I'm in year 10, and looking to go to Oxford in a few years, I can follow what you say at 0:57 although we have not covered it in class, 1:35 (the clever clogs way) we have NOT even attempted anything near that in our class. Now I know that this is an interview for Oxford, so a 14 year old (Year 10) most likely will not be expected to be able to attempt these questions, my question is: At my age (just turned 15) would you have been able to attempt these questions to some degree of success? Thanks
@Olliek94 Um... I seriously doubt I could have answered that many of these questions in year 10! I remember going through one of the old physics aptitude tests with some friends for a laugh in about year 10 and between us we could do maybe two questions :/
As for the clever clogs way, that's what they teach you here - so that's why it would be impressive to use it in an interview! It is also a beautiful bit of maths by Euler - ask your maths teacher about Euler's theorem.
Just a suggestion, for the last question, I have a suspicion that the last question they asked you will have been something to the effect of "how many people do there have to be in a room for there to be a greater than even chance of them sharing a birthday" ? It's in the same sort of category of birthday probability questions.
hi Simon...the maths questions you talked about seem very difficult...
i have a physics interview next week (@keble) and i have not done further maths...what should i expect in my interviews...will one of them be a maths interview?
also...please do u have any other things for preparation or tips during the interview?
anything would be much appreciated...and thanks for the video :)
@rohitmkiller if you haven't done further maths then they might be a bit easier on you (though, not to scare you or anything) but Keble is notoriously maths-based in its teaching. You will still most likely have a maths interview though.
In terms of preparation I would recommend doing as many papers as you can get your hands on and talk aloud whilst solving the problems - it's important to be able to communicate how you think. And stay calm! Just try not to build it up in your head
@rohitmkiller I would read around a little bit so you know the biggest stories at the moment (e.g. the neutrino experiment) but don't invest too much time in your research - it's much more important to have a sharp and clear mind in the interview so be sure to relax and socialise a bit, and don't get overloaded with new information. If there's something that interests you then by all means research that if you'll enjoy it!
@rohitmkiller (cont.) too much and you'll be fine! Try to think of it as a chance to sit down for twenty minutes with some of the most switched on minds in the field you're interested in, which isn't something you can do every day. Relax, take your time and you'll be ok :)
Hi, I've got an interview for chemistry at Jesus, will I have a maths interview like that? I'd expect the physics maths interview to be harder but it would be nice to know :)
@electrowhip I think the chemistry maths interview questions will be slightly easier, though to be honest I think you would serve yourself best by assuming it will be just as had (that way, if it is easier then it's a nice surprise!) as the two courses assume the same initial subjects, and the maths involved at degree is broadly similar (certainly in quantum mechanics anyway).
@dylanparker72 I think most people do them in Further Maths - fp1 in the syllabus I was on. As for the sin(x)=kx question, the question was for what values of k do the two lines intersect only once in the x>/0 domain
@05swanbe Dude i was like wtf? on taylor expansion also that in fp2 so i ddnt know that but if u use the sine addition formulae and then u say that cos1 is very close to 1 and sin1 is very close to 0 you end up with sin60= 0.866 rounded to 0.87 which is close enough to the real answer. @SimonOxfPhys Dude for the question about the 2nd derivative u ploted the function of sinx not -sinx is that meant to be like tht? since maybe if -y=-sinx then y=sinx i dno can u clarify?
@69alaniz I actually can't remember what I said in the interview- I don't think they were interested in a numerical answer anyway. I suppose you could use the sine addition formula but when they were giving me guidance they were leading me in the direction of the expansion, which is a more significant idea than memorising. trigonometric identities.
As for the second derivative question the point isn't that the solution is a sine function, the point is that it is sinusoidal, or more explicitly...
@69alaniz cont. that it is a linear superposition of e^ikx and e^-ikx where i is (-1)^0.5. If you plug that into the differential equation that they have set up (although they don't explicitly describe it as such) then you find that that is the general answer.
@05swanbe I cheated and used a calculator! The point of the question is to establish the technique of expansion, rather than how good you are at mental arithmetic. Though being able to do that kind of mental arithmetic can only be a bonus!
@SimonOxfPhys Hmmm... but surely in an interview you aren't allowed a calculator, without which I probably wouldn't get it to even 1sf. Or would they just stop you on the line before?
What module is the Taylor Expansion in anyway? I just tried the sin addition formula but it wasn't pretty :/
@alextutorworld I'm afraid that I recorded this using my shitty old Olympus camera so this is the best quality available (I actually cleaned up the audio on iMovie too!). Sorry!
