Got my interview in a few days, my only worry is that I haven’t done loads of integration yet as we haven’t covered it in depth yet at school so I’m going to have to get caught up with that. Super useful video, thanks!
Intégration is simple, double triple multi doesnt matter. Anyone that knows trig, Total and partial derivatives van integrate. Trust me ive been where youre at, and the difficulty lays in defining boundaries on multivariable coördinates of intégration in pôle coordinates of bodys in Space.
I don't want to be overly picky but I thought that the first integral required rather more careful treatment, and in a real interview could generate some trickier questions. For example, an examiner who wanted to stretch a candidate may ask: 1. Is it sensible to use x for both the dummy variable of integration and the upper limit? 2. Can the upper limit x take on any real value, or must we impose a restriction on its domain? If so, what is that restriction, and why? 3. With a sensible domain selected for x, what does that mean for the theta-limits with the substitution x=sin(theta)? 4. If we instead choose the substitution x=cos(theta), as we may well do, how does that change the limits of integration? 5. With the subsitution x=cos(theta), the final answer looks different to that with the substitution x=sin(theta). Does that mean that we have found a different result for the integral? If not, why not?
1. YES For engineering this is an applied context. 2. The domain of the function is between -1 and one and therefore the substitution is valid. 3. Same as 2 4. You have to make sure your limits are within the domain of x. 5. Cos theta gives the same result with pi/2 - arccostheta = arcsin theta. All questions were based of real interview questions Thanks for the comments and good luck with your channel
Dont panic guys they just Test Your Patience and sharpness by giving such questions, couple of years ago I secured 99.7% in this interview & currently enjoying Aerospace engineering.
5:30 Unless I'm missing something, when x = x, theta = arcsin(x), and this should be the upper limit. Although the correct answer was reached, I think the method was subtly wrong. The confusion comes from using the symbol "x" for 2 variables: the upper limit of the integration (a free variable), and the bound variable of the integration. Unless this is part of the test, it is clearer to use a symbol such as "t" for the bound variable.
@@ZantierTasa you start by saying y= arcsinx then x = sin(y) then differentiating both sides dy/dx = 1/cosy replace value of y dy/dx = 1/cos(arcsin(x)) then taking arc sin (x) as theta we can write cos theta as sqrt (1-sin^2 theta) thus giving us 1/ sqrt(1-sin^2(arcsinx)) then we know that sin(arcsin(x)) is just x thus the final answer is 1/sqrt(1-x^2)
@@siddhantsatpathy1742 Ok nice, maybe that would have been acceptable in the interview :). Of course, the interviewer could always tell you that they want to see you using integration techniques in order to solve it.
Although the first one was a standard arcsin integral, what would happen if I just directly wrote arcsinx? Yes, I know he asked to work out the integral.
These interviews are about showing how you think, this is what the interviewers want to see. So despite recognising it is a standard I integral, it’s always good to show your thinking which is what they want.
My guess is that if you just wrote arcsinx, they would give you a different integration question that makes you think a bit more as this integral is standard.
I have a masters degree in mechanical engineering from ucl lol even i found this hard. How do they expect someone doing a levels to know thermo in this much depth?
Depends on the interview but in general, no. I'd expect a PhD interview to cover the candidate's research experience and maybe about the host lab's research if applicable
@@dhruvacharya2602sure if you took university physics & calc 2 in hs. But the difference is this guy doesn’t have a formula sheet, isn’t given a specific forces question and needs to understand which formulas to use learned all through the class and understand rules
No it should be arcsin(x), and even further the notation doesn't make sense. You can't use the variable of integration as a bound as this is nonsensical.
Why exactly is the upper limit θ? If ULI is x = x’ and x = sin θ, that implies that x’ = sin θ, which implies that θ = arcsin x’. Which is technically the correct answer. You could then say that θ = arcsin sin θ = θ (or likewise x = x => sinθ = sinθ => θ=θ) but isn’t that circular logic??? Or is that valid and just a tautology.
It's because they used the same letter for the upper limit and the variable in the integral. The upper limit should be something like u instead of x, so it couldn't cause this confusion. I didn't understand at first neither, but this is what makes sense to me.
@@Gabe-ch2ol 1st one was terrible. I was very nervous. I did the 1st q alright (took around 13 min) then for the 2nd q, the tutor explained something to me 3 times and asked me the same q but I got it wrong so finally he just gave me the equation. After that interview I thought I had no chance of getting in so I was kinda calm in the 2nd one. On the 3rd one I guess the questions were harder than usual but I got through. I'm just praying so that I get an offer. I really don't wanna get rejected at this point.
