Oxford University Mathematician vs High School Further Maths Exam
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- Опубліковано 25 чер 2024
- Oxford Mathematician Dr Tom Crawford completes a high school A-level Further Maths exam as quickly as possible... The paper taken is the Edexcel Pearson AS Core Pure Maths Paper from 2018.
You can download the test for yourself here: tomrocksmaths.files.wordpress...
And the mark scheme is here: tomrocksmaths.files.wordpress...
Watch Tom complete an A-level Maths Exam here: • Oxford University Math...
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: www.seh.ox.ac.uk/people/tom-c...
For more maths content check out Tom's website tomrocksmaths.com/
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths / tomrocksmaths
/ tomrocksmaths
/ tomrocksmaths
Get your Tom Rocks Maths merchandise here:
beautifulequations.net/collec...
Music: Corncob Kevin MacLeod (incompetech.com)
Licensed under Creative Commons:
By Attribution 3.0 License creativecommons.org/licenses/b...
If you haven't seen it already, be sure to watch the first video in the series where I attempt a Maths A-level exam here: ua-cam.com/video/uupjxztr2q8/v-deo.html
Do IAL maths P4 even though I am sure you would crush it.
do an elementary school math test (as a speedrun)
IIT MATHS exam in their limited time 😁
@@tudor__ now 69 likes
Get a haircut.
I wish I could.
Going bald. Aaaaggh. It was nice whilst it lasted.
Technically he completely failed as he was talking the whole way through and brought a camera into the exam.
spitting facts
@@TomRocksMaths lol indeed
😂😂🤣
😂🤣
What a sarcasm 👍
Is it just me or does the number 69 appear in maths tests a little too often to be random...
Please nobody else like while it is at 169 likes...!
@@geddes4253 oh shoot! It's 206 now, let's aim at 269...
@@witkofhf 268
322 now...
I give up...! :-)
Imagine having a phd in mathematics and having this much drip
HAHAHAHA SO TRUE. THIS GUY IS SOO COOL
And not having hair loss too
Just imagine being this good at maths, I left a levels maths when i started working and have forgotten it all
his drip balances his dead trim
This style should go like ice cream with tuna but instead of tuna it's somehow hot caramel
"There's gotta be a better way to do this, but I've gone down this rabbit hole."
RELATABLE
Basically me during a math test
me during my life*
lol
@@TomRocksMaths as someone sittign their Further maths core pure 1 mock tomorrow, this fulls me with hope that failing is ok
As a human I have no idea what’s going on.
As a gcse maths student, I’ve got no idea what the hell is going on.
Same lol
The step up the a-level is massive but if your good at gcse and work hard you'll be fine
I’m an a level further maths student and I am still confused
Lol sameee I’m trash at maths😬😑
i got an a* for maths and a for further maths and i remember almost little to none of this lmaoo
Can confirm that the first question (inverting the matrix) can indeed be done on a calculator.
I KNEW IT
@Oliver Dixon doing it on a calculator takes no longer than entering all the numbers, it's definitely faster than by hand
Like other comments, I'd have gone for the adjoint... Assuming basic calculator. Just a tad of flexing, did my A level equivalent without a calculator... I suppose the questions were just more proof based
@@myself0510 Yeah, a lot of the marks for A levels are for method rather than the actual answer.
In reality you just use MATLAB in the real world.
@@lesserspottedmugwump.363 Please don't tell me you're in the "but why are we learning this?!" camp! It's important to know the methods and frankly I'm bored by "Maths" that you dump in a calculator or MATLAB or, hey, Geogebra (free) does determinants. It's so not the numerical answer, but the method and the general result! Unless you talk applied Maths
Imagine how fun it would be to have him as your professor
inb4 he's the toughest of them all. never judge a book by its cover :D nah j/k i'm sure he's the coolest
that profile lmaoo
ikr he would be so fun to be around
@@TheVeganFreediver You wouldn't expect an Oxford professor to be easy
Its utterly frustrating and totally unfair how genetic quirks allow people to grasp maths easily. Not saying hard work is not involved as well of course it but you people are already 3/4 of the way up the ladder before us mere thick people have just got off the bottom step. Still most of these folk cant wire a plug without killing themselves so its horses for courses :)
There’s something satisfying about watching a maths test getting stomped through by an expert.
