• Best of luck to the class of 2024 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • YOU can help the next generation of students in the community!
    Share your trial papers and notes on our Notes & Resources page
MedVision ad

HSC 2013 MX2 Marathon (archive) (4 Viewers)

Status
Not open for further replies.

HAX0R

Member
Joined
Sep 24, 2013
Messages
125
Gender
Male
HSC
2018
Re: HSC 2013 4U Marathon

Sy, to edit the title, press edit, and then go advanced.
 

Ikki

Active Member
Joined
Oct 29, 2012
Messages
130
Gender
Male
HSC
2014
Re: HSC 2013 4U Marathon

Wassup guys, i'm part of the 2014 cohort, how do you guys post solutions in here? Latex only?

Anyways, a bit of an intro:
Like I said i'm in class of 2014 and basically gonna start coming on here more often cause this forum is awesome.

Subjects:
4 Unit Maths
Advanced English
Physics
Chemistry
ATAR GOAL: 97+ (But might as well reach for the stars right? 99? LOL)

Let me make my addition to this thread haha
Integrate secxtanx/sqrt(1-sec^2x) between b and a where b>a
BTW: Is it just 4u questions or can interesting 3u ones come in here as well?
 
Last edited:

Ikki

Active Member
Joined
Oct 29, 2012
Messages
130
Gender
Male
HSC
2014
Re: HSC 2013 4U Marathon

Put a new 2014 thread? I dislike years getting mixed up =[









(Q1)

5-12i and 3+4i.
----------
z=4(1-i)+-sqrt(-63-16i) (After simplification) (Quadratic Formula)
----------
Delta=-63-16i
Root Delta= +-(1-8i)
-----------------------------

Therefore,
z=4-4i+-(1-8i)
z=5-12i and 3+4i

(Q2) Drew up parallelogram with z1 being on real axis and z2 being on imaginary axis. Then using head to tail etc etc.
Formed a square -> right angled triangles using diagonals.
In other words: (using pythagorus)
|z1|^2+|z2|^2=|z1+z2|^2 <-(1)
and
|z1|^2+|z2|^2=|z1-z2|^2 <-(2)

Now, (1)+(2):
|z1+z2|^2 + |z1-z2|^2 = 2(|z1|^2+|z2|^2)
Therefore, proven.

(Q3)-- Having problems knowing where to start, hint maybe? LOL

Anyways, thanks guys, this forum is awesome.
Keep the hard complex questions coming, 4u assessment is pure complex :)
 

obliviousninja

(╯°□°)╯━︵ ┻━┻ - - - -
Joined
Apr 7, 2012
Messages
6,624
Location
Sydney Girls
Gender
Female
HSC
2013
Uni Grad
2017
Re: HSC 2013 4U Marathon

Wassup guys, i'm part of the 2014 cohort, how do you guys post solutions in here? Latex only?

Anyways, a bit of an intro:
Like I said i'm in class of 2014 and basically gonna start coming on here more often cause this forum is awesome.

Subjects:
4 Unit Maths
Advanced English
Physics
Chemistry
ATAR GOAL: 97+ (But might as well reach for the stars right? 99? LOL)

Let me make my addition to this thread haha
Integrate secxtanx/sqrt(1-sec^2x) between b and a where b>a
BTW: Is it just 4u questions or can interesting 3u ones come in here as well?
there's a separate 3u thread, but if its under harder 3u, post here.
 

Ikki

Active Member
Joined
Oct 29, 2012
Messages
130
Gender
Male
HSC
2014
Re: HSC 2013 4U Marathon

Alright. this might pass as harder 3u, not sure lol. It's pretty interesting for 4u anyways:
Just learning latex off others haha:



LOL My noob latex skillz.
Could someone tell me how to put boundaries on integration and seperate the dx from the fraction to make it look more nice
Thankyou :)
 
Last edited:

Kurosaki

True Fail Kid
Joined
Jul 14, 2012
Messages
1,167
Location
Tubbytronic Superdome
Gender
Male
HSC
2014
Re: HSC 2013 4U Marathon

Alright. this might pass as harder 3u, not sure lol. It's pretty interesting for 4u anyways:
Just learning latex off others haha:





LOL My noob latex skillz.
Could someone tell me how to put boundaries on integration and seperate the dx from the fraction to make it look more nice
Thankyou :)

Is this what you mean?
 

seanieg89

Well-Known Member
Joined
Aug 8, 2006
Messages
2,662
Gender
Male
HSC
2007
Re: HSC 2013 4U Marathon

"\," is a common spacing string used to separate integrand from the "dx".
 