Because the limits are being set with respect to the variable theta, not the variable x. The transformation between the two variables occurs by transforming the integrand and the differential. Admittedly, having the same variable in the integrand and the limits isn’t good mathematical practice (should use a dummy variable) but it gets the job done in this case.
X = sinθ So what would θ be? arcsin(x) But arcsin(x) is θ so it might be the reason why Idk I may be wrong(someone pls tell of this is correct I am curious now lol)
Let the integral from 0 to x_ then x_=sin(theta_) theta_=arcsin(x_) the result of integral is theta. Sub upper bound arcsin(x_) into theta. The final solution is therefore arcsin(x_). Sub lower bound zero into theta will give zero.
Hi I was going to say I love your videos for Oxbridge but their is something I need to tell you when I was doing my GCSES I was mentally depressed and I had really bad anxiety originally I had full plans and potential to apply to Oxford or Cambridge but the problem was I did not get good GCSES and at college I am doing BTECS at my sixth Form College I really do love Oxford and Cambridge so I looked at their entry requirement if they accept BTECS and for the course I want to do is Music Oxford say they do and Cambridge don’t so do you think it would be fine for me to apply to Oxford since they do say they accept BTECs for the Music course thanks for reading this message
Sounds like applying to Oxford is a better idea given they do count BTECs. Also look at their other admissions requirements and see if you can meet them. You should be able to explain your extenuating circumstances somewhere in your application.
Can someone explain for the first one he couldn’t have just done (7 x 7 )and then (x 7) for the remaining until he got to the power of 6. His method of splitting and expanding didn’t work.
Are you supposed to be able to answer these questions after your A-levels? I can see that further maths is probably way harder than these questions but for an interview... it's hard.
It's fine to say that you don't know, but it's good if you do try to use what you know already to give the interviewers something to work with. Staying quiet after saying "I don't know" isn't good, but it's fine if you follow it up with e.g. "could it have to do with X or Y?". And asking for clarification or some help is fine too.
Hey i have a question. If we are an a a level student who is applying to oxford for engineering science, do we expect the same level of difficulty as shown in the video?
This is probably the hardest you can get. Also, questions 3 and 4 seem a little extreme (I've never learned anything about calculating centers of mass). I did a Cambridge Engineering interview and I can tell you it was much less difficult (Oxford may be different)
Is that for undergrad or graduate studies ? I think the structure of the interviews for the master and PhD programs are different. Can sme please confirm that ?
Hii, for the first question could we have not used differential approximation to do it? we can say that for some exponential function a^x = f(x) x=2 and delta(x)=4 and then applied the approximation formula?
The integral at min 5:00 gave me cancer. You can't integrate something over a variable x, pay attention VARIABLE, x is changing value in an interval, and evaluate it, waiiiit for it, in x? Out of all the possible values for the upper interval of integration, he picked the only wrong one.
I'd also mention that Oxford has also published some mock interviews including engineering in advance of this year's interviews! This one featuring yours truly messing up some simple physics also includes tutor commentary at the end: czcams.com/video/c8fI6i0aR-M/video.html
Hi oxcentric! do u have more mock interview for engineering? I just did my engaa last wed and i felt I messed up.....so i need more help for interview/...tysm QWQ
Why not? You are advised to be prepared for how a interviewer will behave in a interview which is a factor to consider while talking about the candidate's anxiety And advice here is used as help(ig) and this helps obviously
Although I'm not in Uni anymore, I understand the feeling of being nervous! Take it easy and always write out your thought process/steps.
Dont we all???
the integral technically does not make sense. You cannot use the endpoint of integration "x" to be the same as the dummy variable of integration "x"
I had a similar reaction
Got my interview in a few days, my only worry is that I haven’t done loads of integration yet as we haven’t covered it in depth yet at school so I’m going to have to get caught up with that. Super useful video, thanks!
i’d recommend solving GN berman..its a great book if you want grasp the basics of integrals and increase your speed :)
How was the interview?
Intégration is simple, double triple multi doesnt matter. Anyone that knows trig, Total and partial derivatives van integrate. Trust me ive been where youre at, and the difficulty lays in defining boundaries on multivariable coördinates of intégration in pôle coordinates of bodys in Space.