@km11293 if we assume that d/dx(e^ix) = ie^ix and then define f(x)=cosx + isinx and differentiate we get d(f(x))/dx= -sinx + icosx. This equals if(x). We can equate the two and say that f(x)= e^ix = cosx + isinx.
Substitution of x=pi/2 yields f(x) = 0 + i(1) = i.
As for the problem at 3:14 I meant that between x=pi/2 and x=5pi/2 there exists one solution, but at x=5pi/2 there are two, so the solution is a < inequality.
@km11293 Because e^iPi = -1 (Euler's theorem). Thus if you root both sides (i.e. raise them to the power of a half), you have e^(iPi/2) = (-1)^(1/2), and the square root of -1 is i.
@10tacle21 I would recommend reading any of Feynman's stuff such as 6 easy pieces, and 6 not so easy pieces for general background (specifically on special relativity). For linear algebra I highly recommend 'An introduction to linear algebra with applications' by Steven Roman and 'Mathematical Methods' Riley, Hobson and Bence for all other first year maths! Classical Mechanics by Steve Morin is good too. Make sure that you get really comfortable with doing calculus as you will be doing a lot!
You made the sin(60 question overly complicated. All that was needed was an equilateral triangle. Then using PT you could see that a triangle with sides length 2 would have a height of root 3 and as sin(x=O/H then it is root 3 over 2
@jembishop Yes, however the point of the question is to work out sin(61) using knowledge of the value of sin(60). If asked how to prove the value of sin(60) that's how I would have done it though
Interesting. I had a Cambridge physics interview a few years ago (and got in) but it was definitely easier than yours. I just harped on about relativity for a while, because I'd read a little about it before and solved a nifty circuits problem. Two interviews.
What you said at 0.37 confused me so much. I was spending ages trying to work out how you could argue that sqrt(i) is minus one. Shouldn't've believed him. Cambridge professors are much better - they don't tell lies. :p
Hi, great video! The only think that scared be was the large amount of further maths that was present in your interview. Do you think that it is necessary to study further maths so as to not look like a buffoon at the interview.
@mynameislegion5 I would certainly recommend studying further maths if at all possible - the course is very mathematical and people who don't have the extra experience of doing 2 maths A levels are at a disadvantage. That said, there are people who get in who only did A level maths, so while it's most definitely recommended to do further, it's by no means compulsory.
hi i'm going to have an interview for earth science at st hughs! are the questions for earth science of this sort as well. I'm also confused because I applied to University college initially but they put me in St Hughes.So is it likely that university will interview me as well?
@peace1202 it probably means that univ was oversubscribed for earth sciences, so some candidates are sent to have interviews for other colleges with less applicants. I've got an interview for physics at univ if you're wondering. After about an hour of research i am sh*ting bricks.
@covo6624 Yes. The idea is that the solution is sinusoidal. You could also say that any linear combination of e^kx and e^-kx is also a solution, which is equivalent (but more elegant)
I refuse to believe that maths is not your strong point!
Butdidudie 1 month ago
@Butdidudie Ha! tell that one to my tutors...
SimonOxfPhys 2 weeks ago
I'm in year 10, and looking to go to Oxford in a few years, I can follow what you say at 0:57 although we have not covered it in class, 1:35 (the clever clogs way) we have NOT even attempted anything near that in our class. Now I know that this is an interview for Oxford, so a 14 year old (Year 10) most likely will not be expected to be able to attempt these questions, my question is: At my age (just turned 15) would you have been able to attempt these questions to some degree of success? Thanks
Olliek94 1 month ago
@Olliek94 Um... I seriously doubt I could have answered that many of these questions in year 10! I remember going through one of the old physics aptitude tests with some friends for a laugh in about year 10 and between us we could do maybe two questions :/
As for the clever clogs way, that's what they teach you here - so that's why it would be impressive to use it in an interview! It is also a beautiful bit of maths by Euler - ask your maths teacher about Euler's theorem.
SimonOxfPhys 1 month ago
@Olliek94 To be brutally honest I probably could have managed a couple of these, but certainly not most of them.
SimonOxfPhys 1 month ago
@SimonOxfPhys Thanks:)
Olliek94 1 month ago
Just a suggestion, for the last question, I have a suspicion that the last question they asked you will have been something to the effect of "how many people do there have to be in a room for there to be a greater than even chance of them sharing a birthday" ? It's in the same sort of category of birthday probability questions.
