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# Intermediate Maths Challenge 2010 watch

1. (Original post by Revolution is my Name)
I think I got a Merit or something, which was top 50% of the people doing the Olympiad.
Awesome!
2. (Original post by TattyBoJangles)
I signed up to do it in maths yesterday, and I've really no idea what it is, but I've got nothing to lose I suppose xD
You won't regret it .
Unless, of course, it turns out to be a disastrous embarrassingly self-confidence-damaging debacle, the result of which being you wanting the ground below you to open up and swallow you brutally, in which case it wouldn't be quite such a good idea.
3. (Original post by DerBoy)
You won't regret it .
Unless, of course, it turns out to be a disastrous embarrassingly self-confidence-damaging debacle, the result of which being you wanting the ground below you to open up and swallow you brutally, in which case it wouldn't be quite such a good idea.

Yes, true :P
Looking at the 2009 paper, it seems all right.. but it seems more puzzle-y than 'normal maths'.. I'm not great at those :P
Ah, well, I'll see how it goes
4. (Original post by TattyBoJangles)
Yes, true :P
Looking at the 2009 paper, it seems all right.. but it seems more puzzle-y than 'normal maths'.. I'm not great at those :P
Ah, well, I'll see how it goes
i've found that in these type of competition question, training your mind to see the word "integer" in a question and to hence instantly think "prime factorisation" helps a lot
5. (Original post by zdo0o)
i've found that in these type of competition question, training your mind to see the word "integer" in a question and to hence instantly think "prime factorisation" helps a lot
The prime factorisation of 2010 is bound to come up (=2*3*5*67)
6. (Original post by DerBoy)
The prime factorisation of 2010 is bound to come up (=2*3*5*67)
and 2009 = 7*7*41, and 2011 is prime
7. (Original post by zdo0o)
and 2009 = 7*7*41, and 2011 is prime
And here are a few others:

If the sum of the digits of a number is a multiple of 3, then that number is a multiple of 3 (e.g. for 6234=3*2798 and 6+2+3+4=15=3*5).

If the sum of the digits of a number is a multiple of 9, then that number is a multiple of 9 (e.g. 7254=9*806 and 7+2+5+4=18=9*2).

The sides of half an equilateral triangle- if you have a 90-60-30 degree triangle then the hypotenuse is double the size of the smaller leg.

Other divisibility rules- there are unique ones for 7 and 11 I think, but I can't quite remember then.

You should know a lot of the first few primes (<113). http://en.wikipedia.org/wiki/List_of..._prime_numbers

And some others might hit me later .

Edit:
Oh yeah, I remembered this one:
Impossible scores to obtain in the challenge- for example, you can have 135 marks if you answer every answer correctly, 129 if you miss out one 6-mark one out, 127 if you get a 6-mark question after Q20 wrong, so numbers like 131-134 are impossible.

Internal angles and external angles of regular polygons:
Each internal angle in a pentagon is 108 degrees, in a hexagon they are 120. Calculate the external angles yourself.

A few circle theorems:
(Especially for us Scots, who don't get taught this at school (this is me thinking circle theorems are in the GCSE course)). The angle subtended at the centre is twice the angle subtended at the circumference. Angles in the same segment and angles subtended by arcs (if two angles subtended by two different arcs are equal then those arc are equal- providing they subtend at both the minor arc or both the major arc ).
Also a cyclic quadrilateral is one that can have a circle constructed that touches all four vertices. Opposite angles in a quadrilateral total 180 degrees (prove it).

Similar triangles:
If you can find two angles in two different triangles to be equal (and hence the third) then they are similar. Look at SAS, ASA, SSS for congruence or AAA for similarity.

Squares are non-negative (probably won't come up, just saying ).

One mile=1609m ( 40^2 + 3^2)

One tonne=1000000 grams

Some Pythagorean triples:
3n, 4n, 5n,
5n, 12n, 13n

There are 365 days in a year, and 365=1 (mod 7) consequently if one year starts on a Monday, then the next starts on a Tuesday. Excluding leap years
8. (Original post by DerBoy)
And here are a few others:

If the sum of the digits of a number is a multiple of 3, then that number is a multiple of 3 (e.g. for 6234=3*2798 and 6+2+3+4=15=3*5).

If the sum of the digits of a number is a multiple of 9, then that number is a multiple of 9 (e.g. 7254=9*806 and 7+2+5+4=18=9*2).

The sides of half an equilateral triangle- if you have a 90-60-30 degree triangle then the hypotenuse is double the size of the smaller leg.

Other divisibility rules- there are unique ones for 7 and 11 I think, but I can't quite remember then.

You should know a lot of the first few primes (<113). http://en.wikipedia.org/wiki/List_of..._prime_numbers

And some others might hit me later .
first 2 are pure primary school wisdom ;D

triangle one is obvious no?
9. I didn't get taught that in primary school

Yeah the triangle one is obvious but it comes up quite often, and sometimes in obscure places (hexagons). Or at least sometimes it did in the link posted before.
10. hello everyone, wow i haven't posted in TSR for like 2 months :P

i'm hoping for 115+ (& Hamilton Olympiad) and i really hope i can get into Top 100 in Olympiad..... (that's just a hope...lol)

i think Top 100 are awarded medals
and Top50 are awarded medals AND book prize
(Plus, there's a summer camp for top 20 or something... but not sure)

good luck to everyone~
11. (Original post by DerBoy)
The IMO is the International Mathematical Olympiad, an international (obv) event where the top 6 people from each country sit two 3-and-a-half-hour papers, with 3 questions on each.
(Original post by Small123)
...then about 100 people go to BMO2 which is a 3 hour paper with 4 questions...
The IMO papers are actually 4.5 hours long, and both BMO-1 and BMO-2 are 3.5 hours long, but enough pedantry.