How was is?
I don't want to be overly picky but I thought that the first integral required rather more careful treatment, and in a real interview could generate some trickier questions. For example, an examiner who wanted to stretch a candidate may ask:
1. Is it sensible to use x for both the dummy variable of integration and the upper limit?
2. Can the upper limit x take on any real value, or must we impose a restriction on its domain? If so, what is that restriction, and why?
3. With a sensible domain selected for x, what does that mean for the theta-limits with the substitution x=sin(theta)?
4. If we instead choose the substitution x=cos(theta), as we may well do, how does that change the limits of integration?
5. With the subsitution x=cos(theta), the final answer looks different to that with the substitution x=sin(theta). Does that mean that we have found a different result for the integral? If not, why not?
1. YES For engineering this is an applied context.
2. The domain of the function is between -1 and one and therefore the substitution is valid.
3. Same as 2
4. You have to make sure your limits are within the domain of x.
5. Cos theta gives the same result with pi/2 - arccostheta = arcsin theta.
All questions were based of real interview questions
Thanks for the comments and good luck with your channel
clever, well done.
Thanks for this! I have an interview in 5 days for engineering!
at oxbridge?
@@Ilan101 how'd it go?
@boomy is plagued, it went quite well! The Cambridge one I had also went well, and this and other videos of the kind were really helpful!
@@Ilan101 where are you now?!
@@Ilan101did you get in?
Dont panic guys they just Test Your Patience and sharpness by giving such questions, couple of years ago I secured 99.7% in this interview & currently enjoying Aerospace engineering.
oxford don't do aerospace engineering
5:30 Unless I'm missing something, when x = x, theta = arcsin(x), and this should be the upper limit. Although the correct answer was reached, I think the method was subtly wrong.
The confusion comes from using the symbol "x" for 2 variables: the upper limit of the integration (a free variable), and the bound variable of the integration. Unless this is part of the test, it is clearer to use a symbol such as "t" for the bound variable.
You're right, it is misleading at best. He probably went on autopilot tbh
i dont understand why a "method' was used here this is just a direct integral to get arcsinx as the differentiation of arcsin(x) is 1/sqrt(1-x^2)
@@siddhantsatpathy1742 Can you prove that differentiating arcsin(x) gives you 1/sqrt(1-x^2)?
@@ZantierTasa you start by saying y= arcsinx then x = sin(y)
then differentiating both sides
dy/dx = 1/cosy
replace value of y
dy/dx = 1/cos(arcsin(x))
then taking arc sin (x) as theta
we can write cos theta as sqrt (1-sin^2 theta)
thus giving us 1/ sqrt(1-sin^2(arcsinx))
then we know that sin(arcsin(x)) is just x
thus the final answer is 1/sqrt(1-x^2)
@@siddhantsatpathy1742 Ok nice, maybe that would have been acceptable in the interview :). Of course, the interviewer could always tell you that they want to see you using integration techniques in order to solve it.
Although the first one was a standard arcsin integral, what would happen if I just directly wrote arcsinx? Yes, I know he asked to work out the integral.
These interviews are about showing how you think, this is what the interviewers want to see. So despite recognising it is a standard I integral, it’s always good to show your thinking which is what they want.
My guess is that if you just wrote arcsinx, they would give you a different integration question that makes you think a bit more as this integral is standard.
I have a masters degree in mechanical engineering from ucl lol even i found this hard. How do they expect someone doing a levels to know thermo in this much depth?
It's not too much about what you know but more about how you think.
Damn this was harder than my Oxford PhD interview 😂
are the phd interviews the same style as the undergrad ones? just curious
Depends on the interview but in general, no. I'd expect a PhD interview to cover the candidate's research experience and maybe about the host lab's research if applicable
@@IlyasCambridgeAdvice that makes sense. thank you!
This is basically 11th-12th grade math phy :)
@@dhruvacharya2602sure if you took university physics & calc 2 in hs. But the difference is this guy doesn’t have a formula sheet, isn’t given a specific forces question and needs to understand which formulas to use learned all through the class and understand rules
How did the upper limit x not become sin titha
No it should be arcsin(x), and even further the notation doesn't make sense. You can't use the variable of integration as a bound as this is nonsensical.
If you could do a chemistry one that’d be great!