RealiseNothing

what is that?It is Cowpea
Joined
Jul 10, 2011
Messages
4,591
Location
Sydney
Gender
Male
HSC
2013
Re: HSC 2013 4U Marathon

Alright. this might pass as harder 3u, not sure lol. It's pretty interesting for 4u anyways:
Just learning latex off others haha:





LOL My noob latex skillz.
Could someone tell me how to put boundaries on integration and seperate the dx from the fraction to make it look more nice
Thankyou :)
Hints aren't welcomed here.
 

hit patel

New Member
Joined
Mar 14, 2012
Messages
568
Gender
Male
HSC
2014
Uni Grad
2018
Re: HSC 2013 4U Marathon

A string is attached to a mass and its other end attached to the pivot of a circular disk of radius R. The disk in on a shaft (assume the shaft and the disk is weightless) and the length of the string is h metres. The shaft rotates anticlockwise and as the speed of shaft increases the mass swings outward. Let the Mass be m and the disk rotates about its axle with a constant angular velocity. This constant angular velocity w produces an angle θ with the vertical.
a) Find the relation of w, h, R, g in terms of theta.
b) Use graphical means to show that for a given w there is just one value of theta in the range of 0<θ<pi/2 (less than or equal to symbol), which satisfies this relation.
c) Given R=6, h=2, θ=60 and g=10, find w relative to ground.


I cant seem to get part b). a nd c is done. Please help 2013 ers. Question open to all .

Thanks
 
Joined
Sep 20, 2010
Messages
2,225
Gender
Undisclosed
HSC
2012
Re: HSC 2013 4U Marathon

Alright. this might pass as harder 3u, not sure lol. It's pretty interesting for 4u anyways:
Just learning latex off others haha:





LOL My noob latex skillz.
Could someone tell me how to put boundaries on integration and seperate the dx from the fraction to make it look more nice
Thankyou :)
"\," is a common spacing string used to separate integrand from the "dx".
Alternatively you can use the \mathop{dx} command (mathematical operation) which spaces things nicely.
 

Ikki

Active Member
Joined
Oct 29, 2012
Messages
130
Gender
Male
HSC
2014
Re: HSC 2013 4U Marathon


Is this what you mean?
Yeah, thanks :)

Hints aren't welcomed here.
Step back bro, too pro LOL

"\," is a common spacing string used to separate integrand from the "dx".
Thanks, works great. :)

A string is attached to a mass and its other end attached to the pivot of a circular disk of radius R. The disk in on a shaft (assume the shaft and the disk is weightless) and the length of the string is h metres. The shaft rotates anticlockwise and as the speed of shaft increases the mass swings outward. Let the Mass be m and the disk rotates about its axle with a constant angular velocity. This constant angular velocity w produces an angle θ with the vertical.
a) Find the relation of w, h, R, g in terms of theta.
b) Use graphical means to show that for a given w there is just one value of theta in the range of 0<θ<pi/2 (less than or equal to symbol), which satisfies this relation.
c) Given R=6, h=2, θ=60 and g=10, find w relative to ground.


I cant seem to get part b). a nd c is done. Please help 2013 ers. Question open to all .

Thanks
Shii, is this mechanics already?
 
Last edited:

bottleofyarn

Member
Joined
Sep 22, 2013
Messages
50
Gender
Male
HSC
2013
Re: HSC 2013 4U Marathon

A string is attached to a mass and its other end attached to the pivot of a circular disk of radius R. The disk in on a shaft (assume the shaft and the disk is weightless) and the length of the string is h metres. The shaft rotates anticlockwise and as the speed of shaft increases the mass swings outward. Let the Mass be m and the disk rotates about its axle with a constant angular velocity. This constant angular velocity w produces an angle θ with the vertical.
a) Find the relation of w, h, R, g in terms of theta.
b) Use graphical means to show that for a given w there is just one value of theta in the range of 0<θ<pi/2 (less than or equal to symbol), which satisfies this relation.
c) Given R=6, h=2, θ=60 and g=10, find w relative to ground.


I cant seem to get part b). a nd c is done. Please help 2013 ers. Question open to all .

Thanks
Mechanics already!
I'm not sure if I'm missing a force or my diagram is wrong, but I get which is missing h. Graphing this for w>0, it has an inverse function (autonomous increase is the phrase I think) and so there is only one value for theta for any w.
My answer for c) is .
Also, is the pivot of the disc the centre?
 