TheRainbowAngel 2 months ago
hi Simon...the maths questions you talked about seem very difficult...
i have a physics interview next week (@keble) and i have not done further maths...what should i expect in my interviews...will one of them be a maths interview?
also...please do u have any other things for preparation or tips during the interview?
anything would be much appreciated...and thanks for the video :)
rohitmkiller 2 months ago
@rohitmkiller if you haven't done further maths then they might be a bit easier on you (though, not to scare you or anything) but Keble is notoriously maths-based in its teaching. You will still most likely have a maths interview though.
In terms of preparation I would recommend doing as many papers as you can get your hands on and talk aloud whilst solving the problems - it's important to be able to communicate how you think. And stay calm! Just try not to build it up in your head
SimonOxfPhys 2 months ago
@SimonOxfPhys okay...thanks simon :)
true...i've heard that from a lot of people...just to relax and enjoy it...
your help is much appreciated...i go there tonight...
i just wondered how much u think it is worth reading around physics e.g. the latest research and things that interest me...:)
rohitmkiller 2 months ago
@rohitmkiller I would read around a little bit so you know the biggest stories at the moment (e.g. the neutrino experiment) but don't invest too much time in your research - it's much more important to have a sharp and clear mind in the interview so be sure to relax and socialise a bit, and don't get overloaded with new information. If there's something that interests you then by all means research that if you'll enjoy it!
SimonOxfPhys 2 months ago
@SimonOxfPhys okay that's really helpful :D
thank you...so i guess i just start relaxing now lol
thanks a lot simon :)
rohitmkiller 2 months ago
@rohitmkiller (cont.) too much and you'll be fine! Try to think of it as a chance to sit down for twenty minutes with some of the most switched on minds in the field you're interested in, which isn't something you can do every day. Relax, take your time and you'll be ok :)
SimonOxfPhys 2 months ago
Hi, I've got an interview for chemistry at Jesus, will I have a maths interview like that? I'd expect the physics maths interview to be harder but it would be nice to know :)
Thanks
electrowhip 2 months ago
@electrowhip I think the chemistry maths interview questions will be slightly easier, though to be honest I think you would serve yourself best by assuming it will be just as had (that way, if it is easier then it's a nice surprise!) as the two courses assume the same initial subjects, and the maths involved at degree is broadly similar (certainly in quantum mechanics anyway).
Good luck in your interview!
SimonOxfPhys 2 months ago
@dylanparker72 I think most people do them in Further Maths - fp1 in the syllabus I was on. As for the sin(x)=kx question, the question was for what values of k do the two lines intersect only once in the x>/0 domain
SimonOxfPhys 3 months ago
@05swanbe Dude i was like wtf? on taylor expansion also that in fp2 so i ddnt know that but if u use the sine addition formulae and then u say that cos1 is very close to 1 and sin1 is very close to 0 you end up with sin60= 0.866 rounded to 0.87 which is close enough to the real answer. @SimonOxfPhys Dude for the question about the 2nd derivative u ploted the function of sinx not -sinx is that meant to be like tht? since maybe if -y=-sinx then y=sinx i dno can u clarify?
69alaniz 3 months ago
@69alaniz I actually can't remember what I said in the interview- I don't think they were interested in a numerical answer anyway. I suppose you could use the sine addition formula but when they were giving me guidance they were leading me in the direction of the expansion, which is a more significant idea than memorising. trigonometric identities.
As for the second derivative question the point isn't that the solution is a sine function, the point is that it is sinusoidal, or more explicitly...
SimonOxfPhys 3 months ago
@69alaniz cont. that it is a linear superposition of e^ikx and e^-ikx where i is (-1)^0.5. If you plug that into the differential equation that they have set up (although they don't explicitly describe it as such) then you find that that is the general answer.
SimonOxfPhys 3 months ago
@SimonOxfPhys At 4:47 how did you manage to get a value to 3sf without a calculator?
05swanbe 4 months ago
@05swanbe I cheated and used a calculator! The point of the question is to establish the technique of expansion, rather than how good you are at mental arithmetic. Though being able to do that kind of mental arithmetic can only be a bonus!
SimonOxfPhys 3 months ago
@SimonOxfPhys Hmmm... but surely in an interview you aren't allowed a calculator, without which I probably wouldn't get it to even 1sf. Or would they just stop you on the line before?
What module is the Taylor Expansion in anyway? I just tried the sin addition formula but it wasn't pretty :/
05swanbe 3 months ago
can you re-up with better quality sound? thanks.
alextutorworld 5 months ago
@alextutorworld I'm afraid that I recorded this using my shitty old Olympus camera so this is the best quality available (I actually cleaned up the audio on iMovie too!). Sorry!
