Oxbridge Maths Interview Questions - Daily Rep

Is there some kind of sylabbus online on what topics they might cover during the interview? I mean, they can't expect you to know toppography or chaos theory of a high school student.

Reply 601

Zacken

22

Original post by FutureOxford3

Is there some kind of sylabbus online on what topics they might cover during the interview? I mean, they can't expect you to know toppography or chaos theory of a high school student.

Your A-Level syllabus is all you need.

Reply 602

FutureOxford3

2

Original post by Zacken

Your A-Level syllabus is all you need.

Can you link me to it please. I forgot where I put it. Thanks.

Reply 603

Smaug123

15

Original post by FutureOxford3

Can you link me to it please. I forgot where I put it. Thanks.

Consider using a device known as a "computer" to access a search engine hosted externally via the Internet. I'm told they make this kind of task much easier nowadays.

maths is hard

Original post by Mop3476

maths is hard

You'll be fine, don't stress

Posted from TSR Mobile

Reply 606

Skoh7645

3

Do u still hav the document with all answers to these question?

Reply 607

Mark Robinson

2

Could you post your solutions?

Reply 608

Jasmine Xu

I think question No.4 is not as easy as what the author written in the spoiler. :smile:

70) 166 zeroes

Original post by BlackChess7531

70) 166 zeroes

Question means "how many trailing zeroes", and you are not supposed to use a caclculating device.

Reply 611

TangoPangolin

11

Is the answer for 12) 1225?

Reply 612

DFranklin

18

Original post by Shrootz

Is the answer for 12) 1225?

I think that's quite a bit too high (but I didn't exactly spend much time on it). Care to explain your reasoning?

Reply 613

TangoPangolin

11

Original post by DFranklin

I think that's quite a bit too high (but I didn't exactly spend much time on it). Care to explain your reasoning?

Yeah, I realised the mistake I made. I drew four dots then six, eight and realised there was a pattern in the number of squares but when I drew the dots it was an n by 2 grid not an n by n grid as the question specifies :indiff:

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Reply 614

Jushae

3

Original post by Shrootz

Yeah, I realised the mistake I made. I drew four dots then six, eight and realised there was a pattern in the number of squares but when I drew the dots it was an n by 2 grid not an n by n grid as the question specifies :indiff:

.

That one I got 285 as the answer, noticing that every time you increase the grid dimensions byone, you add (n-1)^2 new potential squares to the possibilities.

So for a grid of 2x2 dots, it's 1^2, grid of 3x3 dots it's 1^2 +2^2, for a grid of 4x4, it's 1^2 +2^2 + 3^2. And so on for all values of n.

Reply 615

Maor Nativ

1

Original post by El Matematico

17. Prove 4n - 1 is a multiple of 3

This is true if the difference is divisible by 3, i.e.

4^(n+1) - 1 - (4^n - 1) is divisible by 3. So we have

4^(n+1) - 4^n
=4^n(4-1)
= 3*4^n

Hence is divisible by 3.

Really good. I liked the way you used induction to prove it. Do you think it's possible to prove it just by explaining that subtitue 1 from any multiplication of 4 will give a multiplication of 3 because it's the previous number. Thanks