RealiseNothing

what is that?It is Cowpea
Joined
Jul 10, 2011
Messages
4,591
Location
Sydney
Gender
Male
HSC
2013
Re: HSC 2013 4U Marathon

Mechanics already!
I'm not sure if I'm missing a force or my diagram is wrong, but I get which is missing h. Graphing this for w>0, it has an inverse function (autonomous increase is the phrase I think) and so there is only one value for theta for any w.
My answer for c) is .
Also, is the pivot of the disc the centre?
Monotone increasing would be a better phrase.
 

seanieg89

Well-Known Member
Joined
Aug 8, 2006
Messages
2,662
Gender
Male
HSC
2007
Re: HSC 2013 4U Marathon

Show that for n greater than 2, there are no positive integer solutions for a^n+b^n=c^n
"Positive integer solutions" means a,b,c must be positive integers. You have not restricted n though beyond saying that it is larger than 2.

So

a=b=3, c=4 solves the equation with n=log(1/2)/log(3/4).

Hence the claim is untrue.
 

Ikki

Active Member
Joined
Oct 29, 2012
Messages
130
Gender
Male
HSC
2014
Re: HSC 2013 4U Marathon

Show that for n greater than 2, there are no positive integer solutions for a^n+b^n=c^n
I'm not sure where you got this from but it is a very famous problem:

Fermat's Last Theorem

No way, any of us on here could probably do it...

Anyways, Check it out,
http://en.wikipedia.org/wiki/Fermat's_Last_Theorem
and
https://www.youtube.com/watch?v=qiNcEguuFSA

UNLESS:
"Positive integer solutions" means a,b,c must be positive integers. You have not restricted n though beyond saying that it is larger than 2.

So

a=b=3, c=4 solves the equation with n=log(1/2)/log(3/4).

Hence the claim is untrue.
LOL nice one, caught on technicality? But pretty sure it's referring to fermat's last theorem. Where n must also be an integer.
 
Last edited:

hit patel

New Member
Joined
Mar 14, 2012
Messages
568
Gender
Male
HSC
2014
Uni Grad
2018
Re: HSC 2013 4U Marathon

Mechanics already!
I'm not sure if I'm missing a force or my diagram is wrong, but I get which is missing h. Graphing this for w>0, it has an inverse function (autonomous increase is the phrase I think) and so there is only one value for theta for any w.
My answer for c) is .
Also, is the pivot of the disc the centre?
Oh okkkkk... Right thanks. Yep mechanics is funn... I literally think mechanics is gonna be my best subject but havent done conics yet so cant say too much about the combination but mechanics with parametrics is yeh good, (physics seems like a kid in front of it- apparently i heard they took out mechanics from physsics and putit in four unit) nope the pivot is at the end of the circular disk thereby given radius R; If it was the centre of the disk and therfore the shaft , then i donot see why would it be required am i right? Thanks I got everything except the meaning of autonomous?

Monotone increasing would be a better phrase.
Oh ok i get that.
Show that for n greater than 2, there are no positive integer solutions for a^n+b^n=c^n
Whow How do you show that?> Is that harder ext 1?
"Positive integer solutions" means a,b,c must be positive integers. You have not restricted n though beyond saying that it is larger than 2.

So

a=b=3, c=4 solves the equation with n=log(1/2)/log(3/4).

Hence the claim is untrue.
I dont get it.
 

RealiseNothing

what is that?It is Cowpea
Joined
Jul 10, 2011
Messages
4,591
Location
Sydney
Gender
Male
HSC
2013
Re: HSC 2013 4U Marathon

Whow How do you show that?> Is that harder ext 1?
Don't worry about it. It was an unsolved problem for about 300 years until Wiles solves it in the 90's after progress and links from many previous mathematician's work.

You'll be able to do it by half yearlies.
 

hit patel

New Member
Joined
Mar 14, 2012
Messages
568
Gender
Male
HSC
2014
Uni Grad
2018
Re: HSC 2013 4U Marathon

Don't worry about it. It was an unsolved problem for about 300 years until Wiles solves it in the 90's after progress and links from many previous mathematician's work.

You'll be able to do it by half yearlies.
haha i feel dumb, :). But hope so. What topic is it in?
 
Status
Not open for further replies.

Users Who Are Viewing This Thread (Users: 0, Guests: 4)

Top