Maths Ext 2 Predictions/Thoughts (1 Viewer)

ExtremelyBoredUser

Bored Uni Student
Joined
Jan 11, 2021
Messages
2,554
Location
m
Gender
Male
HSC
2022
thx to the dude who provided the copy of the paper. kinda thrown off by this m/c a bit. Ended up picking C in the end just felt like it looks like a regular projectile motion graph.....probs got it wrong tho, anyone got any ideas?View attachment 33774

I just thought abt centripetal force, which would have to be to the centre, and acceleration would have to be in the same direction since its moving in a circular motion.
 

ohnose

New Member
Joined
Apr 20, 2021
Messages
15
Gender
Male
HSC
2021
What would a raw mark of 73 or 74 ish scale to roughly?
 

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,556
Location
Outside reality
Gender
Male
HSC
2016
How then?
Suppose T(2n) = H(m) for some integer m.

2n(2n+1)/2 = m(2m-1)

2n²+n = 2m²-m

m+n = 2m²-2n² = 2(m-n)(m+n)

Since m and n are positive integers, we can divide.

1 = 2(m-n)

This is impossible, as integers cannot have a difference of ½.

Therefore, the even triangular numbers are never equal to any hexagonal numbers.
 

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,556
Location
Outside reality
Gender
Male
HSC
2016
Meme Solution for 15. (d).

If the result were true, this would be a non-trivial solution to Fermat's Last Theorem for every integer n>2.

Hence, the result must be false for all n>2.

The result is clearly false for n=2 by manually checking.

QED ⬛
 

vishnay

God
Joined
Sep 6, 2020
Messages
905
Gender
Male
HSC
2021
Meme Solution for 15. (d).

If the result were true, this would be a non-trivial solution to Fermat's Last Theorem for every integer n>2.

Hence, the result must be false for all n>2.

The result is clearly false for n=2 by manually checking.

QED ⬛
i did that in the exam
 

CM_Tutor

Moderator
Moderator
Joined
Mar 11, 2004
Messages
2,644
Gender
Male
HSC
N/A
Meme Solution for 15. (d).

If the result were true, this would be a non-trivial solution to Fermat's Last Theorem for every integer n>2.

Hence, the result must be false for all n>2.

The result is clearly false for n=2 by manually checking.

QED ⬛
I posted a version of that in the discussion in the MX2 forum... I wonder how markers will evaluate anything like it?
 

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,556
Location
Outside reality
Gender
Male
HSC
2016
I WAS ABOUT TO DO THIS IS THIS THE CORRECT ANSWER??? IF IT IS IM GOING TO BE HANGING FROM THE CHANDELIER
I can't say. I know that for proving the irrationality of the nth root of 2, the proof of fermat's last theorem does in fact require some elementary irrationality results (including this very thing) so it would be circular reasoning. This would need the consultation of an expert in algebraic number theory to resolve.
 

Alistruggles

Member
Joined
Jun 17, 2019
Messages
34
Gender
Undisclosed
HSC
2021
did you figure this one out? i also got lost with this lol and ran outta time to look at it properly
i'm not the person u quoted and idk if this would be accepted but i noted that they want u to prove for every odd number and an odd number can be represented by 2n - 1 so....subbing 2n - 1 into the Triangle equation actually gets u the hexagonal equation, therefore hexagonal number??? seems way too simple lol (lmk if you think this would get any marks)
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top