cambridge interview for maths Watch

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robert_harrison
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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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Riotu
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(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
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Juwel
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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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Riotu
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(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!
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Juwel
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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...
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meepmeep
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Except e^pi is greater than pi^e. Doh!
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Juwel
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(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?
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spack2000
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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.
Bigcnee
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(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.
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lgs98jonee
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so in an interview, u r given grapg paper and time to draw a graph
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GH
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For Cambridge science, you are given paper to do workings
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Nima
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(Original post by 2776)
For Cambridge science, you are given paper to do workings
Talk about on the spot.
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GH
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(Original post by bono)
Talk about on the spot.
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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lgs98jonee
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(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 :-)
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fishpaste
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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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lgs98jonee
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how do u do that then?
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lgs98jonee
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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
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lgs98jonee
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#18
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every third odd number is divisible by three
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fishpaste
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(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.
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john !!
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(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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