I'll look into it :)
I really get these type of questions in my iit-jee examination study
Why exactly is the upper limit θ? If ULI is x = x’ and x = sin θ, that implies that x’ = sin θ, which implies that θ = arcsin x’. Which is technically the correct answer. You could then say that θ = arcsin sin θ = θ (or likewise x = x => sinθ = sinθ => θ=θ) but isn’t that circular logic??? Or is that valid and just a tautology.
It's because they used the same letter for the upper limit and the variable in the integral. The upper limit should be something like u instead of x, so it couldn't cause this confusion. I didn't understand at first neither, but this is what makes sense to me.
this question 1 was so cool
I have my physics interviews for oxford this week. Very nervous and scared as I believe that I didn't do too good in the PAT.
The pat was hard…
how did it go?
@@Gabe-ch2ol 1st one was terrible. I was very nervous. I did the 1st q alright (took around 13 min) then for the 2nd q, the tutor explained something to me 3 times and asked me the same q but I got it wrong so finally he just gave me the equation. After that interview I thought I had no chance of getting in so I was kinda calm in the 2nd one. On the 3rd one I guess the questions were harder than usual but I got through. I'm just praying so that I get an offer. I really don't wanna get rejected at this point.
@@mistymodhu8569 I wish you luck!
@@mistymodhu8569 what's this interview about?
5:35 Why is = theta not sine theta
Because the limits are being set with respect to the variable theta, not the variable x. The transformation between the two variables occurs by transforming the integrand and the differential. Admittedly, having the same variable in the integrand and the limits isn’t good mathematical practice (should use a dummy variable) but it gets the job done in this case.
I'm still a bit confused on this, when we make that substituion don't we change the limits on the integral based on our substitution choice?
X = sinθ
So what would θ be? arcsin(x)
But arcsin(x) is θ so it might be the reason why
Idk I may be wrong(someone pls tell of this is correct I am curious now lol)
Ah I kind of see it now, thanks
Let the integral from 0 to x_ then x_=sin(theta_) theta_=arcsin(x_) the result of integral is theta. Sub upper bound arcsin(x_) into theta. The final solution is therefore arcsin(x_). Sub lower bound zero into theta will give zero.
That integral is hella weird, having x inside and outside of the integral is not a great choice of notation…
Can you use linear approximation in the first question?
I thought you could only use linear approximation with nth roots
@@charlottebuckner9592I’m pretty sure you can use linear approximations with any differentiable functions
Hi I was going to say I love your videos for Oxbridge but their is something I need to tell you when I was doing my GCSES I was mentally depressed and I had really bad anxiety originally I had full plans and potential to apply to Oxford or Cambridge but the problem was I did not get good GCSES and at college I am doing BTECS at my sixth Form College I really do love Oxford and Cambridge so I looked at their entry requirement if they accept BTECS and for the course I want to do is Music Oxford say they do and Cambridge don’t so do you think it would be fine for me to apply to Oxford since they do say they accept BTECs for the Music course thanks for reading this message
Sounds like applying to Oxford is a better idea given they do count BTECs. Also look at their other admissions requirements and see if you can meet them. You should be able to explain your extenuating circumstances somewhere in your application.
@@IlyasCambridgeAdvice Thanks and since Oxford does accept BTECs for the course I want to do why not you know what I mean
@@raumaankinghave you gotten in?
God knows I only had an idea about the first question, outside that, it’s crazy how y’all understand the rest
Ps- I study chemical engineering
the second and third questions are basic Calculus. While the last one is a bit tricky, but still a combination of mechanics. That's all basic stuff
How’s that possible? The second is literally calc 2 and a must know technique for integration
Can someone explain for the first one he couldn’t have just done (7 x 7 )and then (x 7) for the remaining until he got to the power of 6. His method of splitting and expanding didn’t work.
they asked for an estimate not an exact answer
Amazing it’s help me a lot!!
Isn't the integral in thumbnail very easy?
I tried to do that question on the thumbnail in my head and it made me mad
isnt the final answer to the centre of mass of a hemisphere 3R/8 cm?
cant the first question 1/sqrt 1-x^2 can be solved using direct formula of sin^-1(x/a)?
the formula comes from the same derivation my man
Are you supposed to be able to answer these questions after your A-levels? I can see that further maths is probably way harder than these questions but for an interview... it's hard.
Hello! I have a question. What should we do in case we have no idea what to do with the question? In case of a blackout?
