When I was 12 years old (I'm now 21) I remember taking this pretty hard math test as part of some international...

When I was 12 years old (I'm now 21) I remember taking this pretty hard math test as part of some international competition.

I was digging through my old room earlier and found the question booklet. So I ask you Veeky Forums, what kind of maths were you doing when you were 12?

Other urls found in this thread:

hci.sg/aphelion/apmops/sample.htm
math.stackexchange.com/questions/910479/simplifying-a-product-written-in-capital-pi-notation
twitter.com/AnonBabble

Is it sad if I am unable to answer at least one of these question?

When I was twelve? Prealgebra.

And I was reading Goosebumps books and riding my bike to my friends' houses to play 3DO and build model rockets and catch grasshoppers in the green belt in our neighborhood and play spy games and argue about which of us had a bigger crush on girl X. You know, Wonder Years shit.

How was being pushed to succeed by overbearing parents?

I was playing football.
The real question is what kind of math are you doing now ?

Those seem okay, except 26, anyone clue me in on that one?
>math

My parents were pretty hands off, I only took this test because I was invited to through my school.


For full disclosure, I didn't get a single question in the attached photo correct when I was 12. Overall I scored 36/150, which ended up being 11th in my country.


Mostly basic calculus.

The colour of the circle's is based on how many other circles they are tangent to.
How do you 27 and 29?

Is 26 yellow?
It seems yellow + blue = green

To answer your question, I was staring out the window in algebra 1, and blundering through the tests.

We did prealgebra, but our school used to pick some students to represent the school in an in an international maths competition as well. If I recall correctly the questions were a lot easier than these though

I think it's green.
If it borders 1 circle it's red.
If it borders other 2 circles it's green.
If it borders 3 other circles it's blue.

Green.
All circles with one tangent circle are red.
Are circles with two tangent circles are green.
All circles with 3 tangent circles are blue.
etc

Ah that makes more sense
I always scored terribly on these math competitions we had to take

This is the number I get for question 27. Am I doing something wrong?
>inb4 dumb codemonkey memes

If anyone's interested I did some digging and found the full question booklet with answers. Ironically the sample they has is almost (but not exactly) identical to the test I took in 2007.

hci.sg/aphelion/apmops/sample.htm

Dude I really want to know what the colour of circle A would be and why damnit!

Green. Read the thread.

I was in the PANGEA math olympiad.
>smug friend who thinks he's better than me gets weeded out in the first round
>i make it to the finals

get fucked

question 27
How the fuck is a 12 year old supposed to solve this?
This makes me feel retarded

How do i solve 27? Give some tips, please, not the full answer.

I get this decimal approximation. Not sure what fraction it is though.
There's probably some clever way to cancel stuff.

27 is 1004/2007 desu

[eqn]\Prod_{k=2}^{2007} \left( 1 - \frac{1}{n^2} \right)[/eqn]

And how is this supposed to make it easier? You and the python guy are both retarded, find out yourself why.

math.stackexchange.com/questions/910479/simplifying-a-product-written-in-capital-pi-notation
tip here

the answer is 1/2
write out a few simple cases and try to come up with a formula and then prove it by induction (if you're a mathemathician) or write some script to do it for ya (if you are anything else) to check your result
start only with the first term, ignore the rest. then add another one. after the third one you should have the formula figured out.

anyways, any ideas for 29? I don't see how there could be a minimum for that sum, you can have negative terms so you could just take n_100 to be -999999999999999999999 or smth like that

No the answer is 1004/2007 but converges to 1/2

oh yeah that's the answer, I was used to the ->infinity thing from higher math xD

i can`t figure out whats going on in the numerator.

27: 1004/2007?
Difference of 2 squares -> Summing terms -> Cancelling terms.

i think with 29 it must mean natural numbers rather than integers and is just an error of poor english, as otherwise you're quite right in just taking huge negative numbers

difference of squares
that's what I thought too... nice but rather trivial example of AM-GM

29.
-2, - 3, - 4...
27.
2005.38
26.
Blue

I don't understand 28

30 is just a geometric sum

Simillar things, it was easier I think, but also math competitions, and I am also 21

Not that hard if you mess around with it a bit

[eqn](1-\frac{1}{2^2})(1-\frac{1}{3^2})\cdots(1-\frac{1}{2007^2})[/eqn]
[eqn]\frac{(2^2-1)(3^2-1)\cdots(2006^2-1)(2007^2-1)}{2^2\cdot 3^2 \cdots 2006^2\cdot 2007^2}[/eqn]
[eqn]\frac{(2-1)(2+1)(3-1)(3+1)\cdots(2006-1)(2006+1)(2007-1)(2007+1)}{2^2\cdot 3^2 \cdots 2006^2\cdot 2007^2}[/eqn]
[eqn]\frac{1\cdot 2\cdot 3^2\cdot 4^2\cdots 2006^2\cdot 2007\cdot 2008}{2^2\cdot 3^2 \cdots 2006^2\cdot 2007^2}[/eqn]
[eqn]\frac{2008}{2\cdot 2007}=\frac{1004}{2007}[/eqn]

xxDDDDD

30 sounds like it should be 198
The rest l don't know

what's the answer for 29?

Damn son, how is a kid gonna prove 29 without induction?
Or do chingchongs learn induction when they are 12?

Posit [math]n_{k} = (2 \cdot k) - 1[/math] then prove it by induction.
I just can't find a more elegant way.

Calc 2

Chingchongs learn induction at 12

Ehm if this was ment for 12 year olds how are they suposed to prove it?

I tool algebra when I was 12, although I was quite immature and didn't really care about school back then. Everything I didn't learn there got filled in with algebra 2 and calc. Sounds weird, but it worked. Just finished dif eq and loved it.

I think it's 220.
180 + 2*18* \sum_{n=0}^\infty 0.1^n = 180 + 36 * \frac{1}{1-0.1} = 180 + 36 * \frac{10}{9} = 220

Its green you idiot

algebra. i aced that shit with like a 99%. but it went downhill from there until i got to calculus

Why not -1000, -1001 etc. @29?

I think for 29 you can minimize the sum by minimizing n_1, then n_2, then n_3, etc. So pick n_1 to be 1, Then n_2 has to be 3. So n_3=4, etc. From there you use the gauss summation trick but subtract off the missing 2.

For 27 I'm guessing you can find a pattern if you multiply out the first few, but I'm too lazy to try it.

>So n_3=4
Way to fuck up a reccurence on the third step BROSKI

Nowhere are they asked to prove it you donut.

Fuck, you're right! But I think that is the idea.

see

I'm not sure why you're quoting me. I'm pretty sure 1+3+5+... will work.

The day Veeky Forums can't do 12 year old math. Fucking retards

2005.38 is utterly wrong. The first bracket (1-1/2^2) is smaller than one, as are the rest of the brackets, although they strive towards one. So how can the product of multiple terms smaller than one result in a value higher than 1? let alone >1? The correct answer, according to my calculator is 0,5002491281

he got everything wronge
it is hard twelve year old maths though, most people would not be able to solve these.