# Hardest Questions In HSC maths? (1 Viewer)

#### Hi there444

##### Active Member
In the 1998 (I think?) 4U HSC there was a question to prove the AM-GM inequality which iirc only 4 people successfully answered according to the marker's notes. There was also a tricky proof for the irrationality of pi sometime in the early-mid '00s iirc
oh that shit. when i was attempting the paper, took me like 30 minutes just to do that question lel

#### leehuan

##### Well-Known Member
ohhh fck half the state doing 4u got stuck doing the last integration question in 2014 despite it being easy. it probs the fact that the last question was only 3 marks that confused everyone.
It was deceptive, the 2014 last question

#### DatAtarLyfe

##### Booty Connoisseur
http://www.boardofstudies.nsw.edu.au/hsc_exams/2013/pdf_doc/2013-hsc-maths-ext-1.pdf
Q14(b). Go do it.

But yeah 2003 MX1 last question.. that was a horrible projectiles question to do
Lol i did that question whilst studying for my term 4 exam on binomial. I've done it but i can't remember how, only that it took me a while to do
It was deceptive, the 2014 last question
That took me like 3 secs, just used reverse quotient rule.
Its only coz ive seen a similar question in...terry lee? Or was it a worksheet? I cant remember

#### leehuan

##### Well-Known Member
Lol i did that question whilst studying for my term 4 exam on binomial. I've done it but i can't remember how, only that it took me a while to do

That took me like 3 secs, just used reverse quotient rule.
Its only coz ive seen a similar question in...terry lee? Or was it a worksheet? I cant remember
How often did I use reverse quotient rule in my life...never until I started realising I needed to take my integration skills beyond that of the easy

Pretty sure most of the state wouldn't have considered reverse quotient rule either. Heck, even reverse product rule throws me off at times.

#### DatAtarLyfe

##### Booty Connoisseur
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

#### tywebb

##### dangerman
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.

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#### leehuan

##### Well-Known Member
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

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...

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#### tywebb

##### dangerman
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.

#### Nailgun

##### Cole World
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?

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#### captainhelium

##### water enthusiast
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.

#### Drongoski

##### Well-Known Member
I'll try the 2003 4U Q8b (i) only for now:

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

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

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#### Drongoski

##### Well-Known Member
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.

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#### Hi there444

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

#### jathu123

##### Active Member
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

#### Commando007

##### Member
do ruse and grammar papers
especially the last questions
pree hard

#### 1039213

##### New Member
Without a doubt the hardest HSC, like this can't be argued is 1989 extension 2 hsc last question i think its 8b. the board of studies were actually told to not write questions that difficult because it was long and only a couple of people in the cohort managed to pass the question.

#### supR

##### Trials are the best
1989 is so hard to understand, at one point it feels like subbing in numbers and the next it feels beyond the syllabus