Ask for clarification, said that you don't understand, and back to the basic concept, they will guide you through 👍
It's fine to say that you don't know, but it's good if you do try to use what you know already to give the interviewers something to work with. Staying quiet after saying "I don't know" isn't good, but it's fine if you follow it up with e.g. "could it have to do with X or Y?". And asking for clarification or some help is fine too.
@@Daniel-tp4ue Thank You :)
@@IlyasCambridgeAdvice Thank You! I'll keep that in mind. :)
@@IlyasCambridgeAdvice Great! I'll keep that in mind!
Shudnt the first integral be arcsinx - npi where n is any integer
It’s a definite integral
If it was indefinite, then yes
Honestly Now I realise why JEE ADVANCED is one of the hardest exams in the world…cause I got most of these right( I’m preparing for jee)
First thing came to my mind after seeing thumbnail was sin inverse x
Would Cambridge be an better option for Engineering over Oxford?
Both good
Sin inverse (x) is the ans
Hey i have a question. If we are an a a level student who is applying to oxford for engineering science, do we expect the same level of difficulty as shown in the video?
Not necessarily but it is possible
This is probably the hardest you can get. Also, questions 3 and 4 seem a little extreme (I've never learned anything about calculating centers of mass). I did a Cambridge Engineering interview and I can tell you it was much less difficult (Oxford may be different)
Is that for undergrad or graduate studies ? I think the structure of the interviews for the master and PhD programs are different. Can sme please confirm that ?
This is mock interview is for engineering undergrad. Master's and PhDs will have different interviews.
Hii, for the first question could we have not used differential approximation to do it? we can say that for some exponential function a^x = f(x) x=2 and delta(x)=4 and then applied the approximation formula?
This was painful to watch, I'm hoping the awkwardness was on purpose?
Yeah sorry they're from Oxford
The integral at min 5:00 gave me cancer. You can't integrate something over a variable x, pay attention VARIABLE, x is changing value in an interval, and evaluate it, waiiiit for it, in x? Out of all the possible values for the upper interval of integration, he picked the only wrong one.
why is this so easy.. JEE people solve these questions while having lunch
Truee bro
im really sorry but is it odd that im going 10x times harder questions in my high school for my jee prep ? 😭💀
why cant i use sin^-1 x formula in q 3 why???
what is the point of this?
For the first one I said 7^6 = 49^3 which is close(ish) to 50^3. Which is way easier to calculate.
Edit. Damn I actually got it.
I'd also mention that Oxford has also published some mock interviews including engineering in advance of this year's interviews! This one featuring yours truly messing up some simple physics also includes tutor commentary at the end: czcams.com/video/c8fI6i0aR-M/video.html
shameless plug from oxf*rd smh
Hi oxcentric! do u have more mock interview for engineering? I just did my engaa last wed and i felt I messed up.....so i need more help for interview/...tysm QWQ
Good
That's okay, I'll be a taxi driver.
I got these equations in 10th grade (Technology)
What do I need in GCSE English to apply to Oxford engineering?
At which level of education is the dude who is getting interviewed here?
4th year at university so master's
@@IlyasCambridgeAdvice what the actual fuck
The thumbnail qs 's anwer is sin inverse x , right? I haven't watched the video actually so I'm asking 😅
My idea of absolute. Hell.
Second math problem was completely illposed.
7^6 ~ 50^3 = 10^3*5*3 = 125000. Not sure how that would have faired but it was my gut. EDIT: ok that is what he did...
Same. He was incredibly slow. Could have worked out the actual answer in that time
As a certified Indian 10th grader, these questions were easy af
This doesn't really seem like "Cambridge Advice"..... Unsubscribed
Gonna drop you on belay tomorrow
Good banter lad
Why not? You are advised to be prepared for how a interviewer will behave in a interview which is a factor to consider while talking about the candidate's anxiety
And advice here is used as help(ig) and this helps obviously
@@adityaekbote8498 Sorry m8 u can't get into Cambridge with that noggin.
Neither can I ofc
@@Oh-lk2qd ouch but ok
Too easy
Mate oxford isnt for engineering
www.ox.ac.uk/admissions/undergraduate/courses-listing/engineering-science
@@IlyasCambridgeAdvice lol
🤣🤣🤣🤣,these questions are very easy ,here in india we do more difficult ques than this while preparing for jee
Try applying for oxford’s phd programme and see how easily you get rejected
Bro don't embarrass yourself
Haaahaa he’s so bad