Same here
I never knew Machine Gun Kelly was also a Mathematician
Side project
@@TomRocksMaths lol legend
mathine gun kelly
@@TomRocksMaths Low-key best reply I've ever read.....
This man is a teacher. A good one. Classical exams done by an expert hand always teaches an insight dealing with quotidian standard problems. He always device a clean strategy to solve them. This guy enjoys his job as it should.
Kudos.
This man is a man.
It really hurt watching you do the matrix inverse by elementary row operations. Even though I sat the further maths exam over 40 years ago, I did remember about calculating determinants and cofactors and the adjugate matrix.
Yeah it's just
adjoint(matrix)/determinant(matrix),
and calculating adjoint is way easier than elementary row operations.
I still do it by elementary row operations if I have to, once u get used to it it can be quite fast, also I don't like the fact that I could inadvertedly screw up some sign in the adjoint.
Although the easiest way is just to put it in the calculator, which does that kind of operations.
I'm not quite sure if computing so many determinants would really be more efficient than simply doing ERO
@@nikolai228 The determinants will be of order 2, that's why it will be relatively easier. If this determinant was 4x4 or above then surely ERO would be more useful.
@@eskosh well thank god that a level further maths only goes up to 3x3
Tom looks more like a rock star than an Oxford University maths professor.
As an A level Maths Student, I ugh have no words lol. Respect to my further maths brothers and sisters
thanks next yer will be so painful looll
as a further maths student.
Help
@@kaipablanca yay which is ur faverout parts of maths?
@@thenungod that my final exams in 2 weeks
I did both Maths and Further Maths at A level, even got 100% no mistake on one of the Further Pure Maths exams (FP2). It was really hard but at the end, all my university choices accepted me right away!
U look more like a rockstar lmao, No one can guess that u have a Phd in mathematics
@@TomRocksMaths tom could you solve the questions on the board in goodwill hunting? I think alot of us would like that. You remind us of Will Hunting
Yeah, you'd normally just bam that Q1 into a calculator 😂😂
And even if you didn't, that man did such a long method than what is taught.
@@PsychoSquadPilot Yeah, i was taught: Matrix of minors, Correspondence, Transpose then have 1/determinant infront of the matrix
@@Chach1001 Same
Yeah I've never seen the method he used
@@harrisonprocter8947 Are u sure about that? that's a fundamental theory of matrices
This is a really good video. For a person living in a developing country, not only is this enlightening but inspiring as well. Much love and keep up the good work.
U really fired my relationship with maths👍
Did my A Level Maths 4 years ago this video brings back lots of memories just got a 1st class in aero engineering. Nice thing about these papers from what I remeber was learning the method the questions just chnaged numbers with 1 or 2 surprises in each paper
It'd be really cool to see you do an A level physics paper next. I love these videos, it's so great to see you work through a problem out loud
Great idea!
The mark schemes on physics are ridiculous, I guarantee your average physics nobel prize winner wouldn't get more than a B
Edit: because you basically have to memorise the answers because the mark scheme is awful about wording
@@asd-ro5yk bruh so true. I remember once marked me down cos i said opposing force instead of resistive force.
@@ArvinTharumalinagam bro i just did this in my exam, i hope i get the mark lol
@@asd-ro5yk you can get an a without answering any of the wordy questions
Hello Tom! Just came here to say you're a true inspiration to all of us. Cheers from Malaysia!
YESSS! You actually did it! That's so exciting!
Have a go at Stats & Mechanics next 🙌😄
Oblique collisions and Chi squared moment
Met you at the department a couple of years ago, Prof! So lovely to see you - you put me right at ease.
Man this helped me soo much in my studies 😭 thanks for your efforts.
Happy to help :)
I cant lie A-Level maths wasnt for me, but watching you go through this paper was kinda fun. I salute you!
Would be super interesting to see you take a year 13 test, the AS is hard but the A2 is where things get really interesting.
Year 13 further maths is madness. Those second order differential equations with the particular integrals and complementary functions were like crazy
I'm going through that phase rn it's kinda mad balancing between 4 subs, idek how those kids who take 5 to 6 subs manage @@mythicaldragon2260
It would probably be easier for him than the basic exam, more recent and similar to what he teaches?
