# cambridge interview for maths

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16 years ago
#21
(Original post by fishpaste)
It'a case of saying that a set of triple primes will be in the form

n, n + 2, n + 4

and in a set of three consecutive integers you have

n, n + 1, n + 2

one must be divisible by three

n and n + 2 cannot be divisible by three if these numbers appear in a set of triple primes
so n + 1 must be divisible by three, but if n +1 is divisible by three then n + 4 must be, and so n + 4 is not prime unless n = 3, which is why 3,5,7 is the only set.
that is sort of wot i said isnt it? i have seen much harder qs than that
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16 years ago
#22
well i now know that e^pi is bigger...but how could u show that again?
was it by drawing the graphs of y=pi^x and y=e^x and then seeing which was bigger when x=e and x=pi respecitively
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16 years ago
#23
yeurck you get a test before your interview for cambridge? how AWFUL! thats so nasty, i dont think i could cope with it! i mean...interviews are bad enough, hmm..
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16 years ago
#24
What like medicine?
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16 years ago
#25
(Original post by Dill)
yeurck you get a test before your interview for cambridge? how AWFUL! thats so nasty, i dont think i could cope with it! i mean...interviews are bad enough, hmm..
Interviews are much worse. They're like tests, with impatient tutors glaring at you.
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16 years ago
#26
(Original post by lgs98jonee)
that is sort of wot i said isnt it? i have seen much harder qs than that
Well when presented with a sheet of A3 paper, a pen, and told "Prove that the only triple primes are 3, 5 and 7." I was rather distressed. It's a pretty plain, uninteresting proof to look back on, but when you've never seen it before, and don't know where to start, I assure you it's a really terrifying prospect.
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16 years ago
#27
(Original post by fishpaste)
Well when presented with a sheet of A3 paper, a pen, and told "Prove that the only triple primes are 3, 5 and 7." I was rather distressed. It's a pretty plain, uninteresting proof to look back on, but when you've never seen it before, and don't know where to start, I assure you it's a really terrifying prospect.
i believe u....i am not looking forward to a cambridge interview at all + a hard test...isnt the trinity one, called 'the trinity quiz'.
just hope i get a q that i have seen be4
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16 years ago
#28
(Original post by lgs98jonee)
i believe u....i am not looking forward to a cambridge interview at all + a hard test...isnt the trinity one, called 'the trinity quiz'.
just hope i get a q that i have seen be4
I had my interview in december at Trinity College, I attempted the following questions (applied for maths with comp sci):

(yes Trinity test is called Trinity mathematics Quiz 2003)

1) Prove that the product of four consecutive numbers is always a multiple of 24.
2)What is the highest power of 2 which will divide 20! as close as possible i.e. near 1 and what will be the highest power of 10 which will divide 20!?
3)Definite Integral [dx/1+sinx] with limits being pi and 0
4)Find all pairs of integers m and n which satisfy m^n = n^m.
5)y^2 + (x-2)^2 = k^2 and y = kx find all possible values of k.

I did extremely bad did not even get one question right!! and guess what got rejected.. I know the answers for all except (4) which is solved by theone anyway.

Anyone wnat to have a go at them?

You can also look at a past Trinity Maths Interview Quiz at

http://www.trin.cam.ac.uk/show.php?dowid=4

I would imagine it to be near impossible that you would get a questions which you have seen before otherwise the whole point of the test will be wasted.

Thanks (deserve reputation for this!)
1
16 years ago
#29
For the first one, write the consecutive numbers
n(n+1)(n+2)(n+3), then if n is odd, n+1, and n+3 are multiples of 2. Either n+1 or n+3 is a multiple of 4. n or n+2 must be a multiple of 3.

n - even. Same arguements.

2) A great trick i read. The highest power of a prime into a factorial is found as follows.
Sum from i=1 to infinity of [20/2^i]
Where [x] is the greatest integer function.

Lol, except it doesnt seem to work.
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16 years ago
#30
(Original post by integral_neo)
I would imagine it to be near impossible that you would get a questions which you have seen before otherwise the whole point of the test will be wasted.

Thanks (deserve reputation for this!)
I beg to differ. I had one question that I had seen and done a couple of times before:

If f(n) is the nth fibonnacci number, prove that f(n+1)f(n-1) - (f(n))^2 = (-1)^n.
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16 years ago
#31
I mistyped 2 in my calculator to check, it is infact correct, 18 is the highest power.
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16 years ago
#32
how would you find the answer to question (3) the definite integral one
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16 years ago
#33
For 5, if you differentiate the first equation, then find k such that y = kx is a tangent to the circle, then all k greater than that, satisfy those conditions, because we have a line crossing a circle with centre (2,0)

Actually, we will have 2 solutions to the tangent, so k will be above one number or less than some other number.
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16 years ago
#34
(Original post by integral_neo)
how would you find the answer to question (3) the definite integral one
I think you might want to try the substitution t = tan(x/2), correct me if this doesn't lead anywhere.
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16 years ago
#35
(Original post by JamesF)
For 5, if you differentiate the first equation, then find k such that y = kx is a tangent to the circle, then all k greater than that, satisfy those conditions, because we have a line crossing a circle with centre (2,0)

Actually, we will have 2 solutions to the tangent, so k will be above one number or less than some other number.
there is no doubt that ur right. However, a gemetrial approach was needed to solve this, at my interview, i suggested algebriac manipulation and the interviwer responded it can be solves far more easily using geometry. anyone try that
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16 years ago
#36
(Original post by theone)
I think you might want to try the substitution t = tan(x/2), correct me if this doesn't lead anywhere.
It doesnt work, however ur right that a substitution is needed.

i obviously know the answer as they told me during the interview..
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16 years ago
#37
(Original post by integral_neo)
It doesnt work, however ur right that a substitution is needed.

i obviously know the answer as they told me during the interview..
Are you sure it doesn't work, maybe i've got a problem with the limits or something but I get 2, which is the right answer...
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16 years ago
#38
(Original post by theone)
Are you sure it doesn't work, maybe i've got a problem with the limits or something but I get 2, which is the right answer...
Yeah 2 is the right answer but they used the substitution of t = cosx
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16 years ago
#39
didnt know that tan (x/2) will work as well.. how did u realise this?
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16 years ago
#40
(Original post by integral_neo)
Yeah 2 is the right answer but they used the substitution of t = cosx
Interesting, I thought the standard way to approach these types of question was the t-substitution... I can't get their substitution to work any easier...
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