# cambridge interview for maths

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Hey Ive got a cambridge interview at Girton College in 2 weeks for maths does anyone know what type of questions i will get asked in the test before or the 2 interviews. Please help me im so screwed otherwise

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#2

(Original post by

Hey Ive got a cambridge interview at Girton College in 2 weeks for maths does anyone know what type of questions i will get asked in the test before or the 2 interviews. Please help me im so screwed otherwise

**robert_harrison**)Hey Ive got a cambridge interview at Girton College in 2 weeks for maths does anyone know what type of questions i will get asked in the test before or the 2 interviews. Please help me im so screwed otherwise

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#3

What the hell, I'm also going for Maths at Girton! My interview is the 7th...

As for pi^e or e^pi, where my calculator at?! Then I can work out how to work it out...

As for pi^e or e^pi, where my calculator at?! Then I can work out how to work it out...

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#4

(Original post by

What the hell, I'm also going for Maths at Girton! My interview is the 7th...

As for pi^e or e^pi, where my calculator at?! Then I can work out how to work it out...

**ZJuwelH**)What the hell, I'm also going for Maths at Girton! My interview is the 7th...

As for pi^e or e^pi, where my calculator at?! Then I can work out how to work it out...

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#5

But couldn't you do it like:

e<3 and pi>3, so if we had x^y then we could bung in numbers that are proxies for e and pi so that the proxies are less than and greater than (or equal to?) 3 respectively. Using this 2^3 gives 8, and 3^2 gives 9, so pi^e > e^pi...

Sounds so stupid and basic doesn't it...

e<3 and pi>3, so if we had x^y then we could bung in numbers that are proxies for e and pi so that the proxies are less than and greater than (or equal to?) 3 respectively. Using this 2^3 gives 8, and 3^2 gives 9, so pi^e > e^pi...

Sounds so stupid and basic doesn't it...

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#7

(Original post by

Except e^pi is greater than pi^e. Doh!

**meepmeep**)Except e^pi is greater than pi^e. Doh!

But how do you go about showing that?

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#8

you can prove it as follows:

You draw a graph with e^x and x^e. At x=e, both graph touch/cross.

With first deviation you find out that they touch. so they rise at same rate in this point. But as

1.) x^e (which represents the graph on which pi^e is situated at x=pi in this case) is a function where the exponent stays the same all the time, and

2.) e^x (representing e^pi for x=pi) where the exponent rises as x rises, the function e^x will have an increased gradient, thus be higher than x^e when x>e. As x=pi in our problem, and pi>e, we can say that e^pi is a larger number than pi^e.

You draw a graph with e^x and x^e. At x=e, both graph touch/cross.

With first deviation you find out that they touch. so they rise at same rate in this point. But as

1.) x^e (which represents the graph on which pi^e is situated at x=pi in this case) is a function where the exponent stays the same all the time, and

2.) e^x (representing e^pi for x=pi) where the exponent rises as x rises, the function e^x will have an increased gradient, thus be higher than x^e when x>e. As x=pi in our problem, and pi>e, we can say that e^pi is a larger number than pi^e.

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#9

(Original post by

Told you it was stupid...

But how do you go about showing that?

**ZJuwelH**)Told you it was stupid...

But how do you go about showing that?

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#12

(Original post by

For Cambridge science, you are given paper to do workings

**2776**)For Cambridge science, you are given paper to do workings

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#13

(Original post by

Talk about on the spot.

**bono**)Talk about on the spot.

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#14

(Original post by

Some of the questions are rock. Like work out what happens when a piston of circlar area of x cm^3 is pushed 10cm. How much pressure is extered. Or something like this.

**2776**)Some of the questions are rock. Like work out what happens when a piston of circlar area of x cm^3 is pushed 10cm. How much pressure is extered. Or something like this.

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#15

Hardest question I got was "Prove that the only set of triple primes is 3,5,7." which I thought was absolutely solid and of course needing leading through.

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#17

i suppose u could say:

must all be odd no's: three consecutive odd numbers will have one which is a mulitple of three so therefore 3,5,7 is only possible trio

must all be odd no's: three consecutive odd numbers will have one which is a mulitple of three so therefore 3,5,7 is only possible trio

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#19

(Original post by

how do u do that then?

**lgs98jonee**)how do u do that then?

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 (unless n = 3)

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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#20

(Original post by

I just know one question, e to the power of pi, pi to the power of e, which one is bigger, without using a calculator. and show how you work it out

**Riotu**)I just know one question, e to the power of pi, pi to the power of e, which one is bigger, without using a calculator. and show how you work it out

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