# Mathematics Interview Questions

This may have already been asked, but I was wondering if anyone who applied for Mathematics (or one of the joint courses in it) at Oxford (well or Cambridge maybe, since the questions asked might be of a similar type) remembers any questions they were asked at interview? Were there any common/frequently asked topics (that I should maybe make sure I revise well)? I don't really mean the big long paper they set you, rather the actual interview with an admissions tutor, but any help will be useful!

Also, apart from doing the 2 papers that they have on the website, plus STEP papers, does anyone have any more advice on how to prepare for the interview?

One of my mates applied to maths at Oxford, can't remember his questions though, but I remember they involved calculus with logarithms etc.
Differentiating xlnx seemed to be very common among maths interviews (although it wasn't asked in the Oxford one)
I seriously can't remember what the details of the questions were...
In one of the interviews I was given a sheet that contained various questions from calculus to complex numbers
One question that I fully remember is a quiz:
There is a large circular table and you and I put a coin (also circular) in alternating order (i.e. you, me, you, me etc)
the coins can't overlap. they also can't stick out at the edge of the table.
Whoever puts the last coin (i.e. if putting the next coin without overlapping another coin is impossible) wins
If you can lay the first coin, what strategy would you use so that you can win whatever happens?
(I told the professor that I'd use a huge coin but he said no, the coin has to be very small compared to the table )
In my second interview, I had lots of really hard questions about prime numbers and similar things. I can't remember them, but my brain went into overdrive.
The first interview had only one question and this was to solve a^b=b^a for all real a and b. Did pretty well in that I guess as I got in.
My questions were

1.) How many solutions does

ln x = kx

have

2.) Do you know what twin primes are? Yes. (they are a pair of prime numbers separated by 1...e.g. 3,5 .....11,13) Can you prove that that the only triple prime is 3,5,7?

3.) Sketch y = x^2. sin(1/x)

4.) If you drawn N lines on a plane, how many interesections and how many regions are there? Prove it by induction
fishpaste
4.) If you drawn N lines on a plane, how many interesections and how many regions are there? Prove it by induction

Yannis

yep I'd seen it before too *was very grateful*
fishpaste
yep I'd seen it before too *was very grateful*

I never heard it before, but I answered it pretty well, scribbled on a piece of paper, then asked if the Professor was Russian, which he was and had a little chat about random stuff!
fishpaste
2.) Do you know what twin primes are? Yes. (they are a pair of prime numbers separated by 1...e.g. 3,5 .....11,13) Can you prove that that the only triple prime is 3,5,7?

jees. That took me a whole 30 seconds to get... I felt stupid when I couldn't work out what it was about.
Thanks for all the replies so far!
S@sha
jees. That took me a whole 30 seconds to get... I felt stupid when I couldn't work out what it was about.

huh...i still dont get the question??...how do u do ittt
hajira
huh...i still dont get the question??...how do u do ittt

To find another triple prime, you need to find a twin prime with either a prime above it, or a prime below it. However, since the twin prime is two consecutive odd numbers that aren't multiples of 3, the odd numbers above and below it must be multiples of three, ie. not prime. Hence all possible triple primes will contain 3, as it is the only prime multiple of 3 (!) and so 3, 5, 7 is the only triple prime.
And this is all on top of the Oxford maths test...I'm applying for Computer Science and I still have to take it!