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The Proof is Trivial! Watch

1. (Original post by Renzhi10122)
Someone's been doing some BMO1
haha you know the papers too well Thats where I first saw it, but for some reason I had a dream about doing this question the other night so thought I should share . I have been doing some BMO recently though- I saw a comment (perhaps by you) about people who say olympiad stuff isnt proper maths, mainly because they cant do it themselves, and I dont want to be one of them!
2. (Original post by EnglishMuon)
haha you know the papers too well Thats where I first saw it, but for some reason I had a dream about doing this question the other night so thought I should share . I have been doing some BMO recently though- I saw a comment (perhaps by you) about people who say olympiad stuff isnt proper maths, mainly because they cant do it themselves, and I dont want to be one of them!
Lol that was me.
BMO is wonderful I think great problem solving.

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3. (Original post by 16Characters....)
Problem 581*

You select a real number entirely at random from the interval . What is the probability that is greater than 1 in magnitude?

Disclaimer: I made this up myself. I think my logic is correct, but my probability is **** so if this is an impossible question (or significantly harder than the * I gave it) then my apologies.
Am I being dozy or is this just a half?
4. (Original post by physicsmaths)
Lol that was me.
BMO is wonderful I think great problem solving.

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I agree Although the final result for some questions I might not find amazing, the techniques involved are always quite nice. Did you notice a significant improvement in all your maths problem solving skills (including STEP) after BMO 2 revision or does it just help your number theory/ geometry stuff?
5. (Original post by joostan)
Am I being dozy or is this just a half?
Not being dozy. I just write easy questions haha.
6. (Original post by EnglishMuon)
I agree Although the final result for some questions I might not find amazing, the techniques involved are always quite nice. Did you notice a significant improvement in all your maths problem solving skills (including STEP) after BMO 2 revision or does it just help your number theory/ geometry stuff?
It helps alot with general spots aswell alot of step are off theorems simplified with stepsI seen a serious improvement after doing BMO2 properly to the extent where most of step is fairly straightforward and obvious. Ofcourse only will actually know until the 18th august but I should be ok for S,1 this year. I seen a serious significant improvement.
I only answered a few questions in III 2014 and 2015 so when I redo those papers not including the questions i already did then I will know how much I improved.

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7. Problem 582

Let b and c be uniformly distributed with and .

Find the probability that has real roots less than 1 in magnitude.
8. (Original post by physicsmaths)
It helps alot with general spots aswell alot of step are off theorems simplified with stepsI seen a serious improvement after doing BMO2 properly to the extent where most of step is fairly straightforward and obvious. Ofcourse only will actually know until the 18th august but I should be ok for S,1 this year. I seen a serious significant improvement.
I only answered a few questions in III 2014 and 2015 so when I redo those papers not including the questions i already did then I will know how much I improved.

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Thanks, Ill have another look at BMO then. Im getting to the stage where most step qs are pretty straight forwards and BMO feels like how I used to find step when I was just getting into it. I still make dumb mistakes though so hopefully it will help to phase those out . Im pretty sure you'll get those grade atleast though, my personal goal is Ss so if you cant get them I most certainly wont!
9. (Original post by 16Characters....)
Problem 581*

You select a real number entirely at random from the interval . What is the probability that is greater than 1 in magnitude?

Disclaimer: I made this up myself. I think my logic is correct, but my probability is **** so if this is an impossible question (or significantly harder than the * I gave it) then my apologies.
My probability is far crappier than anybody, but this looks very/quite nice, so:

Solution 581

So for that to be greater than one in magnitude we need

So that gives us

That's a total width of in the total interval length of - so the probability is . I quite liked this!!
10. (Original post by EnglishMuon)
Thanks, Ill have another look at BMO then. Im getting to the stage where most step qs are pretty straight forwards and BMO feels like how I used to find step when I was just getting into it. I still make dumb mistakes though so hopefully it will help to phase those out . Im pretty sure you'll get those grade atleast though, my personal goal is Ss so if you cant get them I most certainly wont!
Lol my goal is sss aswell. 100+ in each paper is the goal!

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11. (Original post by 16Characters....)
Problem 582

Let b and c be uniformly distributed with and .

Find the probability that has real roots less than 1 in magnitude.
Just to check the obvious, is that all roots <1 or sum of roots less than 1? (I guess the former)
12. (Original post by Zacken)
My probability is far crappier than anybody, but this looks very/quite nice, so:

Solution 581

So for that to be greater than one in magnitude we need

So that gives us

That's a total width of in the total interval length of - so the probability is . I quite liked this!!
Pi/2Pi= 1/2(pi/pi)=1/2

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13. (Original post by EnglishMuon)
Just to check the obvious, is that all roots <1 or sum of roots less than 1? (I guess the former)
-1< aswell

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14. (Original post by physicsmaths)
-1< aswell

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ah yep. Hurray for skim reading
15. (Original post by physicsmaths)
Pi/2Pi= 1/2(pi/pi)=1/2
16. (Original post by EnglishMuon)
Just to check the obvious, is that all roots <1 or sum of roots less than 1? (I guess the former)
Yes the former, both roots are < 1 in magnitude.

(Original post by Zacken)
That's a total width of in the total interval length of - so the probability is . I quite liked this!!
Yup, now try 582 above :-)
17. (Original post by 16Characters....)
Yup, now try 582 above :-)
Did you get this idea off a STEP paper? I remember something similar. (referring to the roots of a quadratic, not the sin x + cos x)
18. (Original post by Zacken)
Did you get this idea off a STEP paper? I remember something similar. (referring to the roots of a quadratic, not the sin x + cos x)
I have been discovered.
19. (Original post by Zacken)
Did you get this idea off a STEP paper? I remember something similar. (referring to the roots of a quadratic, not the sin x + cos x)
Yeah I think this was in a Siklos booklet (or similar)
20. Problem 583

and
Prove that is divisible by 4.

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