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# UKMT Senior Individual Maths Challenge 2016 - Preparation and Tips watch

1. (Original post by tryeeme)
I did it a way I haven't seen here yet. Taking each side to be length 1, QU = 1/2.

Where TU touches the arc QS, I have called Z. PZ=PQ=1 (radius). Because both are tangents, QU=UZ=1/2.

The same argument can be made for ST, which equals TZ. Take TZ to be n, and therefore TR=1-n.

therefore 1/2 squared + (1-n)^2 = (1/2 + n)^2, which I solved to get n=1/3, so TR=2/3. 2/3:1/2 = 4:3

Edit: Just seen it was posted 5 mins ago, as I was typing this xd
Here's a stupid way to do it:
(2+i)^2 = 3+4i
QED
2. I think I got 80. Do you think that could be a gold?
3. (Original post by SushiBunny)
Here's a stupid way to do it:
(2+i)^2 = 3+4i
QED
ahh i think i remember you from imc last year, how did you do in smc this year
4. (Original post by 123Master321)
ahh i think i remember you from imc last year, how did you do in smc this year
Fine, probably
BDBCA
DABCB
DDEDE
CCEBD
5. Anyone know when the official answers will come out?
6. (Original post by SushiBunny)
Fine, probably
BDBCA
DABCB
DDEDE
CCEBD
Pretty sure that's 100%
7. Too embarrassed to put my score here, probably haven't even qualified for kangaroo. I deserve to be shot, feel like such a ****ing idiot. Maths really isn't my strong point. Good thing I'm doing a joint honours maths degree. ****.
8. (Original post by louisforrest)
Pretty sure that's 100%
Yaaaayyy, it's satisfying to know you haven't made any mistakes
9. (Original post by SushiBunny)
Yaaaayyy, it's satisfying to know you haven't made any mistakes
hope I'm in the same situation although had to miss 4 of the questions
10. Were you guys not given all the official answers at the end of the challenge? My school got sent an envelope which just wasn't allowed to be opened until afterwards, so our teacher just read it out after we'd handed our papers in...

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11. how to do 19: the quadrilateral one?
12. (Original post by HapaxOromenon3)
No, you can draw the diagram and see it's 84. That's what everyone else at my school got, and we at Westminster are considered to be the brightest kids in the country given our performance in GCSE and A-Level results tables.

(Original post by HapaxOromenon3)
We did that one in class and it wasn't found to be that difficult, though my experience is probably atypical since I'm at Westminster, one of the top academic schools in the UK. Nevertheless you are correct that it was harder than this year, hence the low boundaries. In my view this year was slightly, but not much, harder than last year, so the BMO1 boundary is likely to be around 100.
didn't catch that mate, what school are you at again?
13. (Original post by SCandium)
Were you guys not given all the official answers at the end of the challenge? My school got sent an envelope which just wasn't allowed to be opened until afterwards, so our teacher just read it out after we'd handed our papers in...

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Same here lol
14. Hi everyone!
Am I likely to get any certificate with a score of 89? I don't mind getting one or not as I was literally told last week about this challenge and had no preparation for it.
15. (Original post by JickDee)
how to do 19: the quadrilateral one?
I said the sum of the other 3 smaller sides had to be greater than the largest(like the triangle inequality), so choosing 1,2,3 then we know n>=6 means it is impossible, so 1,2,3,6 , since 2+3+6=11, the last side had to be 11 =m -->C
16. (Original post by JickDee)
how to do 19: the quadrilateral one?
If you have four lengths that cannot make a quadrilateral, then one of the sides is "too long", i.e. it is greater than or equal to the sum of all the other sides.

Picking the smallest options for the first three numbers in the set (1, 2, 3), we find that the fourth number must be at least 6, and so the fifth and largest number is at least 2+3+6 = 11
17. Can anyone who has the answers post them up (or PM me)? I'm rly desperate to know!
18. (Original post by louisforrest)
Pretty sure that's 100%
I got:

BDBCA
DABCB
DDEDE
?CCBE

That's 22/25, should be enough for the BMO1!
19. (Original post by Treblebee)
Can anyone who has the answers post them up (or PM me)? I'm rly desperate to know!
We got given these at the end:

1.B
2.D
3.B
4.C
5.A
6.D
7.A
8.B
9.C
10.B
11.E
12.C
13.A
14.D
15.B
16.D
17.D
18.E
19.D
20.E
21.C
22.C
23.E
24.B
25.D

Of course I might have made a mistake copying these up, please correct me if so

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20. What should someone who's hoping to go to top unis such as Cambridge to do maths get on this challenge.
Im in yr 12 and this was my first ever challenge!

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