. Try it yourself in the last 2 pages in this pdf: http://4unitmaths.com/hsc1981-1989.pdf

The stats verify what Coroneos said. 1989 had one of the largest candidatures ever for 4 unit and guess how many successfully answered this question? ZERO!

So this might qualify as one of the hardest.
I think OP wanted questions within this century though. But oh wow that looks dodge...

3. ## Re: Hardest Questions In HSC maths?

Originally Posted by leehuan
I think OP wanted questions within this century though. But oh wow that looks dodge...
It's not in the first post in this thread. That only came after.

Anyway, if the hardest questions did not come from this century then I won't adhere to this restriction. Otherwise it would defeat the purpose of the thread. The first HSC exam was in 1967. So that is the only restriction.

4. ## Re: Hardest Questions In HSC maths?

Originally Posted by tywebb
It's not in the first post in this thread. That only came after.

Anyway, if the hardest questions did not come from this century then I won't adhere to this restriction. Otherwise it would defeat the purpose of the thread. The first HSC exam was in 1967. So that is the only restriction.
Out of curiosity, what is the hardest 2U question you know of?

bump

bump

7. ## Re: Hardest Questions In HSC maths?

I don't know about you guys but 2003 4U Q8 b) was almost impossible for me personally. I think it was proving that pi was irrational using integration or something.

8. ## Re: Hardest Questions In HSC maths?

I'll try the 2003 4U Q8b (i) only for now:

$I_n = \frac {q^{2n}}{n!} \int ^* _{-*} \left( \frac {\pi ^2}{4} - x^2\right )^n cos x dx\\ \\ = \frac {q^{2n}}{n!} \left( \int ^* _{-*} (\frac {\pi^2}{4} - x^2)^n dsinx \right) \\ \\ = \frac {q^{2n}}{n!} \left ( [sinx ({\frac {\pi ^2}{4} - x^2})^n]^* _{-*} - \int ^* _{-*} sin x \cdot n(\frac {\pi^2}{4} - x^2)^{n-1} (-2x) dx \right) \\ \\ = - \frac {q^{2n}}{n!} \left ( 0 - 2n \int ^* _{-*} x (\frac {\pi ^2}{4} - x^2)^{n-1}dcos x \right) \\ \\ = - \frac {2q^{2n}}{(n-1)!} \left ( [cos x \cdot x (\frac {\pi ^2}{4} - x^2)^{n-1} ]^* _{-*} - \int ^* _{-*} cos x \cdot d [x(\frac {\pi ^2}{4}-x^2)^{n-1}] \right ) \\ \\ = - \frac {2q^{2n}}{(n-1)!} \left ( 0 - \left [\int ^* _{-*} cos x \cdot (\frac {\pi ^2}{4} - x^2)^{n-1} dx + \int ^* _{-*} xcos x \cdot (n-1) (\frac {\pi ^2}{4} - x^2)^{n-2} (-2x)dx \right ]\right) \\ \\ = \frac {2q^{2n}}{(n-1)!} \int ^* _{-*} (\frac {\pi ^2}{4} - x^2)^{n-1} cos x dx - \frac {4q^{2n}}{(n-2)!} \int ^* _{-*} x^2 (\frac {\pi^2}{4} - x^2)^{n-2}cos x dx$

ps: the LaTeX input is killing me; have not even fully proof-checked. So I'll just give up here

9. ## Re: Hardest Questions In HSC maths?

Originally Posted by captainhelium
I don't know about you guys but 2003 4U Q8 b) was almost impossible for me personally. I think it was proving that pi was irrational using integration or something.
Captain: I've done part (i), the easy bit. Now you can finish the rest.

10. ## Re: Hardest Questions In HSC maths?

I remember those 1990s volume and harder ext1 combos questions really throw me off

11. ## Re: Hardest Questions In HSC maths?

Originally Posted by captainhelium
I don't know about you guys but 2003 4U Q8 b) was almost impossible for me personally. I think it was proving that pi was irrational using integration or something.
ah yes that a beautiful question

12. ## Re: Hardest Questions In HSC maths?

do ruse and grammar papers
especially the last questions
pree hard

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