Interview Questions I was asked at Oxford St Catz College.

(First Interview)

1) Why do you want to study maths?2) You wrote something on your personal statement about the Mclaurins series, tell me

about it?3) Prove that when p 3, then p - 1 is divisible by 3 (where p is a prime number)4) Sketch a graph of the points that satisfy: sin(x) = cos(y)

5) a) How many different paths are there from A to B? (in terms of n)b) What if a road block is introduced at (p,p)?c) What if another road block is introduced at (q,q)? How many

ways from A to B are there avoiding the roadblocks? (in terms of n, p and q)

(Second Interview)

1) Sketch f(x) = xsin(x) (I was briefly asked if there was any symmetry)

(I was then asked the following true or false questions about the function I sketched)

a) There are real values of y such that f(x) > yb) For some value of x there are real values of y such that f(x) > yc) There are real values of y such that for some value of x, f(x) > yd) For real values of x and y there is some value z such that z > x and f(z) > y

(there were more of these, I think about 7 in total but I wasn't doing well so they decided to change question, also not 100% sure if that is how b and c were worded)

2) What is the longest pipe that can be taken round the corner of this corridor. (you ignore the width of the pipe and just deal with its length. Give the answer in terms of a and b)

(p,p)

B

(q,q)

A

nn

a

b

Pipe

(Third interview)

1) Sketch the graph of

2) If two nodes are connected by an arc, they cannot be the same colour. There are n colours. How many different ways can the following diagrams be coloured?

3) How many different ways can the following corridor be tiled?

Using 2 by 1 tiles

2

n

Interview questions that I was asked at Oxford University College.

1) Why do you like maths?2) What areas of A level maths did you enjoy - can you expand?3) What job can you see yourself doing in the future?4)

You start with 10 1sYou then take x and y and replace them with: x + y + xyFor

example let these two be x and y, you then get:

1 1 1 1 1 1 1 1 1 1 yx

1 1 3 1 1 1 1 1 1

Say you keep repeating this with two of the numbers, what will the final number be?

I was then asked, will it always be this number? What if you pick different values for x and y each time?

Finally I was asked to find a general formula for the number at the end and prove that it was true

For the one above I was proving the general formula at the end when all the numbers you start with are of the form 2 - 1n