You are literally my role model. A math genius with such a great personality. A professor at one of the most prestigious colleges. And you don't even look 30
Claps to him for not even using the correct calculator and actually managed to pull the test off. He probably should've tried using something like Desmos, because he was living "the best life" over there with the first question at least 😂
Sharp > Casio🙄🙄
Currently doing Maths Higher Level AA in IB. It was really interesting to see how easily you dissect the questions. Great content!
Glad you enjoyed it :)
Maths Specialist in Australia. I know how to do the majority of this but the way you set it out and do it really intrigues me
Solving the first problem (matrix inversion) is actually fairly straightforward (and quickly) by calculating the adjugate matrix / using Cramer’s rule.
Just want to say thank you man, this vid rly helping me revise for my exams next week.
shouldnt the theta value be less than 90 in 21:44 since theta is acute?
I also do a type of further maths at school similar to this, HS too. This was really fun to watch :)
I find this really helpful thanks I’m preparing for my further maths exam in January so am watching this thank you very much
Proud to see ur video Dr. Tom Rocks...
The calculator we use in A level papers is the casio 991EX classwiz. You can input the elements of matrix and find the inverse that way.
Had my last a level further maths test 2 weeks ago and I've never been so happy that it's over 😭
But that first question has a much easier method than what you did, even without plugging it straight into the classwizz calculator
Livesolving. This is oddly satisfying. Please do more!
Nice solutions, in particular the summation question. An ordinary A-Level student might have been intimidated by the appearance of the cos term in the summation.
Thanks for the further maths exam!
I love that he used the graphs of sin and cos to find the angles instead of a mental (or drawn) unit circle, very interesting
a true mathematician, thinking outside of the box
I'm from new zealand, and when I was learning trig earlier this year we were taught through sin and cos graphs. When I wanted to look at some tutorials on yt I immediately came across unit circles, and thought wtf is that lol
I use a mixture of graph and ASTC depends on whether is it basic or transformed function
@@francisyang5661 That's interesting! Honestly sounds a lot more practical too 😅
45 years since I did my A levels, but I did remember something about Determinants and Adjoints while I was watching you tackle question 1a. I have to admit that I couldn't remember the method until I googled it. I mean who does it by hand when every programming language has an inverse function!
"I mean who does it by hand when every programming language has an inverse function!" If you were programming a matrix in C you would probably end up doing it from scratch. I haven't stumbled across an inverse matrix function in the standard library.
@@lethalsub whats stopping you from using libraries that have those implementations?
@@perhapsso1909 "whats stopping you from using libraries that have those implementations?" Using an existing library is boring if you're able to write one yourself.
@@lethalsub Well idk what kind of programming work you do, but wasting time to implement something that has already been implemented and optimized to a far better extent than we could ever do within the time frame of a much larger project is just a waste.
Like at that point why even use the standard library? Might as well write code from scratch on assembly.
@@perhapsso1909 "Well idk what kind of programming work you do..." I'm an amateur programmer.
"...but wasting time to implement something that has already been implemented and optimized to a far better extent than we could ever do within the time frame of a much larger project is just a waste." What library are you referring to?
"Like at that point why even use the standard library? Might as well write code from scratch on assembly." Way ahead of you there, I'm planning on learning some assembly. Also, I've already written a few of the parsing functions from the C standard library, such as strtol (which I implemented in C, not assembly).
I’m doing Further Maths and the paper you did is the spec I’m doing right now. I went through this exact paper today for revision (only attempting questions on stuff I’ve already learned)
I finished my A-Levels, one of them being FM, last summer and I can confirm the method we were taught for inverting a 3x3 matrix has about 5 steps if I remember correctly.
I recently did my last further maths exam and I really enjoyed the subject
Hope it went well!
Just finished my advanced higher maths in high school (Scottish equivalent) and its funny finally recognising everything and all the methods you're using😁
im doing ma GCSE prep whilst watching ( actually just listening) this n i dont even know what youre talking bout, but it helps....i swear it helps
Wow... you got so much time you even got a youtube channel. I think getting a phd in math is very rewarding
Never judge a book by its cover. Professors can have tattoos, smoke cigars and a beer. This guy is so cool tbh.
I too love smoking beer
@@anenzyme1968 the result of typing too fast 🤣
3:23 this is me doing math, like all the time... a realization that there was certainly a more expedient and efficient solution, followed by the sense of accomplishment that my ridiculously overcomplicated solution actually found a correct answer.
