# cambridge interview for maths

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#21

(Original post by

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.

**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.

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#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

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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#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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#25

(Original post by

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..

**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..

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#26

(Original post by

that is sort of wot i said isnt it? i have seen much harder qs than that

**lgs98jonee**)that is sort of wot i said isnt it? i have seen much harder qs than that

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#27

(Original post by

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.

**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.

just hope i get a q that i have seen be4

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#28

(Original post by

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

**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

(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!)

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#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.

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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#30

(Original post by

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!)

**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!)

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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#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.

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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#34

(Original post by

how would you find the answer to question (3) the definite integral one

**integral_neo**)how would you find the answer to question (3) the definite integral one

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#35

(Original post by

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.

**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.

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#36

(Original post by

I think you might want to try the substitution t = tan(x/2), correct me if this doesn't lead anywhere.

**theone**)I think you might want to try the substitution t = tan(x/2), correct me if this doesn't lead anywhere.

i obviously know the answer as they told me during the interview..

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#37

(Original post by

It doesnt work, however ur right that a substitution is needed.

i obviously know the answer as they told me during the interview..

**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..

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#38

(Original post by

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...

**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...

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#40

(Original post by

Yeah 2 is the right answer but they used the substitution of t = cosx

**integral_neo**)Yeah 2 is the right answer but they used the substitution of t = cosx

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