SimonOxfPhys 5 months ago
hey simon, at 3:14, you cut the curve and then hit the curve at 5pi/2.
Doesn't that mean that the line has two solutions as you touched the function twice?
km11293 6 months ago
@km11293 if we assume that d/dx(e^ix) = ie^ix and then define f(x)=cosx + isinx and differentiate we get d(f(x))/dx= -sinx + icosx. This equals if(x). We can equate the two and say that f(x)= e^ix = cosx + isinx.
Substitution of x=pi/2 yields f(x) = 0 + i(1) = i.
As for the problem at 3:14 I meant that between x=pi/2 and x=5pi/2 there exists one solution, but at x=5pi/2 there are two, so the solution is a < inequality.
Good questions!
SimonOxfPhys 6 months ago
may I ask how does i = e^(i pi/2)?
I can't deduce it...
km11293 6 months ago
@km11293 Because e^iPi = -1 (Euler's theorem). Thus if you root both sides (i.e. raise them to the power of a half), you have e^(iPi/2) = (-1)^(1/2), and the square root of -1 is i.
05swanbe 4 months ago
Love the video; could I quickly ask you for any reading recommendations that you think would be a good prep for 1st year content??? :)
10tacle21 7 months ago
@10tacle21 I would recommend reading any of Feynman's stuff such as 6 easy pieces, and 6 not so easy pieces for general background (specifically on special relativity). For linear algebra I highly recommend 'An introduction to linear algebra with applications' by Steven Roman and 'Mathematical Methods' Riley, Hobson and Bence for all other first year maths! Classical Mechanics by Steve Morin is good too. Make sure that you get really comfortable with doing calculus as you will be doing a lot!
SimonOxfPhys 7 months ago
are complex numbers covered in the further maths syllabus ?
petervsthechicken 7 months ago
@petervsthechicken It varies from syllabus to syllabus but I was on AQA and we did complex numbers in FP1
SimonOxfPhys 7 months ago
@SimonOxfPhys Thanks : ] i should cover them then!
petervsthechicken 7 months ago
Ahh. Sorry. Wasn't listening hard enough, I can see now the Taylor expansion is the best option. My bad.
jembishop 8 months ago
You made the sin(60 question overly complicated. All that was needed was an equilateral triangle. Then using PT you could see that a triangle with sides length 2 would have a height of root 3 and as sin(x=O/H then it is root 3 over 2
jembishop 8 months ago
@jembishop Yes, however the point of the question is to work out sin(61) using knowledge of the value of sin(60). If asked how to prove the value of sin(60) that's how I would have done it though
SimonOxfPhys 8 months ago
Interesting. I had a Cambridge physics interview a few years ago (and got in) but it was definitely easier than yours. I just harped on about relativity for a while, because I'd read a little about it before and solved a nifty circuits problem. Two interviews.
What you said at 0.37 confused me so much. I was spending ages trying to work out how you could argue that sqrt(i) is minus one. Shouldn't've believed him. Cambridge professors are much better - they don't tell lies. :p
BreachedWall 9 months ago
That A-wave purely looks like someone givin ya the finger
Curt1678 1 year ago
Hi, great video! The only think that scared be was the large amount of further maths that was present in your interview. Do you think that it is necessary to study further maths so as to not look like a buffoon at the interview.
mynameislegion5 1 year ago
@mynameislegion5 I would certainly recommend studying further maths if at all possible - the course is very mathematical and people who don't have the extra experience of doing 2 maths A levels are at a disadvantage. That said, there are people who get in who only did A level maths, so while it's most definitely recommended to do further, it's by no means compulsory.
SimonOxfPhys 1 year ago
hi i'm going to have an interview for earth science at st hughs! are the questions for earth science of this sort as well. I'm also confused because I applied to University college initially but they put me in St Hughes.So is it likely that university will interview me as well?
peace1202 1 year ago
@peace1202 it probably means that univ was oversubscribed for earth sciences, so some candidates are sent to have interviews for other colleges with less applicants. I've got an interview for physics at univ if you're wondering. After about an hour of research i am sh*ting bricks.
jjoonnaassdb 1 year ago
For the second derivative question, aren't y=cosx, y=-cosx and y=-sinx also valid solutions?
covo6624 1 year ago
@covo6624 Yes. The idea is that the solution is sinusoidal. You could also say that any linear combination of e^kx and e^-kx is also a solution, which is equivalent (but more elegant)
SimonOxfPhys 1 year ago
@covo6624 sorry, I meant e^ikx and e^-ikx where i is (-1)^0.5
SimonOxfPhys 1 year ago