HSC 2016 Maths Marathon (archive) (1 Viewer)

Drsoccerball · Feb 1, 2016

Re: HSC 2016 2U Marathon

Nailgun said:
what day was it specifically lol

It's whenever 2 unit kids learn the rule hahahah

InteGrand · Feb 1, 2016

Re: HSC 2016 2U Marathon

Drsoccerball said:
I think it's time to explain the burning lady rule. So what happened is on that day we had assembly and there were these dancing people. Just as the show opens the lady puts a ball of flames into her mouth and she screws up and it catches her face on fire... So she was alright afterwards but ojn that day we learnt that rule. And it made sense to call it the burning lady rule as the ladies standing and then she falls because shes on fire to put it out.

$\log_a{b^c}$ When she's standing.

$c \log_a{b}$ When she fell.

And the broken pippet rule happened on the same day that the next year learnt that rule so we can predict the time each year something bad's going to happen lol...

So were these terms ("burning lady log rule" and "broken pipette rule") basically made up by you and your friends? (I can't see the connection between that log law and those terms haha.)

Nailgun · Feb 1, 2016

Re: HSC 2016 2U Marathon

Oh jokes, as in on the day that the grade learnt the rule lol
Fun times

Nailgun · Feb 1, 2016

Re: HSC 2016 2U Marathon

Drsoccerball said:
$\log_a{b^c}$ When she's standing.
$c \log_a{b}$ When she fell.

imo her head fell off

Drsoccerball · Feb 1, 2016

Re: HSC 2016 2U Marathon

InteGrand said:
So we're these terms ("burning lady log rule" and "broken pipette rule") basically made up by you and your friends? (I can't see the connection between that log law and those terms haha.)

Yeah our maths teacher always referred to that rule as the burning lady rule after that point.

davidgoes4wce · Feb 4, 2016

Re: HSC 2016 2U Marathon

Not sure how to do this one, answer is 1.0921 radians. A bit thrown off by the wording of ' show the cross section of a trough of length 5m'

leehuan · Feb 4, 2016

Re: HSC 2016 2U Marathon

davidgoes4wce said:
Not sure how to do this one, answer is 1.0921 radians. A bit thrown off by the wording of ' show the cross section of a trough of length 5m'

Volume = Area * some length
= h/2(a+b) * 5

A CROSS SECTION, is when you slice a part of the shape, view it from any appropriate view (in this case front view), and draw the 2D version of the FRONT view.

davidgoes4wce · Feb 4, 2016

Re: HSC 2016 2U Marathon

leehuan said:
Volume = Area * some length
= h/2(a+b) * 5

A CROSS SECTION, is when you slice a part of the shape, view it from any appropriate view (in this case front view), and draw the 2D version of the FRONT view.

Still cant get the answer Im getting a different radian value

davidgoes4wce · Feb 4, 2016

Re: HSC 2016 2U Marathon

Forget about it, I got the answer. My excuse is, I went overseas for a month and Im rusty.

davidgoes4wce · Feb 4, 2016

Re: HSC 2016 2U Marathon

Here is the full working out:

davidgoes4wce · Feb 5, 2016

Re: HSC 2016 2U Marathon

Need a kick start on a) and b). Had a few problems deriving the formula.

wu345 · Feb 6, 2016

Re: HSC 2016 2U Marathon

Part a:
Let R=cone radius, h=cone height, r=sphere radius

sorry im missing pi in the last two lines

Part b:
Let s=slant height of cone

Nailgun · Feb 6, 2016

Re: HSC 2016 2U Marathon

wu345 said:
Part a:
Let R=cone radius, h=cone height, r=sphere radius
View attachment 32862

sorry im missing pi in the last two lines

Part b:
Let s=slant height of cone
View attachment 32863

btw If you're using daum just copy/paste into $tags (closing one will have a slash before the tex) and it will render on the forum, also daum has a pi button lol also, how did you get [tex]R=r\sin { 2x } $ and/or $ { R }^{ 2 }=4r\sin ^{ 2 }{ x } \cos ^{ 2 }{ x } ?$

wu345 · Feb 6, 2016

Re: HSC 2016 2U Marathon

thanks for the tip! sorry for not including a diagram earlier-hopefully this makes it clear
(angle subtended at centre double angle subtended at circumference from circle geo)

Also: my bad i used 3u identities to transform sin2x - you can do it with cosine rule and simple trig

Nailgun · Feb 6, 2016

Re: HSC 2016 2U Marathon

wu345 said:
thanks for the tip! sorry for not including a diagram earlier-hopefully this makes it clear
(angle subtended at centre double angle subtended at circumference from circle geo)
View attachment 32864

Also: my bad i used 3u identities to transform sin2x - is this question from a 3u or 2u textbook?

Ohh okay, is the circle geo 3u as well?
Spent like 30 mins on this yesterday lol, figured I was doing something wrong

wu345 · Feb 6, 2016

Re: HSC 2016 2U Marathon

Nailgun said:
Ohh okay, is the circle geo 3u as well?
Spent like 30 mins on this yesterday lol, figured I was doing something wrong

nono you can do it without any 3u i just did a dumb way hahaha

edit: Wait nvm you need 3u identity to transform cos 2x if youre using cosine rule oops

$Let\quad s=slant\quad side\quad of\quad cone\\ { s }^{ 2 }={ r }^{ 2 }+{ r }^{ 2 }-2{ r }^{ 2 }cos(180°-2x)\\ { s }^{ 2 }=2{ r }^{ 2 }+2{ r }^{ 2 }cos(2x)\\ { s }^{ 2 }=2{ r }^{ 2 }+2{ r }^{ 2 }(2\cos ^{ 2 }{ x } -1)\\ { s }^{ 2 }=2{ r }^{ 2 }+4{ r }^{ 2 }\cos ^{ 2 }{ x } -2{ r }^{ 2 }\\ s=4{ r }^{ 2 }\cos ^{ 2 }{ x } \\ s=2rcosx\\ R=s\sin { x } ,h=s\cos { x } \\ sub\quad into\quad Vcone=\frac { 1 }{ 3 } \pi { r }^{ 2 }h\\ \\$

wu345 · Feb 6, 2016

Re: HSC 2016 2U Marathon

I thought basic circle geo was assumed knowledge but maybe your school didnt do it in year 10?

Nailgun · Feb 6, 2016

Re: HSC 2016 2U Marathon

idk maybe we did lol

i figured if the textbook goes through even like basic algebra, everything that could be tested would be in it lol

wu345 · Feb 6, 2016

Re: HSC 2016 2U Marathon

yeah just be wary of it - but anyways sorry for all the spam earlier, i found a way to do it without any 3u will post soon

leehuan · Feb 6, 2016

Re: HSC 2016 2U Marathon

wu345 said:
I thought basic circle geo was assumed knowledge but maybe your school didnt do it in year 10?

Circle geometry is not assumed knowledge for mathematics 2 unit as the three LOBES of 10 5.3 are ONLY RECOMMENDED for those who intended to take Extension 1 mathematics.

Those that do 5.3 withOUT the LOBES are highly recommended to have sticked with 2 unit to begin with.
The LOBES were recommended for those that specifically wanted to do 3 unit.

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