One of the 4 unit teachers at my school mentioned the UNSW mathematics competition to me today and wondered whether or not i am going to participate in it. How many others generally go in the maths competition and how hard is the actual test... He mentioned that you are allowed to bring in whatever resources you wish and you have 3 hours to complete 5 questions... sounds very hard to me...
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UNSW Maths Competition (1 Viewer)
- Thread starter sasquatch
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funnybunny
funniest bunny in th land
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- 2005
lol...i did the exam and was asked to go to the unsw to receive this ceritficate...u can bring in whatever resources u wish..prob best to bring maths formulas etc...mathematics tool chest is pretty good...usually half the paper is okish...and the other half is bit challenging...geometry part is usally fun
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pLuvia
Guest
Do you have anymore information on this?sasquatch said:
Not really... the only information i know i got whilst walking out of the building for recess, so i didnt get to talk for much. I did however find a website (as i was looking for past questions), but its not very good... Here it is anyway:pLuvia said:
http://www.maths.unsw.edu.au/highschool/unsw/highcomps.html
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acullen
Povo postgrad
I've got a lot of these UNSW Maths certificates dating from year 6 onwards. In hindsight, I don't really see the purpose of actually sitting the test due to university entrace being based almost exlusively on the UAI.
airie
airie <3 avatars :)
Never heard anything about it at school x.x How does the difficulty compare with AMO and APMO? Or the AIMO (ok maybe not this...considering only two questions are free responses ) and the Senior Contest?
EDIT: There seems to be another maths comp held by UNSW, and it was already done on 11 May. Weird. And my friend who's doing the one which you seem to be talking about told me that it's on June 20. So UNSW must have two maths comp or something. Hmmm.
) and the Senior Contest?EDIT: There seems to be another maths comp held by UNSW, and it was already done on 11 May. Weird. And my friend who's doing the one which you seem to be talking about told me that it's on June 20. So UNSW must have two maths comp or something. Hmmm.
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acullen
Povo postgrad
$100 isn't much. It wont even buy you a big night out or one uni textbook.modezero said:
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pLuvia
Guest
But this is just a small competition, a little cash for a test wouldn't hurt. But I can understand where you are coming from.acullen said:
Does anyone know roughly how many people do this test?
There are two UNSW maths comps actually, the multiple choice one (there's science, computer science, English as well) and the real proper one with 6 questions. It's not very hard, certainly easier than AMO and AMOC Senior and ridiculously simple compared with APMO (which in recent years are comparable with the IMO).
airie
airie <3 avatars :)
Goodie. 'Cos that APMO really murdered me.
Wooz
^wooz*y^
It's too late airie the comp was last week.
airie
airie <3 avatars :)
Nope I'm not too lateWooz said:
Entry applications close around 5 June or something Read the previous posts, I'm not referring to the one that was already held on 11 May Wooz
^wooz*y^
Oh, i thought you were talking about the EAS UNSW maths comp.
These questions are pretty hard actually... im considering to not actually do it as i might just make a fool of myself.
Heres some of the questions from past years:
Problem 1. A disc of radius 1 unit is cut into quadrants (identical quaters), and the quadrants are place in a square of side 1 unit.
i) What is the leat possible area of overlap?
ii) What are the other possible areas of overlap?
Problem 2. Prove that if a >= b >= c >= 0 then a2 + 3b2 + 5c2 <= (a+b+c)2.
Can you prove a more general inequality.
Problem 3. The triangular numbers are given by Tn = 1 + 2 + ... + n for n a positive integer (T1 = 1).
Discover and prove a formula for Tn[ (1/T1) + (1/T2) + ... + (1/Tn) ).
Hence find the sum of the recipricals of all the triangular numbers.
Problem 4. In an alleyway with tall buldings on both sides, a ladder of length 3.9m leans from the foot of the west wall on to the east wall, while a ladder of length 2.5m leans the other way across the alleyway from the foot of the east wall to the west wall. Looking north along the alleyway, the ladders appear to cross 1(2/7) m above the roadway. How wide is the alleyway?
Problem 5. Conisder the diophantine equation
(1/a) + (1/b) + (1/c) + (2/abc) = (15/(a+b+c))
i) If a = 3, and b = 5 find c.
ii) Show that the equation has infinetly many solutions in integers.
Problem 6.
i) Two people play a game by taking turns to toss a coin. The first to throw both heads and tails wins. What is the probability the first to throw wins?
ii) What are the probabilites with three people playing?
What are the probabilites whith n players?
iii) Two people play a game by taking turns to spin a spinner with three equally likely outcomes. The first to obtain all three results wins. What is the probabilty the starter wins?
Have fun....
Heres some of the questions from past years:
Problem 1. A disc of radius 1 unit is cut into quadrants (identical quaters), and the quadrants are place in a square of side 1 unit.
i) What is the leat possible area of overlap?
ii) What are the other possible areas of overlap?
Problem 2. Prove that if a >= b >= c >= 0 then a2 + 3b2 + 5c2 <= (a+b+c)2.
Can you prove a more general inequality.
Problem 3. The triangular numbers are given by Tn = 1 + 2 + ... + n for n a positive integer (T1 = 1).
Discover and prove a formula for Tn[ (1/T1) + (1/T2) + ... + (1/Tn) ).
Hence find the sum of the recipricals of all the triangular numbers.
Problem 4. In an alleyway with tall buldings on both sides, a ladder of length 3.9m leans from the foot of the west wall on to the east wall, while a ladder of length 2.5m leans the other way across the alleyway from the foot of the east wall to the west wall. Looking north along the alleyway, the ladders appear to cross 1(2/7) m above the roadway. How wide is the alleyway?
Problem 5. Conisder the diophantine equation
(1/a) + (1/b) + (1/c) + (2/abc) = (15/(a+b+c))
i) If a = 3, and b = 5 find c.
ii) Show that the equation has infinetly many solutions in integers.
Problem 6.
i) Two people play a game by taking turns to toss a coin. The first to throw both heads and tails wins. What is the probability the first to throw wins?
ii) What are the probabilites with three people playing?
What are the probabilites whith n players?
iii) Two people play a game by taking turns to spin a spinner with three equally likely outcomes. The first to obtain all three results wins. What is the probabilty the starter wins?
Have fun....
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