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Intermediate Maths Challenge - UKMT - 5th February 2015

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Original post by ChildOfTheMist
Who knows the answer to Q19? Im really confused

wat was the question
Original post by CaptainArctic
Somehow I got 5. I saw some other guy on this thread also say it was 5, but the majority on this thread are saying it's 4, which is also what most people in my school seemed to get.

I also got 4
Original post by CaptainArctic
Somehow I got 5. I saw some other guy on this thread also say it was 5, but the majority on this thread are saying it's 4, which is also what most people in my school seemed to get.


I feel discouraged...:'( from the answers that the thread have told me, I've got quite a lot wrong.
Original post by Dizgurl
I feel discouraged...:'( from the answers that the thread have told me, I've got quite a lot wrong.


What was the answer to the pentagon question with 10 missing values
Original post by arvindsha
What was the answer to the pentagon question with 10 missing values


I got 720
Original post by Dizgurl
I feel discouraged...:'( from the answers that the thread have told me, I've got quite a lot wrong.

Don't worry, boundaries will probably fall
Original post by Dizgurl
I got 720

I got 720 too
Original post by alpegu66
Don't worry, boundaries will probably fall

thank you :')
I made so many silly mistakes. I feels so depressed :mad:
Original post by alpegu66
I got 720 too


and me! My reasoning was that there were two sets of exterior angles which means its 2 x 360 = 720.
what certificate do u think 50 marks will get
Original post by TH3-FL45H
and me! My reasoning was that there were two sets of exterior angles which means its 2 x 360 = 720.


Never thought of that one.
What I did was, as the interior angles of a pentagon are 108 degrees.
(n - 2) * 180 degrees, where n = number of sides.
540 / 5 = 108 degrees.
Therefore, the opposite angles are the same, and add up to 216 degrees.
The remaining angles which all make a circle add up to 360, the other 2 angles are opposite and therefore, each angle will equal to (360 - 216) / 2 = 144 / 2 = 72 degrees.
There were 10 angles, and they were 5 pairs of 2 angles opposite to each other and the angle of the pentagon on 1 side, therefore all those angles were the same.
Total : 72 * 10 = 720 degrees.
When do UKMT publish the answers to the maths challenge
if you guys are wondering the reason the remainder is definitely 4 is because the question said
2^2* something *something etc
which means the product is a multiple of 4
a multiple of 4 when divided by 8 only gives a remainder of 0 or 4 (4 if its multiplied by an odd which in this case was true), and 0 wasnt an option so immediately 4 becomes the only possible answer
Original post by Dizgurl
I feel discouraged...:'( from the answers that the thread have told me, I've got quite a lot wrong.


Don't worry too much. I've pretty much got everything wrong. I really wish we had much more than an hour to complete the whole thing. I could have checked so many more questions, rather than rushing over the whole paper.
for the vouchers question, did it say positive integers?
Original post by dinglebells
for the vouchers question, did it say positive integers?

hmm... never thought of that
but even if it allows negatives the answer will be 3*19*18=1026
which isnt an option
how were you supposed to work out the flag question (q15)
i got 3*10*9 =270 btw
flag question...?

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