Bmo1

Anyone else take it?

How did you think it was? I thought it was quite hard, a lot harder than last year's imho. I managed to completely do 1 and 2, and did q4 but my reasoning might not have been completely correct (I got 504 for q4).

Hope everyone did well...

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Reply 1

Ralfskini

theone

can you remember any of the questions?

Reply 2

theone

Ralfskini

can you remember any of the questions?

1. Solve the simultaneous equations:

ab + c + d = 3
bc + d + a = 5
cd + a + b = 2
ad + b + c = 6.

2. ABCD is a rectangle, P is the midpoint of AB, and Q is the point on PD such that CQ is perpendicular to PD.

Prove that the triangle BQC is isosceles.

3. Alice and Barbara play a game with a pack of 2n cards, on each of which is written a positive integer. The pack is shuffled and the cards laid out in a row, with the numbers facing upwards. Alice starts, and the girls take turns to remove one card from either end of the row, until Barbara picks up the final card. Each girl's score is the sum of the numbers on her chosen cards at the end of the game.

Prove that Alice can always obtain a score at least as great as Barbara's.

4. A set of positive integers is defined to be wicked if it contains no three conesecutive integers. We count the empty set, which contains no elements at all, as a wicked set.

Find the number of wicket subsets of the set {1,2,3,4,5,6,7,8,9,10}.

5. Let p, q and r be prime numbers. It is given that p divides qr-1, q divides pr-1 and r divides pq-1. Find all possible values of pqr.

Reply 3

theone

Noone else? :frown:

Reply 4

theone

Noone else? :frown:

Did it, did q1, (got about half of it) then did the triangle geometry ques. (think I nailed that one)

BTW, how did u prove q1?

Reply 5

theone

2776

Did it, did q1, (got about half of it) then did the triangle geometry ques. (think I nailed that one)

BTW, how did u prove q1?

It's a long laborious process of subtracting and factorising certain equations in order to derive 2b+d = 3 and a+c = 2. then the result follows from substitution into the first equation.

Reply 6

theone

It's a long laborious process of subtracting and factorising certain equations in order to derive 2b+d = 3 and a+c = 2. then the result follows from substitution into the first equation.

I subtracted etc and got like (c-1)(x-x)=3 etc etc

and did it for every single one. Then I took c-1=3, -3, -1, 1

And got 2003 for the answer

Reply 7

theone

2776

I subtracted etc and got like (c-1)(x-x)=3 etc etc

and did it for every single one. Then I took c-1=3, -3, -1, 1

And got 2003 for the answer

But c-1 is not neccessarily an integer, you've assumed that.

Reply 8

ShOcKzZ

an i ask what this Bmo1 is ?

Reply 9

theone

But c-1 is not neccessarily an integer, you've assumed that.

Yes, i assumed that it is an interger and that the other side gives 1, and I know thats not really rigerous proofs, but that direction looked so inviting and looked like a pattern, no?

Reply 10

theone

2776

Yes, i assumed that it is an interger and that the other side gives 1, and I know thats not really rigerous proofs, but that direction looked so inviting and looked like a pattern, no?

Quoting the instructions on the handout we got:

'Full proofs are expected not conjectures based on pattern spotting'.

Reply 11

theone

Quoting the instructions on the handout we got:

'Full proofs are expected not conjectures based on pattern spotting'.

Ok OK, it was my first time, and I was naieve. Do u reckon u'll get thru?

Reply 12

theone

2776

Ok OK, it was my first time, and I was naieve. Do u reckon u'll get thru?

I was j/k

I don't know if i'll get through, depends on how many marks i get for 4, as i didn't explain my method particularly clearly.

Reply 13

theone

I was j/k

I don't know if i'll get through, depends on how many marks i get for 4, as i didn't explain my method particularly clearly.

You seem like a really keen maths boffin. Doing physics/maths in uni?

Reply 14

mathboyvn

How many questions should I do to come to next round ? Any one knows what the score of last year ?

Reply 15

theone

mathboyvn

How many questions should I do to come to next round ? Any one knows what the score of last year ?

Last years qualifying mark was 19, and I personally feel this exam is a little bit harder than last year. Anything more than 20 has a reasonable chance of getting through imho.

Reply 16

theone

2776

You seem like a really keen maths boffin. Doing physics/maths in uni?

Maths (Don't like physics :smile:

)

Reply 17

theone

Maths (Don't like physics :smile:

)

What marks did u get for BMO 2 last time?

Reply 18

theone

2776

What marks did u get for BMO 2 last time?

I didn't do BMO 2, i got 14/50 in this exam last year...

Reply 19

mathboyvn

i did the same as you and i got the answer for question 4 is 504, that's definitely the right answer for q4. This is my first time, and I'm not a british, i'm a vietnamese student who is doing first year A-level in London. I wonder that when will the result come out and how can we know the qualifying mark for the next round. Thanks a lot !