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# cambridge interview for maths watch

1. 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
2. (Original post by 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
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
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...
4. (Original post by 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...
You can try to sketch two graph in the same x,y-cordinates,they are e to the power of x, and x to the power of e, they will meet when x=e, but you should also aware that there are two kind of " meeting", one is crossing, the other is touching, you should also work out the derivative of two functions at x=e, you will find they are the same, so the just touch each other tangentially, then try draw a line x=pi, you will get the answer!
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...
6. Except e^pi is greater than pi^e. Doh!
7. (Original post by meepmeep)
Except e^pi is greater than pi^e. Doh!
Told you it was stupid...

But how do you go about showing that?
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.
9. (Original post by ZJuwelH)
Told you it was stupid...

But how do you go about showing that?
It is not easy, but I'll come back to you on it.
10. so in an interview, u r given grapg paper and time to draw a graph
11. For Cambridge science, you are given paper to do workings
12. (Original post by 2776)
For Cambridge science, you are given paper to do workings
13. (Original post by bono)
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.
14. (Original post by 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.
area would be cm^2...i take it that was not a proper q :-)
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.
16. how do u do that then?
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
18. every third odd number is divisible by three
19. (Original post by lgs98jonee)
how do u do that then?
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 (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.
20. (Original post by 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
thats a horribly cruel thing to ask!

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