It’s nice to see you go through the steps for question 1, but I feel like I would’ve just used the adjoint method. That’s what I remember doing until we were able to use calculators, then just enter values.
This is really cool, it brings back my interest in math that I had back in high school. Also cool tattoos 👍🏾😎
Ahh these High School exams really take me back haha. Looking forward to this one!
I love Maths and I have been Math Teacher for about twelve years. I like your content, videos and I also learn English. I would like have a Teacher like you. You are so cool and nice.
Great video Tim 👍
To be a Professor at your age is incredible! You are truly talented!
He’s in his late 30s
Still a superb achievement.
@@clapzy1582 most professors are in their 50s or 60s, especially at such an acclaimed university like Oxford.
It would be really fun to watch you do a STEP 2 paper (example: 2017) since those papers are a notch higher in level and are commonly used as entrance exams for unis. Great content btw :)
Would be fun although the STEP is very much a Cambridge thing not an Oxford thing
@@alistairs3934 STEP is used as a conditional offer for multiple universities like Imperial, Cambridge etc... It should be on par or if not, a bit harder than Oxford's entrance exams too. Hence, it would be fun to watch him do a STEP paper :)
@@ryanpatel2001 I would actually say that it’s roughly at the same level because MAT is done at the start of year 13 whereas STEP is done at the end of year 13, MAT assumes you have just some A Level Maths and AS Further Maths knowledge whereas STEP assumes you know all of A level Maths and Further Maths. I struggled to do STEP papers during September when I was practicing for admission tests but at the moment I find STEP papers to be as hard as MAT papers (although let’s be honest it’s still really hard)
@@itsnotcharan STEP 1 and STEP 2 does not assume any further maths knowledge.
@@itsnotcharan Having done both practice MAT papers, and planning to do STEP 2 and 3, I can say that STEP is definitely harder than the MAT. This is mainly due to needing a lot of FM, including some memorised formulae, and the fact that the questions are a lot longer.
Hey Tom, you should try an Australian math exam. Search up “VCE Specialist Maths exam 1 (or 2) 2019”, you can change the year as you please.
‘Exam 1’ doesn’t allow any calculators, and ‘Exam 2’ allows a calculator like the TI-Nspire one, so it is graphical as well.
This is the highest level of math here, and it covers things like:
calculus, related rates, complex numbers, vector functions, motion/dynamics, and fairly basic differential equations (the most complex one is separable).
For question 3, i found a geometrical approach to be nice.
So, we have the intersection of the circle radius 3 centered at 1+i and the cone centered at 2 which makes angles pi/4 with the real axis. let A be 1+i, B be 2, and W be the point of interest. ABW forms a right angled triangle of hypoteneuse 3, with side AB having length sqrt 2. Therefore, the other side BW has length sqrt 7. Let C be the real part of W. The triangle BCW is a right isoceles triangle having hypoteneuse of length sqrt 7 and therefore sides BC, CW of length sqrt(7/2). Now, we know the real part of W to be 2+sqrt(7/2) and the imaginary part to be sqrt(7/2). Calculating the square of the modulus gives 11+2 sqrt(14)!
IB Mathematics Paper 3 is quite challenging. It can be a nice motivation seeing someone solving those problems :)
You’re the cure to my depression. Watching you 3:30am while I can’t sleep
Just don't be depressed
@@yournan7249 simples
@@yournan7249 apparently hes cured
@@hybmnzz2658 cured of a fake illness?
Dude is a friggin genius and he looks like a killer magician too, never would I expect him to be a math professor
You don’t need to be a genius to this, just hard work ethic and a passion for maths
i remember doing SMP Further Maths during my A-Levels in the year 1995… it was sooo hard, but i managed to get A for it … yay…
I remember the first time solving an oxford university question. I was very happy i did. lol
I was very happy too. I read the first question and happily left to avoid further brain damage🤣
Tom is a joy and inspiration..if you hate Maths,you probably think he is sad and crazy to sit a Further Maths Exam in public ha
But I love seeing how Maths is done!
The Casio FX-CG50 graphing calculator does indeed find the inverse of 3x3 matrices! Although we do learn how to find them by hand, but it’s very tedious as you have shown!!
Enjoyed this!
