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# Intermediate Maths Challenge - UKMT - 5th February 2015 watch

1. (Original post by SpeedieABC)
One strip - Y

X = (Y + Y - X)/8
= 0.25Y - 0.125X
1.125X=0.25Y
9X = 2Y
X = 2/9 x Y

23

First Letter--------------------

C 1st to 24th
I 25th to 48th
K 49th to 72th
M 73th to 96th
U 97th to 120th

Second Letter---------------

C 97th to 102th
I 103th to 108th
K 109th to 114th
M 115th to 120th

Third Letter--------------------

C 109th to 110th
I 111th to 112th
M 113th to 114th

Fourth Letter--------------------

C 111th
M 112th

25.

1/4 x 3/4 x 2 =
3/8

1- 3/8 = 5/8
Got it, thanks very much for these!
2. (Original post by Yuuchin1)
hmm i did the same and i got 35... where do you have your 2*2 square and 1*1 square in your calculation
Yeah there it is, classic 2*2=2 mistake, it was 35

Method remains the same, but by the time I got to these few questions I had 10 minutes left and my brain was starting to emit sparks, especially after working out that plates and cups question (which ended up being wrong)

What a disaster, hope I still have enough for a gold
3. 22. i assumed the small squares were of size root2 in length to ease calculation

therefore, you can figure intuitively the big square is 12x12 there are 24 small root 2 by root 2 squares. 24x2/144 = 1/3
4. Anyone got working for 24? Can't remember how I did it :/
5. I was Supposed to do it, but since our session was before school, I.e 7:45 am, i didn't wake up in time, and therefore missed it

I did the senior one, and that was hard, just missed out by two marks on a Bronze.
Last year I got a silver with 8 marks off the Gold.
How do you prepare for these papers ?
Having just checked over my answers, I'm certain I got only got 45(bronze) ,but after going through a past paper prior a day before the challenge and getting up to around Q22, I'm curious as to what I'm doing wrong in terms of my approach and how quickly I should aim to complete the questions.
To be honest, its very difficult to prepare for something like the UKMT, because you never know what they throw in! But at times, you just need to be fast about your approach to the question. For example you need to know what equation, you are going to do without wasting time, especially for 1-15. For 16-25, I would advise to not guess, and actually work through them, because they're actually not that hard, its just the wording you have to familiarize yourself with....

Apart from that, I would advise looking at the Stanford Maths Challenge, and not only try them but look at their approach, it may help improve your logical approach.

I hope that helps, even though you think you got a bronze, you still have the senior to go
7. (Original post by Infaredz)
Anyone got working for 24? Can't remember how I did it :/
wasnt that the one with a square and a quarter-circle?
if it was it was 13 i think
pythagoras etc

the radius of a circle is always the same, so x^2= (x-8)^2+(x-1)^2
x^2= 2x^2-18x+65
0=x^2-18x+65
=(x-13)(x-5)
as it is impossible to take away 8 from 5 in lengths (always positive)
x=13
8. can someone explain ant question, maybe by using diagram
9. (Original post by Infaredz)
Anyone got working for 24? Can't remember how I did it :/
(im assuming you have the qustion paper)
draw perpendicular line from p to rs and name it A

Draw perpendicuar line from P to TS and name it B

I set the value of AS to x
therefore the radius is also x+8 and PS is x+8
the squares length is also x+8 so PA is x+7

Pythagoras theorem-
ASsquared + PA squared is PS squared

just solve equation

(x+8)2= (x+7)2+x2
10. Thanks, I think that's something along the lines of what I did.

Do you think 83 is still enough for a gold?
11. (Original post by dinglebells)
can someone explain ant question, maybe by using diagram
hmm.. ill try
12. ok draw the diagram in front of you
13. (Original post by Infaredz)
Thanks, I think that's something along the lines of what I did.

Do you think 83 is still enough for a gold?
Easily.
1A
2E
3E
4C
5B
6D
7E
8B
9B
10C
11D
12B (I know this is wrong)
13A
14C
15C
16D
17D
18A
19D
20E
21D
22A

I didn't do 23, 24 or 25
15. (Original post by Infaredz)
Anyone got working for 24? Can't remember how I did it :/
see attachment
Attached Images

16. (Original post by Yuuchin1)
ok draw the diagram in front of you
i forgot how the diagram looked like
17. (Original post by dinglebells)
see attachment
18. (Original post by Dizgurl)
I feel discouraged...:'( from the answers that the thread have told me, I've got quite a lot wrong.
Me too
Normally I get 100ish.... From what I've hears I got 60-70....

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19. (Original post by SpeedieABC)
k good job
different method tho
20. (Original post by theworkkid)
Me too
Normally I get 100ish.... From what I've hears I got 60-70....

Posted from TSR Mobile
I can tell grade boundaries will fall 4-5 marks from last year. I want 97/98 so I can guarantee Hamilton, doesn't seem likely...

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