Australian Maths Competition (2 Viewers)

[MineTurtle]

Re: Australian Maths Competition 2013

Btw guys, in QLD most schools have received the results in the Australian Maths Competition.
My school has published our results and I got Prize Winner
Maybe we can share scores to figure out cut-offs in different states.
I'm soooo happy!!!

 

[obliviousninja]

Re: Australian Maths Competition 2013

Btw guys, in QLD most schools have received the results in the Australian Maths Competition.
My school has published our results and I got Prize Winner
Maybe we can share scores to figure out cut-offs in different states.
I'm soooo happy!!!

congrats.

 

[AhMcean]

Re: Australian Maths Competition 2013

wait isn it root(x+y) + root(y+z) = root(x+z), it probably works your way as well because when i did it i got the same answer as well, what i did was this:

root(x+y) + root(y+z) = root(x+z)

(x+y) + (y+z) + 2root((x+y)(y+z)) = z + x

cancelling out z+x:

2y=-2root((x+y)(y+z))

y^2=(x+y)(y+z)

Looking at this expression, it will only hold when x=z, so y^2=(x+y)^2
solving the quadratic, we get x=0 or y=-x/2

Now substituting x=z back to original equation we get root(x+y) + root(x+y)= root(2x)

so from the solution of the quadratic -x/2, we notice that -x=-2,-4,-6,-8....
However we see that from the root(2x) that x must be half of a even square number, ie. 2, 8, 18, 32...etc.

Picking -x=-2, we get y=-1. Therefore substituting x=1 and y=-1 to original equation, we get 1+1=2, which is true, so 1/x+1/y+1/z = 1/2 +1/2+-1

which equals 0.

 

[Squar3root]

Re: Australian Maths Competition 2013

wait isn it root(x+y) + root(y+z) = root(x+z), it probably works your way as well because when i did it i got the same answer as well, what i did was this:

root(x+y) + root(y+z) = root(x+z)

(x+y) + (y+z) + 2root((x+y)(y+z)) = z + x

cancelling out z+x:

2y=-2root((x+y)(y+z))

y^2=(x+y)(y+z)

Looking at this expression, it will only hold when x=z, so y^2=(x+y)^2
solving the quadratic, we get x=0 or y=-x/2

Now substituting x=z back to original equation we get root(x+y) + root(x+y)= root(2x)

so from the solution of the quadratic -x/2, we notice that -x=-2,-4,-6,-8....
However we see that from the root(2x) that x must be half of a even square number, ie. 2, 8, 18, 32...etc.

Picking -x=-2, we get y=-1. Therefore substituting x=1 and y=-1 to original equation, we get 1+1=2, which is true, so 1/x+1/y+1/z = 1/2 +1/2+-1

which equals 0.

you made an account for this lol

 

[Shadowdude]

Re: Australian Maths Competition 2013

maths is srs bsns

 

[MathsGuru]

Re: Australian Maths Competition 2013

y^2=(x+y)(y+z)

Looking at this expression, it will only hold when x=z

Unfortunately that doesn't follow - take e.g. y = 2, z = 2 and x = -1

 

[sohank]

Re: Australian Maths Competition 2013

Hope this actually makes sense, solution to question 22:

Interesting strategy.

I followed the same logic that the line CW cuts the shaded areas above and below the line equally. Hence it needs to pass through a point equidistant from the centers of two circles (1,1) and (4,1) ie at point coordinate (2.5, 1).

Any tilting of the horizontal line through (2.5, 1) will cut the circles symmetrically above and below the lines.

A line passing through (2.5, 1) and (6, 2) has a slope of 2/7 and y intercept of 2/7. Hence PW = 2/7

 

[sohank]

Re: Australian Maths Competition 2013

No.

Just solve these 4 equations in 4 unknowns:

p+q=r+s

p²+r²=53²

p²+s²=51²

q²+s²=25²

and given that p,q,r,s are positive integers, you get p=45, q=7, r=28, s=24.

It's quite simple really.

Simple to you friend !! I have been trying to solve the above four equations for 2 hours w/o success. Can u pl send me solution working by pm or in the forum. Thanks heaps !! (I know my request is more than 1 year late)

 

[Kaido]

Re: Australian Maths Competition 2013

You must have a lot of time to solve 4 variable simultaneous equations

 

[InteGrand]

Re: Australian Maths Competition 2013

Simple to you friend !! I have been trying to solve the above four equations for 2 hours w/o success. Can u pl send me solution working by pm or in the forum. Thanks heaps !! (I know my request is more than 1 year late)

We have



where .

If you know your Pythagorean triples, you'll know that 7² + 24² = 25². So from Equation (4), (q, s) is a permutation of (7, 24).

We can see from Equations (2) and (3) that r > s. We can see from Equations (3) and (4) that p > q.

Subtracting Equation (3) from (2) gives









Now separately test s = 7 (i.e. s² = 49) and s = 24 (i.e. s² = 576 (if you didn't have this memorised, it's easy to work out using the expansion of (20 + 4)²)), and take the one that gives an RHS which is a perfect square. It turns out that this is using s = 24, which gives r² = 208 + 576 = 784 = 28², so that r = 28.

Also, as s = 24, we must have q = 7.

Now plug everything into Equation (1) and solve for the remaining variable.

It's probably good for these maths competitions to memorise the first thirty square numbers and some Pythagorean triples.

 

[yo_yo]

Re: Australian Maths Competition 2013

Hello guys! Are you ready for Thursday ?

 

[Graceuf]

Re: Australian Maths Competition 2013

Hello guys! Are you ready for Thursday ?

Nope.

 

[yo_yo]

Re: Australian Maths Competition 2013

Some information how was today?

 

[Kittyrules]

Re: Australian Maths Competition 2013

oh it was baddddd

they stupidedly did it during my german lesson! And we only have 5 per cycle, instead of the usual 7!!

the begining was ok though, like the first 20 questions were fine and quite straightforward, but in the last 10 i died. I was already tired and done with maths (double periods today) so yeah i fell asleep and nah
im not a very maths person as you can tell

 

[Graceuf]

Re: Australian Maths Competition 2013

oh it was baddddd

they stupidedly did it during my german lesson! And we only have 5 per cycle, instead of the usual 7!!

the begining was ok though, like the first 20 questions were fine and quite straightforward, but in the last 10 i died. I was already tired and done with maths (double periods today) so yeah i fell asleep and nah
im not a very maths person as you can tell

At least you got the first 20! The first 10 I got okay. Then I got tired and struggled (Had chem and 3 periods of maths prior to the exam) and then wrote random numbers for the free response ones which I've done every year. I deserve a prize if I ever get one right. [emoji39]

I made origami bows when I finished. XD

 

[Sien]

Re: Australian Maths Competition 2013

I remember my friends talking about a dinosaur question

Sent from my D6503 using Tapatalk

 

[Graceuf]

Re: Australian Maths Competition 2013

I remember my friends talking about a dinosaur question

Sent from my D6503 using Tapatalk

Oh yeah... One of the questions I guessed cause I was running out of time and I had no clue how to do it.

 

[MathsGuru]

Re: Australian Maths Competition 2013

Does anyone have all the papers for this year's comp please?

 

[The_Jack]

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?

Maybe that's why people do badly when it comes to tests because they aren't relaxed!!!
Everyone try fall asleep in tests

 

[si2136]

Re: Australian Maths Competition 2013

What did you guys find about this years one?