God I remember some of this... I wasn't very good at it.. but I remembered loving this 😭 god you seem fun though to listen to ❤️
Its 12:30 am and im watching this guys take a math exam 😭 what have done to myself! Brovo man! Those proofs are so hard to approach for me and you just breezed through them!
It comes from a lot of hard work and practice
The math sure is a trait
But the drip is mandatory.
Maths and physics students are pretty cool, its the chem and biochem that are straight up fatneeks
@@fatfrankthepeteacher2503 true dat
@@fatfrankthepeteacher2503 accurate
I think in the question about lines and planes it's not just about the fact that the angle has to be acute. You've calculated the angle between the line and the normal to the plane (and not the plane itself), so you would have to subtract 90 degrees (or if your answer happened to be an acute angle subtract it from 90) to get the desired angle.
This was awesome! I'd love to see you do the A level paper rather than the AS.
Be interesting to see you tackle an old S level paper, though not sure if the further maths paper is it's modern equivalent, been a long time since I did maths to any level of complexity.
bro you look like you should be in a band but you are so smart
my school didnt offer further maths so I had to teach myself this course by myself in lockdown as well as balancing my other subjects
Interesting to watch you work through this although it was only as level. Would love to see you try the full a level exam.
I'm More fan of your hairstyle sir than your mathematical skills 😃
He’s got amazing cheekbones as well
@@fatfrankthepeteacher2503 😂 oh man
Q1 , easy, just work out the the determinant first, then the matrix of minors and then the matrix of cofactors, find the transpose of the matrix of cofactors and divide this by the determinant. :)
Imagine this video being in my feed for no reason good job yt algo
good to see it works sometimes!
The last question has an overlapping shape of cylinder and part of the curve when doing the volume of revolution. You can deduct the volume of the part of the overlapping curve to get a better estimate.
What courses do you usually teach? It'd be interesting to watch you work through an exam you wrote yourself :p
I want a math professor like this, this man dope as fuck.
I would love to see you do some high level international high school exams like Australia or the us to see the differences
I am mesmerized
For the volume of revolution problem I think you should have extended area 1 down to meet area 3 and shrunk the area of 2. It would be a little harder because area 2 would no longer be in contact with the axis of revolution but it would be a slightly better approximation because 1 & 2 don’t articulate perfectly in your model.
Also the model doesn’t take into account the thickness of the glass which I think is part of why you got a larger area.
3:23. I hate it when that happens... and i can relate... Allice, you are lucky to have fallen down a magical rabbit hole than the other kind of rabbit hole...
Cool video, would be interested for you to try some of the new spec papers as this paper is the old spec. Also this paper is actually an AS fmaths papers so would be interesting to see you try a core 3 fmaths paper. Great video tho!
Love this
On Q7, you already had the function expanded out, you just had to compare coefficients again to get p and q from your α,β that you now know. Would be much faster :(
I got a U in my AS further maths when I did it 4ish years ago
I do engineering atm in uni tho so it's not the end of the world
For Q1 M inverse can be found by Adjoint M/Determinant A.
I'm doing normal A-Level maths and this looks utterly ridiculous and mind-bending
Youre a Doctor?! No way! You look like you're 23. Youre so bubbly thats cool!
high school?!?!? i learned this all in college through my engineering courses
Never liked maths but this does grab my attention. Makes me want to understand what is going on
Brilliant !
Me screaming at my laptop-- DUDE, The calculator is RIGHT THERE! Stop doing arithmetic in your head!
You-- I think I am going to use my calculator. hahahaahahahah you heard me, obviously ;-)
I am a law student. I was good in maths in high school and could do mental calculations faster than my class mates who stayed good in maths till A levels. However after grade 8 i didnt see the simplicity or a beauty in it. Becamw more of a chore, I think I didnt learn it well or didnt have it properly taught in my school. This guy gives me hope that maths can be beautiful. I really want to know who taught this guy maths. Cheers!!
high school maths is always a chore because you can't use the computer. You'll need to do your own exploring early or do olympiad maths to learn the "beautiful" stuff.
hey tom, it would be really interesting to see you try an american maths exam! for example the sat math test or the ap calculus ab/bc exam
The first exercise reminds me of the many times I got into the wrong path during an exam during my degree. I think once I spent an hour painstakingly doing calculations fully knowing I was just bullshiting