Oxford University Mathematician takes High School GCSE Further Maths Exam

[@morzee94]

As a maths teacher, I really enjoy teaching GCSE further maths. I think the spec is really well designed to prepare students for further study. In contrast, I think the regular GCSE spec is overloaded with content that isn’t particularly useful.

[@CFC.NobarR]

What do you think should be removed from the normal GCSE spec? Any topics in particular?

[@morzee94]

@@CFC.NobarR I think topics need to pass one of two tests to warrant inclusion in the GCSE spec. 1) Is it a skill or piece of knowledge that a large number of students will use in the future? 2) Does it form prerequisite knowledge for A level or beyond? One topic that springs to mind that doesn’t pass either is Loci which I hate teaching!

[@robmarshall9026]

@@morzee94 I never touched the circle theorems in GCSE maths cause they seemed useless (don't remember using them after GCSE) Just never bothered revising them and skipped the question in the exam cause I just never got it.

[@rogorix4991]

Sorry, at what age do you take this exam usually ? Are A levels harder ? And when do you take those ?

[@morzee94]

@@rogorix4991 GCSEs are normally taken at 16 and A Levels at 18. Most students study 8 GCSEs compared to 3 A Levels. So yes, A levels are substantially harder. GCSE further maths is only taken by the most able students.

[@thomasfoteinos3690]

Great vid man. Would love to see you doing a crazy hard degree/msc paper to show what hard uni maths is like!

[@chrisi359]

Would love to see that

[@jakoolaboo]

We would love to see that please Do a cambridge maths exam

[@georgezhang865]

If you doing math in uni, the exam papers are focused on one single topic. So imagine you have one paper focused only on number theory and one focused on algebra. It’s hard to define how hard it is because each topic have very different content and the difficulty are all different.

[@dogwithwigwamz.7320]

I had to find something to do to occupy my mind after a hard time. I thought to myself, "what`s the most difficult academic subject I can think of ?" Ah, maths : I hated maths at school. I contacted my local college and they told me that if I didn`t already have a grade C or above at GCSE then the GCSE Course would be free of charge, so I enrolled. After an 8 month long course I sat the exam and was given an A*. I then taught myself A Level Maths ( `couldn`t afford to study it at college ). Its depth and breadth was naturally far greater than GCSE, but easily do-able. Then I decided to purchase my first undergraduate level maths textbook, " Numbers, Sequences and Series," in Modular Mathematics, by H.E Hirst. It was ridiculously difficult. For me, at least. But it has not put me off. I`ll carry on until I `get it.`

[@riccardoorlando2262]

@@dogwithwigwamz.7320 The kind of thinking required for uni-level math unfortunately is not well taught by pre-uni courses. However, there is plenty of excellent material online.

[@aryaask]

For Question 8, you can just find the vector from Point A -> Point C, then multiply it by 5/8 to get the Vector from Point A -> Point B, then just add that vector to Point A, and you get (11, -2.5)

[@cameronweiss4044]

Yea I think he overcomplicated it

[@scoopduna]

So pumped I got 100% of this right in the “surname section!”

[@khan99ish]

Perfect just what I need to condense my learning for the final exams… thank you!!! 😊

[@TomRocksMaths]

Happy to help!

[@apophenic_]

Wish I had you during my time at school. Thanks so much for introducing the new generations to it in a proper way.

[@TomRocksMaths]

Any time!

[@przemeklisicki8741]

​​@@TomRocksMaths thankyou, I'm talking this exam in a matter of weeks and it's refreshing to see someone solve the questions to memorise them. But at 37:07 the method you used was something I never learned and seems excessive.

[@HienNguyenHMN]

Your genuine excitement for getting math questions correct is wholesome.

[@stampcrab]

I'm so glad this channel grew this much! Keep rocking Tom!!

[@davidrobins1021]

This Further Maths paper is so much more interesting than the normal GCSE maths; contains more "real" mathematics with none of the boring real-life word problem things about the amount of money it'll cost Bob to tile his bathroom or how much money Paul gets when he invests £5000 at 2% compound interest or whatever. I'd actually have been stuck on that matrix transformation one as I'd completely forgotten the formula for the reflection matrix. Did it at university and haven't looked at it since. I'd be interested to see what you make of one of the UKMT challenge papers.