Good luck to those sitting the intermediate challenge/kangaroos/olympiads this year, but try and enjoy it than hate yourself for not doing as well as you hoped
12. (Original post by lovmaths)
hello everyone, wow i haven't posted in TSR for like 2 months :P

i'm hoping for 115+ (& Hamilton Olympiad) and i really hope i can get into Top 100 in Olympiad..... (that's just a hope...lol)

i think Top 100 are awarded medals
and Top50 are awarded medals AND book prize
(Plus, there's a summer camp for top 20 or something... but not sure)

good luck to everyone~
Did a bit of detective work
There are two summer camps, each lasting one week.
One is for the top 40 or so for the Maclaurin, and a few for Hamilton.
The other is for the top 40 or so who did well in the actual multiple-choice challenge (excluding people who are going to summer camp for being in the top 40 for Maclaurin).
13. (Original post by GHOSH-5)
The IMO papers are actually 4.5 hours long, and both BMO-1 and BMO-2 are 3.5 hours long, but enough pedantry.

Good luck to those sitting the intermediate challenge/kangaroos/olympiads this year, but try and enjoy it than hate yourself for not doing as well as you hoped

14. (Original post by DerBoy)
Did a bit of detective work
There are two summer camps, each lasting one week.
One is for the top 40 or so for the Maclaurin, and a few for Hamilton.
The other is for the top 40 or so who did well in the actual multiple-choice challenge (excluding people who are going to summer camp for being in the top 40 for Maclaurin).
mm niceeee*
do you think... about 117 will get me into summer camp? (since its EXCLUDING those who are in top40 for olympiad... ?)
15. (Original post by lovmaths)
mm niceeee*
do you think... about 117 will get me into summer camp? (since its EXCLUDING those who are in top40 for olympiad... ?)

Honestly I have no idea
16. Well if 500 get into the Olympiads (Cayley/Hamilton/Maclaurin), then that means about 160 or so get more than 100 (assuming that is roughly the cut-off for the Maclaurin). 35(40/160)=8.75..... therefore the top 40 are at most 8.75 off the perfect score of 135 so the top 40 will have over 126.25 points. I don't know how many of these will flourish in the Maclaurin, but if we say 20, I would say that lowers the admission mark to about 121 (I prefer 121 to 120, don't you?). Note this logic uses approximations and assumes even distribution.

However this is a direct quote from the website:
'The UKMT currently runs two summer school weeks in Birmingham in July, each for around forty 14‐16 year olds. Attendance is by invitation only. We are looking for potential and select students for one week based primarily on IMOK scores and the other week based primarily on IMC scores. However, many factors are taken into consideration beyond the pure numerical score.'
One of those factors they mention may be your Maclaurin score.
So you may be in luck
17. If I get in, I'll most probably die of joy, and therefore I will not be able to attend.
18. (Original post by DerBoy)
Well if 500 get into the Olympiads (Cayley/Hamilton/Maclaurin), then that means about 160 or so get more than 100 (assuming that is roughly the cut-off for the Maclaurin). 35(40/160)=8.75..... therefore the top 40 are at most 8.75 off the perfect score of 135 so the top 40 will have over 126.25 points. I don't know how many of these will flourish in the Maclaurin, but if we say 20, I would say that lowers the admission mark to about 121 (I prefer 121 to 120, don't you?). Note this logic uses approximations and assumes even distribution.

However this is a direct quote from the website:
'The UKMT currently runs two summer school weeks in Birmingham in July, each for around forty 14‐16 year olds. Attendance is by invitation only. We are looking for potential and select students for one week based primarily on IMOK scores and the other week based primarily on IMC scores. However, many factors are taken into consideration beyond the pure numerical score.'
One of those factors they mention may be your Maclaurin score.
So you may be in luck
thanks !
i would be thrilled if i get in....
19. It's nearing...
20. Without trying to be a killjoy, I must ask everyone to refrain from revealing any details about the Challenge.
The reason for this is that not every one sits it at the same time- the starting times will sprawl all over the the morning and afternoon, and there are people taking it in other countries and hence different time zones (I think there are a few New Zealanders).

This, as the article at http://www.thestudentroom.co.uk/anno...php?f=38&a=440 says, means you cannot say anything about it. Not whether question X was about triangles, nor your answer for question Y and certainly not what was question Z. You cannot even divulge how difficult you thought it was.

You will be able to discuss it openly on Friday (I think so), and if in doubt wait until the paper is posted on the UKMT website at http://www.mathcomp.leeds.ac.uk/ (note the 2009 paper is currently up, do not confuse it with the 2010 paper). It should be Saturday by the latest.

Gambatte mina!

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