MedVision ad

HSC 2014 MX2 Marathon (archive) (2 Viewers)

Status
Not open for further replies.

nrlwinner

Member
Joined
Apr 18, 2009
Messages
194
Gender
Male
HSC
2010
Re: HSC 2014 4U Marathon

Here is a great question from the HSC a while back.

Untitled.png
 

Axio

=o
Joined
Mar 20, 2014
Messages
484
Gender
Male
HSC
2015
Re: HSC 2014 4U Marathon

a.



b.



Therefore (x+y)/2 is a closer approximation to root n than x is.
 
Last edited:

sepseminar

New Member
Joined
Aug 21, 2014
Messages
12
Gender
Male
HSC
2013
Re: HSC 2014 4U Marathon

Yep, that's correct, Dunjaaa. There is a slightly faster solution in which you make the substitution u=1/x. But all the deft moves are in your solution. First, the use of a substitution to equate the integral with a similar looking integral. Then the use of some basic properties to relate the two integrals together. In this case it was the fact that the inverse tan of a number and the inverse tan of the number's reciprocal is constant.
 

Fade1233

Active Member
Joined
Jun 1, 2014
Messages
345
Gender
Undisclosed
HSC
N/A
Re: HSC 2014 4U Marathon

Capture1.PNG

Fibonacci Based Strong Induction.

Edit: Forgot to put up the condition: U(n)= U(n-1) + U(n-2)
 
Last edited:

mreditor16

Well-Known Member
Joined
Apr 4, 2014
Messages
3,169
Gender
Male
HSC
2014
Re: HSC 2014 4U Marathon

I personally enjoyed this question :)

 

mreditor16

Well-Known Member
Joined
Apr 4, 2014
Messages
3,169
Gender
Male
HSC
2014
Re: HSC 2014 4U Marathon

btw above question was in fort street 2010

only Q3....
 

dunjaaa

Active Member
Joined
Oct 10, 2012
Messages
473
Gender
Male
HSC
2014
Re: HSC 2014 4U Marathon

Since nobody has answered it, I might as well do so Screen shot 2014-09-19 at 2.42.52 PM.png. Strong induction in disguise
 

Fizzy_Cyst

Owner @ Sigma Science + Phys Goat
Joined
Jan 14, 2011
Messages
1,212
Location
Parramatta, NSW
Gender
Male
HSC
2001
Uni Grad
2005
Re: HSC 2014 4U Marathon

A non-real number, w, is such that |w| = 1.

If z = (1+w)/(1-w) find the locus of z as w moves on the complex number plane
 
Status
Not open for further replies.

Users Who Are Viewing This Thread (Users: 0, Guests: 2)

Top