Australian Maths Competition (1 Viewer)

[RealiseNothing]

Re: Australian Maths Competition 2013

Wtf? Can you please provide an example?

Prime factors of 2013 are 3, 11, 61.

They all have powers of 1, thus the amount of consecutive integers that add to 2013 is:



Take another example, say 72, it's prime factorisation is

So we take each power, add one, multiply them together, and minus one:

 

[RealiseNothing]

Re: Australian Maths Competition 2013

Also I worked out how to do question 25 (the 2 spheres) whilst falling asleep last night. It just clicked all of a sudden whilst lying there with my eyes shut lol. It's actually really easy:

Since the small sphere has radius=1 and the large sphere has radius=2, the ratio of their volumes is 1:8.

Now let the ratio that the smaller sphere gets cut into be a:b which can be expressed as .

Now the larger sphere gets cut into the same ratio, but 8 times larger, and the ratio is reversed to get 8b:8a or

Now adding these together to get the total volume of the two spheres together gives:

However, the question told us that the total volume was cut into the ratio 2:1, or , and so:









But remember that is the ratio the smaller sphere gets cut into, and so the answer is E) 2:5

 

[iBibah]

I confirmed with carrot that it was ok to post solutions before I posted any.

Oh I don't mind, my school done it today but they don't let year 12s do it due to trials (it's bullshit).

Just thought I'd let you know if some kid found this thread who was going to do it today, they probably would get a prize lol

 

[jihad1234]

Re: Australian Maths Competition 2013

Yea true maybe it would be wise to take them down even though people (like me and most people in this thread) have done it already/ But thanks tywebb you are awesome!

 

[AnimeX]

Re: Australian Maths Competition 2013

Prime factors of 2013 are 3, 11, 61.

They all have powers of 1, thus the amount of consecutive integers that add to 2013 is:



Take another example, say 72, it's prime factorisation is

So we take each power, add one, multiply them together, and minus one:

can I ask why this works?

the exam was so difficult

 

[iBibah]

Re: Australian Maths Competition 2013

and you know what the teacher would get if they let the kid do it the next day?

the SACK!

LOL!.

i'm not taking it down just because of incompetent teachers who do the wrong thing.

Our whole school doesn't the next day.

And relax, I'm not suggesting you take it down, I honestly couldn't care less lol

 

[Web Addict]

Re: Australian Maths Competition 2013

Prime factors of 2013 are 3, 11, 61.

They all have powers of 1, thus the amount of consecutive integers that add to 2013 is:



Take another example, say 72, it's prime factorisation is

So we take each power, add one, multiply them together, and minus one:

That's an interesting trick. It would of have definitely been very handy in the competition.

 

[hayabusaboston]

Re: Australian Maths Competition 2013

Also I worked out how to do question 25 (the 2 spheres) whilst falling asleep last night. It just clicked all of a sudden whilst lying there with my eyes shut lol. It's actually really easy:

Since the small sphere has radius=1 and the large sphere has radius=2, the ratio of their volumes is 1:8.

Now let the ratio that the smaller sphere gets cut into be a:b which can be expressed as .

Now the larger sphere gets cut into the same ratio, but 8 times larger, and the ratio is reversed to get 8b:8a or

Now adding these together to get the total volume of the two spheres together gives:

However, the question told us that the total volume was cut into the ratio 2:1, or , and so:









But remember that is the ratio the smaller sphere gets cut into, and so the answer is E) 2:5

fuck

 

[Web Addict]

Re: Australian Maths Competition 2013

Is anyone doing the ICAS Mathematics Competition on Wednesday the 14th August 2013?

 

[RealiseNothing]

Re: Australian Maths Competition 2013

Is anyone doing the ICAS Mathematics Competition on Wednesday the 14th August 2013?

Yep I am

Also I had another eureka moment when I was in the city after school today and figured out how to do question 22. Will post in a sec.

 

[RealiseNothing]

Re: Australian Maths Competition 2013

Hope this actually makes sense, solution to question 22:

 

[Makematics]

Re: Australian Maths Competition 2013

turns out im not the only one who solves maths q's whilst falling asleep

 

[iBibah]

Re: Australian Maths Competition 2013

Solving them while awake is too mainstream.

 

[Makematics]

Re: Australian Maths Competition 2013

Solving them while awake is too mainstream.

why not both?

 

[RealiseNothing]

Re: Australian Maths Competition 2013

turns out im not the only one who solves maths q's whilst falling asleep

I always do it. Just as I'm about to fall asleep it hits me lol. Must be a subconscious thing, or maybe our minds just become very clear at that time when we are relaxed?

 

[Vadevalor]

Re: Australian Maths Competition 2013

Anyone got back their paper? Can anyone tell me the real answers?

 

[hayabusaboston]

Re: Australian Maths Competition 2013

I always do it. Just as I'm about to fall asleep it hits me lol. Must be a subconscious thing, or maybe our minds just become very clear at that time when we are relaxed?

I have photographic memory in that phase right before sleep. Also during lucid dreaming, of which I do a lot. I can visualise an event crystal clear, from months or yeeaaars ago, and just play it back in my mind, lurid as ever.

 

[iBibah]

Re: Australian Maths Competition 2013

There is a proof of the AM-GM inequality published in the 1920s by George Pólya. There are many proofs of this, but Pólya's method is called Pólya's Dream.

I'm delighted that it's in the 4 unit Cambridge text book, but disappointed that they did not appropriately accredit it to Pólya.

It's called Pólya's Dream because he actually dreamt the proof!

Wow, that would make studying so much easier if we used sleep time lol

EDIT: Just googled it, and I think I just found a video you uploaded.


Is that you? the teacher?

 

[Vadevalor]

Re: Australian Maths Competition 2013

I thought the answers were provided by AMT?
Anw do you have the alphabet answers can you post them here?

 

[iBibah]

Re: Australian Maths Competition 2013

I thought the answers were provided by AMT?
Anw do you have the alphabet answers can you post them here?

Nah mate the answers are provided later when awards are distributed.