HSC 2016 Maths Marathon (archive) (3 Viewers)

Drsoccerball · Mar 27, 2016

Re: HSC 2016 2U Marathon

Paradoxica said:
I'm not sure that's assumed knowledge for 2U...

My bad

You would just draw the 2 graphs and add their ordinates separately.

leehuan · Mar 28, 2016

Re: HSC 2016 2U Marathon

Have to add ordinates. Only 2U method to do this - auxiliary is 3U.
__________________________

Instructive question:

$$Sketch (or alternatively redefine) the curve ${y}^{x}=1$

Don't spoil it for no reason anyone who's not doing an HSC in some year later than 2015

Nailgun · Mar 28, 2016

Re: HSC 2016 2U Marathon

leehuan said:
Have to add ordinates. Only 2U method to do this - auxiliary is 3U.
__________________________

Instructive question:

$$Sketch (or alternatively redefine) the curve ${y}^{x}=1$

Don't spoil it for no reason anyone who's not doing an HSC in some year later than 2015

isn't this x=0?

InteGrand · Mar 28, 2016

Re: HSC 2016 2U Marathon

Nailgun said:
isn't this x=0?

$\noindent It's $y=1$ or $x=0$, excluding the point $(0,0)$ since $0^0$ is undefined. So it's a pair of lines excluding one point.$

Nailgun · Mar 28, 2016

Re: HSC 2016 2U Marathon

InteGrand said:
$\noindent It's $y=1$ or $x=0$, excluding the point $(0,0)$ since $0^0$ is undefined. So it's a pair of lines excluding one point.$

Ah I see

leehuan · Mar 28, 2016

Re: HSC 2016 2U Marathon

Yep. It's instructive because of the indeterminate form. Besides that it's just knowledge of index laws.

Green Yoda · Mar 28, 2016

Re: HSC 2016 2U Marathon

Next Question:
A magician holds one six-sided die in his left hand and two in his right. What is the probability the number on the dice in his left hand is greater than the sum of the dice in his right?

Drsoccerball · Mar 28, 2016

Re: HSC 2016 2U Marathon

Rathin said:
Next Question:
A magician holds one six-sided die in his left hand and two in his right. What is the probability the number on the dice in his left hand is greater than the sum of the dice in his right?

Cases is the way to go.

leehuan · Mar 28, 2016

Re: HSC 2016 2U Marathon

Drsoccerball said:
Cases is the way to go.

Lol basically what I was thinking... cause the cases are so few.

@2016ers

If you think about it, it's already quite restricting that the die in his left hand has to be at least 3

Speed6 · Mar 28, 2016

Re: HSC 2016 2U Marathon

ownagge said:
Sketch y=2cos(x) - sin(x)

How would you sketch this using the auxiliary form method?

Paradoxica · Mar 28, 2016

Re: HSC 2016 2U Marathon

Speed6 said:
How would you sketch this using the auxiliary form method?

$2\cos{x}-\sin{x} \equiv \sqrt{5} \cos{\left(x+\tan^{-1}{\frac{1}{2}}\right)}$

v_k_9696 · Mar 29, 2016

Re: HSC 2016 2U Marathon

the inflexion point does not make sense
check the working out, its from a past paper. someone confirm it please or am i just coo coo

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leehuan · Mar 29, 2016

Re: HSC 2016 2U Marathon

v_k_9696 said:
View attachment 33037
the inflexion point does not make sense
check the working out, its from a past paper. someone confirm it please or am i just coo coo

Sent from my iPhone using Tapatalk

http://www.wolframalpha.com/input/?i=inflexion+points+x^3-6x^2+9x+4

You're cuckoo. Sorry

v_k_9696 · Mar 29, 2016

Re: HSC 2016 2U Marathon

nevermind i did something wrong in my working out

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Nailgun · Apr 1, 2016

Re: HSC 2016 2U Marathon

Drsoccerball said:
$$ Using the fact that $ \int{f'(x)}dx=f(x) ($ So that new comers who don't know integration can attempt this. $)$

$$ Hence, or otherwise $ \int{x^{2x}(1+\ln{x})}dx$

lelel I tried this again and it was actually pretty easy

that being said this is only really a 2U question if you originally ask to find the derivative of x^(2x)

Rathin said:
Next Question:
A magician holds one six-sided die in his left hand and two in his right. What is the probability the number on the dice in his left hand is greater than the sum of the dice in his right?

4/33?

InteGrand · Apr 1, 2016

Re: HSC 2016 2U Marathon

Nailgun said:
lelel I tried this again and it was actually pretty easy

that being said this is only really a 2U question if you originally ask to find the derivative of x^(2x)

4/33?

I don't think it's 4/33.

Nailgun · Apr 1, 2016

Re: HSC 2016 2U Marathon

InteGrand said:
I don't think it's 4/33.

whhops 5/33 added up wrong

InteGrand · Apr 1, 2016

Re: HSC 2016 2U Marathon

Nailgun said:
whhops 5/33 added up wrong

I don't think it's that either.

Nailgun · Apr 1, 2016

Re: HSC 2016 2U Marathon

InteGrand said:
I don't think it's that either.

rip

There are 11 possible sums for the right hand, and six possible numbers for left hand therefore 66 outcomes possible

0 successful outcomes if you get 1 in the left hand
0 successful outcome if you get 2 in the left hand
1 successful outcomes if you get 3 in the left hand
2 successful outcomes if you get 4 in the left hand
3 successful outcomes if you get 5 in the left hand
4 successful outcomes if you get 6 in the left hand

1+2+3+4=10

10/66 = 5/33

what am i doing wrong lol

edit: jokes i see it now
this is what happens when i dont use a probability tree lel

InteGrand · Apr 1, 2016

Re: HSC 2016 2U Marathon

Nailgun said:
rip

There are 11 possible sums for the right hand, and six possible numbers for left hand therefore 66 outcomes possible

0 successful outcomes if you get 1 in the left hand
0 successful outcome if you get 2 in the left hand
1 successful outcomes if you get 3 in the left hand
2 successful outcomes if you get 4 in the left hand
3 successful outcomes if you get 5 in the left hand
4 successful outcomes if you get 6 in the left hand

1+2+3+4=10

10/66 = 5/33

what am i doing wrong lol

edit: jokes i see it now
this is what happens when i dont use a probability tree lel

Yeah, with the 11 different sums, some of them can happen in more ways than others. So in actuality, there are 36 possibilities for the hand with two dice (Die 1 has 6 possibilities, and Die 2 has 6 possibilities).

HSC 2016 Maths Marathon (archive) (3 Viewers)

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