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UKMT Olympiad 2018

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Original post by Coding_Centurion
For question 3 I used 1/2 sin(30) x^2 but must have messed up my working. How many marks would di lose if I got the method but not the answer.
Question 1 was 12 and question 2 was 112 (have looked back at the paper


I'm not quite sure, I think if you made an arithmetic mistake, you would lose at least 2 marks, and if you made a logical mistake you would lose at least 3.

I couldn't think what sin30 was on the spot so I used another method for q3: I split it into 4 and so I got a triangle and a trapezium and then found 2, 1/2 equilateral triangles but I got the angles the wrong way round so I ended up getting 1:1+(3sqrt3/4) as my answer. Hopefully I get some marks (ideally 4 or 5 so I have chance for a medal).

Also question 6, if you multiplied all the numbers together, you would get 2^17 x 3^10. That would equal a cube number multiplied by another number, the other number being the cente number. The answer is 12 or 96.
How did people attempt Question 5 on the Hamilton Paper?
Original post by Samuel L
How did people attempt Question 5 on the Hamilton Paper?


The digits can be at most 9 so the sum must be at most 18. 2.7*18=48.6 so the number can be at most 48. Repeat this process and you will find it just repeats forever at 29. There are no other solutions as we have proved that there aren't any solution above 29. Note that 2.7-2.6=0.1. If the sum of the digits was below 10, then the sum*2.7-sum*2.6 will be less than 1. You can test the solutions below 10 to show that. 10 won't work as there isn't an integer between 26 and 27.
Original post by Samuel L
How did people attempt Question 5 on the Hamilton Paper?


The digits can be at most 9 so the sum must be at most 18. 2.7*18=48.6 so the number can be at most 48. Repeat this process and you will find it just repeats forever at 29. There are no other solutions as we have proved that there aren't any solution above 29. Note that 2.7-2.6=0.1. If the sum of the digits was below 10, then the sum*2.7-sum*2.6 will be less than 1. You can test the solutions below 10 to show that. 10 won't work as there isn't an integer between 26 and 27.

By the way, I only realised the start of this in the last 10 minutes and my answer is pathetic and doesn't explain things well- I found 29 though. I realised it properly in the next few lessons at school. There also may be other solutions using inequalities but i could't figure them out.
Original post by Samuel L
Hopefully a medal or above :smile:


Wow I hope u do, that would be amazing.
Original post by Luhemnarik
The digits can be at most 9 so the sum must be at most 18. 2.7*18=48.6 so the number can be at most 48. Repeat this process and you will find it just repeats forever at 29. There are no other solutions as we have proved that there aren't any solution above 29. Note that 2.7-2.6=0.1. If the sum of the digits was below 10, then the sum*2.7-sum*2.6 will be less than 1. You can test the solutions below 10 to show that. 10 won't work as there isn't an integer between 26 and 27.

By the way, I only realised the start of this in the last 10 minutes and my answer is pathetic and doesn't explain things well- I found 29 though. I realised it properly in the next few lessons at school. There also may be other solutions using inequalities but i could't figure them out.

I did it with inequalities if anyone wants to see...
Original post by Boucherwowcha
I did it with inequalities if anyone wants to see...

I'm interested as I think there were probably more than one way of going about the question
Original post by Samuel L
I'm interested as I think there were probably more than one way of going about the question

2.7>(10a+b)/(a+b)>2.6
2.7a+2.7b>10a+b>2.6a+2.6b
27a+27b>100a+10b>26a+26b
a+b>74a-16b>0
Now substitute in a=1 (no solutions)
Now a=2 (b=9 is the only one)
No more greater values of a are possible otherwise b>9 which is not possible because it's a digit.
Hey guys, just so u r up to date, all three of the 2018 Olympiad papers r now online for access on the UKMT website, this link will also lead you straight to the PDF file https://www.ukmt.org.uk/pdfs/IMOKOlympiads18All.pdf . Also the solutions will be published on April 2nd so keep a watch out for those and feel free to continue discussing them on this thread :grin:. Since the solutions are published in April i'm assuming that the results will be given back around then, so we will probably receive them after the Easter holidays. Also idk if this is true but for the Olympiad papers do you receive your actual exam paper back so you can see where you made mistakes and do you get to keep them? Thxx P.S Hope this info was useful:excited::grouphugs:
Original post by Yt.shusshhhh
Hey guys, just so u r up to date, all three of the 2018 Olympiad papers r now online for access on the UKMT website, this link will also lead you straight to the PDF file https://www.ukmt.org.uk/pdfs/IMOKOlympiads18All.pdf . Also the solutions will be published on April 2nd so keep a watch out for those and feel free to continue discussing them on this thread :grin:. Since the solutions are published in April i'm assuming that the results will be given back around then, so we will probably receive them after the Easter holidays. Also idk if this is true but for the Olympiad papers do you receive your actual exam paper back so you can see where you made mistakes and do you get to keep them? Thxx P.S Hope this info was useful:excited::grouphugs:


You receive your script with the examiner's comments on it, but it will take time to come.
Original post by Luhemnarik
You receive your script with the examiner's comments on it, but it will take time to come.


Oh thanks. I think that'll be really useful for everyone. I find it so annoying when u get a question wrong but you don't remember where you make a mistake.
I received my gold and best of year certificate this week, anyone else?
I understood that solutions weren't going to be published on 2nd April since it's a bank holiday, but now the suspense is too much...
Results come out on 16th
Albeit with a weeks' delay...the solutions have been posted! I'm very happy :smile:

There are a few steps I might have overlooked in my solutions. Would they deduct marks if I didn't clarify that we can divide by an algebraic variable because we know it isn't 0?
Original post by TheGame314
Albeit with a weeks' delay...the solutions have been posted! I'm very happy :smile:

There are a few steps I might have overlooked in my solutions. Would they deduct marks if I didn't clarify that we can divide by an algebraic variable because we know it isn't 0?


Possibly 1 Mark if it's not obvious
The thresholds are out and results are being emailed this week:
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Aiping
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Anyone gets their results yet?
Original post by Aiping
Anyone gets their results yet?


Just received my Cayley and I'm ecstatic- 60/60!
Original post by TheGame314
Just received my Cayley and I'm ecstatic- 60/60!


Very well done!
I dropped 2 marks last year on the Cayley because I said "by simple logic" which is quite annoying. I emailed my school when the results were out and they still haven't replied. :frown:

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