Australian Maths Competition (1 Viewer)

[hayabusaboston]

Re: Australian Maths Competition 2013

Was the answer to Q26 972?

I got 72 as last as the last two digits, different first digit.

 

[hayabusaboston]

Re: Australian Maths Competition 2013

If there are two spheres connected to each other, one with radius 2, one with radius 1, and a plane cuts the combined volume of those sphere into the ratio 1:2, what ratio does the plane cut the volume of the smaller plane into?
This was Q23

Also one of interest, x^2-2xy+y^2=9
How many ordered pairs for x and y exist?

Also
There are three squares lined up, touching each other by the sides, one has side length 3, next one side length is 5,next one 8. What is the area of the trapezium formed, if u draw a line from bottom left corner of smallest square to top right corner of biggest square, and have a trapezium shaped thing in the middle square?

Also
A square PQRS, points are clockwise, with P top left corner, has a point X within the square. The distance from X to corner P is 53m, the distance from X to S is 51m, and the distance from X to R is 21m. If the perpendicular distance from X to each side of the square is an integer value, find the area of PQRS.

 

[hayabusaboston]

Re: Australian Maths Competition 2013

Also, who lied about the prime number? lol
I but B or E If I remember right.

 

[RealiseNothing]

Re: Australian Maths Competition 2013

Also, who lied about the prime number? lol
I but B or E If I remember right.

Dan (D) is what I got.

 

[RealiseNothing]

Re: Australian Maths Competition 2013

If there are two spheres connected to each other, one with radius 2, one with radius 1, and a plane cuts the combined volume of those sphere into the ratio 1:2, what ratio does the plane cut the volume of the smaller plane into?
This was Q23

That was Q25, and I got 1:3.

 

[RealiseNothing]

Re: Australian Maths Competition 2013

Also one of interest, x^2-2xy+y^2=9
How many ordered pairs for x and y exist?

It was

You make it:





Since the LHS is a perfect square, you find the values of 'x' that make a perfect square.

 

[RealiseNothing]

Re: Australian Maths Competition 2013

Also
There are three squares lined up, touching each other by the sides, one has side length 3, next one side length is 5,next one 8. What is the area of the trapezium formed, if u draw a line from bottom left corner of smallest square to top right corner of biggest square, and have a trapezium shaped thing in the middle square?

Let the heights of the trapezium be 'a' and 'b'. You can then find 'a' by considering one of the larger trapeziums, and then add up all the individual areas of the trapeziums to find an expression for 'b' in terms of 'a' and substitute your value of 'a' to find 'b'. Then just use the formula for a trapezium.

 

[hayabusaboston]

Re: Australian Maths Competition 2013

That was Q25, and I got 1:3.

yay me too haha.

Btw I got 372 for 26, what did u do for 972?

 

[hayabusaboston]

Re: Australian Maths Competition 2013

Let the heights of the trapezium be 'a' and 'b'. You can then find 'a' by considering one of the larger trapeziums, and then add up all the individual areas of the trapeziums to find an expression for 'b' in terms of 'a' and substitute your value of 'a' to find 'b'. Then just use the formula for a trapezium.

Yea dats exactly what I did haha.

 

[hayabusaboston]

Re: Australian Maths Competition 2013

Yea dats exactly what I did haha.

realise, for the benefit of the peeps here, can u recite as many questions as u remember?
Also I am interested what answers u got too, list them if possible.

THere was one, Q28 I think, about some number N and something to do with a 1, lol I forgot the details of that one.

 

[RealiseNothing]

Re: Australian Maths Competition 2013

yay me too haha.

Btw I got 372 for 26, what did u do for 972?

Consider the scores are equal at (x,x), then you have two possibilities (x+1,x) or (x,x+1).

If the scores are unequal at (x,x+1) you also have two possibilities (x+1,x+1) or (x,x+2).

However if the scores are 2 apart (x,x+2) you only have one possibility (x+1,x+2).

Start at (0,0) and apply this, you find the pattern is double then add half of what you have, i.e.:

1) 2
2) 4
3) 6
4) 12
5) 18
6) 36
7) 54
8) 108
9) 162
10) 324
11) 486
12) 972

I might add I don't know for sure if my answers are correct, I'm just posting my personal working out.

 

[RealiseNothing]

Re: Australian Maths Competition 2013

realise, for the benefit of the peeps here, can u recite as many questions as u remember?
Also I am interested what answers u got too, list them if possible.

THere was one, Q28 I think, about some number N and something to do with a 1, lol I forgot the details of that one.

Q28: A positive integer N is made up of only 0's and 1's. When divided by 37, the remainder is 18. Find the smallest amount of 1's N can contain.

 

[RealiseNothing]

Re: Australian Maths Competition 2013

My solutions to question 21 and 23:

Question: If , what is the value of ?

Multiply each side by



Now multiply each side by



Substitute this in gives:



If you repeat this a few times you get the answer of

Question 23:

Question: Given find

Square both sides:



Cancel out the on each side:





Squaring again gives:







We want to find the value of , but if we make this one fraction we get:



But so

 

[Kiraken]

Re: Australian Maths Competition 2013

question 23 seems familiar, has it been in any hsc papers or previous amcs?

 

[Web Addict]

Re: Australian Maths Competition 2013

Wow. You guys got enough time to do the last five questions. I guessed all of them. I have a 1/1000 chance of getting one of the last few questions right.

 

[roonneyge]

Re: Australian Maths Competition 2013

Q28: A positive integer N is made up of only 0's and 1's. When divided by 37, the remainder is 18. Find the smallest amount of 1's N can contain.

Yep I definitely did not even attempt to do this one. It was Q30 in the intermediate paper I did today Q25 was also in the intermediate paper with the variation of the ratio of the area of the smaller circle rather than the volume (it was approx Q20-25).

 

[Makematics]

Re: Australian Maths Competition 2013

lol i got so badly destroyed. was absolutely exhausted after my geo trial, and there was some cunt next door doing his language speaking practice rlly loudly outside but i couldnt do anything cos i was locked in by myself -.- anyways i got a few 4 and 5 markers, but for around 5 of them i was SO close to the answer, but i felt like i made a silly cos my answer wasnt there so i just moved on... like the darts one, i got JUST off the answer so many times -.- also realise do you have the paper? my teacher wouldnt let me take mine home... omg FKN knew it now i do it again and i get it in like 2 seconds...

 

[HSC2014]

Re: Australian Maths Competition 2013

Either you guys are way above my level or 1 extra year of experience makes a lot of difference D: I only got to around Q 17 confidently before I started to break and time was running out (I probably couldn't even do the last ~10 without time restrictions)

 

[Web Addict]

Re: Australian Maths Competition 2013

Does anyone have the paper? I want to retry some of the last few questions and to predict my mark. My school is too cheap to allow us to take the paper home even though there was a space for us to write our name, year and teacher on it. Apparently, they're going to use it as practice for the coming years, but when I asked for some practice papers a few weeks ago, my teacher refused and said something about there not being enough.

 

[Kurosaki]

Re: Australian Maths Competition 2013

Wow. You guys got enough time to do the last five questions. I guessed all of them. I have a 1/1000 chance of getting one of the last few questions right.

Well, the answer is probably never going to be 0 or 999. so make that 1/998!