Australian Maths Competition (4 Viewers)

[PC]

Re: How did people go in the maths comp today?

I had no idea what it was either, and it looked pretty daunting at first sight, but take a look at the examples, is a fraction with the variable x in both the numerator and denominator. , after simplifying is still a fraction with the variable still a power of 1. Following this pattern, will still be a fraction with the variable x in both the numerator and denominator with a power of 1.
Since it asked how many solutions there were to this would result in a quadratic if the denominator is multiplied through. Quadratics have 2 solutions and I think (not completely sure) but the set S means either real or complex solutions, i.e. it doesn't matter if the quadratic doesn't have any real roots. - if this isn't what it means, please elaborate how to distinguish between the answer 1 and 2.
Thus, the answer would be 2, even though I chose 2n in the midst of all the mayhem

I thought it was easier than that. I looked at f₁(x) = x. It's a quadratic with solutions of -2 and 3. Then I looked at f₂(x) = x. It's a quadratic with solutions of -2 and 3. Then I looked at f₃(x) = x. It's a quadratic with solutions of -2 and 3. So on a hunch .... set of real solutions = S = {-2,3} and n(S) = 2.

 

[stevey6404]

Re: How did u go in the Australian Maths Competition?

Actually I thought the multiple choice was quite easy, compared to last year!
Maybe I was feeling good today or something! Hahha!


The last 5 questions was hard except maybe for the hexagon one but I guessed 4/5 of them! :L

 

[Dumbledore]

Re: How did people go in the maths comp today?

i did the stupidest thing, for the question like (x^2+x)^2=(x^2+x)+...
i actually worked out the solutions but i didn't read "what is the sum of the positive solutions" and read instead "what is the number of positive solutions", i was rushed and just put 5 even though i know degree 4 poly's have a max of 4 solutions...

 

[Official]

Re: How did people go in the maths comp today?

Yeh, someone scan the rest, Im really curious as to how many i actually got correct in the questions between 11-20

 

[xXmuffin0manXx]

Re: 2009 AMT Mathematics Competition

for cutoffs, I'm thinking:

below 30 = participation
30 = proficiency
40-55 = credit
55-70 = distinction
70 - 90 = high distinction
90+ = prize

i reckon that would be pretty close

me = 95 yeah? haha..i wish

 

[gurmies]

Re: How did people go in the maths comp today?

http://img411.imageshack.us/img411/1116/scan0002ztk.jpg

http://img256.imageshack.us/img256/2893/scan0003s.jpg

http://img34.imageshack.us/img34/7678/scan0004h.jpg

http://img44.imageshack.us/img44/8655/scan0005s.jpg

Enjoy guys.

 

[Aquawhite]

Re: 2009 AMT Mathematics Competition

Did you get 42 for q26?

What was 26 again?

Oh and did anyone figure out the one about the octahedron? That was kinda confusing... a little hard for me to figure how to get it :S

 

[Aquawhite]

Re: Australian Mathematics Competition

There probably would be the odd one... I wouldn't be surprised since the HSC is all taught and syllabus.

 

[Lukybear]

Re: 2009 AMT Mathematics Competition

I pretty much gave up from 16 onwards... didnt even try the last 5 questions. I know, really bad.

 

[Official]

Re: How did people go in the maths comp today?

http://img411.imageshack.us/img411/1116/scan0002ztk.jpg

http://img256.imageshack.us/img256/2893/scan0003s.jpg

http://img34.imageshack.us/img34/7678/scan0004h.jpg

http://img44.imageshack.us/img44/8655/scan0005s.jpg

Enjoy guys.

Thanks heaps

 

[Official]

Re: How did people go in the maths comp today?

For 18, did everyone get (C)?

 

[Aquawhite]

Re: How did people go in the maths comp today?

For 18, did everyone get (C)?

Ah, I had no idea how to do this question properly :S... I had a wild guess and I'm not exactly what I put down... not one of the end options though. ^^

 

[shaon0]

Re: How did people go in the maths comp today?

Shit. For the n-fold composite one i got as x->inf; f(x)->1.
Should have just picked 2^n

 

[shaon0]

Re: Australian Mathematics Competition

There probably would be the odd one... I wouldn't be surprised since the HSC is all taught and syllabus.

Yeah. It's very possible PLUS AMC can be based on a bit of luck. It's not like they check the working for the questions.

 

[Official]

Re: How did people go in the maths comp today?

Shit. For the n-fold composite one i got as x->inf; f(x)->1.
Should have just picked 2^n

Is it 2^n?

 

[Official]

Re: How did people go in the maths comp today?

I could only put down answers for Q1-7, 9,11,12,16,17 and 20. Read you guys' posts make me feel inadequate..

I got to take my paper home, so I can scan sections if you guys want, if its legal (but i suppose it isnt)

my (probably wrong) answers for q1-10 were
E,E,D,D,A,E,B,B,E,A

I got the same except Q6 where I got $31.

 

[gurmies]

Re: How did people go in the maths comp today?

I got D?

a/b + b/a = (a^2+b^2)/ab = x/60

Finding pairs:

1, 60 gives 1 + 3600 = 3601 ===> 3601/60 is irreducible, so one solution

2, 30 gives 4 + 900 = 904 ===> 904/60 is reducible so still one solution

3, 20 gives 9 + 400 = 409 ===> 409/60 is irreducible so two solutions

4, 15 gives 16 + 225 = 441 ===> 441/60 is irreducible so three solutions

5, 12 gives 25 + 144 = 169 ===> 169/60 is irreducible so four solutions

 

[Kajixtatsu]

Re: How did people go in the maths comp today?

I got the same except Q6 where I got $31.

Yes, YOU'RE MY MAN! =] Not sure bout how I went on some of the other qs....

also that parabola was dodgy... I was originally thinking that it was a difference of two squares (it looked like the roots/zeroes were equal negative) - but then again never trust scale.

 

[Official]

Re: How did people go in the maths comp today?

I got D?

a/b + b/a = (a^2+b^2)/ab = x/60

Finding pairs:

1, 60 gives 1 + 3600 = 3601 ===> 3601/60 is irreducible, so one solution

2, 30 gives 4 + 900 = 904 ===> 904/60 is reducible so still one solution

3, 20 gives 9 + 400 = 409 ===> 409/60 is irreducible so two solutions

4, 15 gives 16 + 225 = 441 ===> 441/60 is irreducible so three solutions

5, 12 gives 25 + 144 = 169 ===> 169/60 is irreducible so four solutions

Oh, darn, I missed 60/1 and 1/60.

 

[gurmies]

Re: How did people go in the maths comp today?

Ah, shame. You'll beat me anyway =]