[@SKAOG21]

Hmm, except that the real-life problems are much more "real" than pure mathematics. The main reason why maths has such a bad reputation is due to its perceived irrelevance to an ordinary person's daily life e.g. using the quadratic formula or matrix multiplication. If maths wasshowcased to be relevant and necessary such as personal finance or determine the best route you could take with your car with different mileages for city and motorway driving, then we would see much more enthusiasm for maths, then people can slowly go into the more pure/theoretical side of maths.

[@broodjekip6775]

@SKAOG Real life problems are more ‘real’ indeed, and that’s exactly why they are not ‘real’ math and boring (imo). The interesting part of math to me is the part that’s not a real world problem, since real world problems make it less clean / interesting. It limits it a lot and makes it less fun.

[@SKAOG21]

@@broodjekip6775 I agree that real world problems are less clean, but at the same time they're less tedious and more relevant. Pure mathematics doesn't make much sense because they don't do it 24/7, so people get put off by its difficultly.

[@broodjekip6775]

@@SKAOG21 You are right about the fact that a lot of people dislike math because of the irrelevance and difficulty that comes with it. And it would indeed be better if math were presented in a more relevant way. I think, however, that math is not about the techniques you learn. It is indeed quite unlikely that you are ever gonna need most of it (unless you choose a very specific job), but by solving math problems you learn to think in a way that is gonna help you. It is gonna make you better at problem solving and other important stuff. This is why I don’t like it when people make math questions that are about the ‘real world’, since math is never gonna be relevant to the ‘real world’ for most people. It is the mindset that is gonna be relevant and I think it’s easier to get that mindset when you are doing ‘real’ math, since the real world won’t help you to get these skills when implemented in math. And also, I just like pure maths more but that’s just me and I understand that that’s different for the majority of the people.

[@SKAOG21]

@@broodjekip6775 pure maths is great for problem solving but it requires really good teachers. With bad teachers, and a tedious discipline of Maths, people get put off from pure maths.

[@wippo42]

As someone who will be siitting their gcse maths exams including further maths exams within the next few months. These videos are really nice

[@richardfarrer5616]

For question 8, treat the points A and B as the endpoints of vectors a and b from the origin. Then the line through them is (1-r)a + rb for any real number r. For 0

[@riccardoorlando2262]

You can even do it separately for the x and y component, no need to think of vectors.

[@juliusteo]

As an IGCSE Maths teacher, watching you go through Q17 with such a lengthy method was hilarious to me. You're right at 39:27, it was entertaining!

[@shaaravguha3760]

Hold up, I'm doing my further maths exam in about 2 weeks and that's how I would've done it, am I missing something?

[@juliusteo]

There's something called "alternate segment theorem"; long story short, angle ABC = 3x. Then, ABO = 3x-37, and BAO = 3x-37 (isosceles). So, 2(3x-37)+2x+46 = 180, And so on... Granted, if you didn't know the "alternate segment theorem", then you have to solve it like he did.

[@createyourownfuture5410]

@@juliusteo can you please tell what the theorem says?

[@juliusteo]

@@createyourownfuture5410 kzbin.info/www/bejne/i2SWiXuIbsuUi6c

[@timothyaugustine7093]

@@createyourownfuture5410 For any circle, the angle formed between the tangent and the chord through the point of contact of the tangent is equal to the angle formed by the chord in the alternate segment. You'll probably need to draw it out yourself to see what that means.

[@careyyyyy]

I'm doing this in like 6 weeks can't wait :)

[@TomRocksMaths]

how did it go?

[@klausbuda7922]

Man your the best math Oxford professor ever

[@TomRocksMaths]

[@alberteinstein3612]

30:25 when I was taught introduction to proofs in higher mathematics, I was always told to never assume the conclusion, so in this case never work with the actual inequality itself, but rather test values that lie within certain intervals as defined by the critical numbers of the LHS of the inequality. Then, you can show that the associated values are always positive

[@jaxverse199]

As somone who is just doing a Higher Maths Edexcel GCSE....most of this is going right over my head

[@stevembanaso2817]

Same

[@samdowning6641]

HIgher maths and further maths are different subjects So you shouldn't understand it anyway since you don't take the subject

[@samleman]

I didn't even know gcse further maths was a thing my school doesn't offer it they only do a level further maths

[@mevsmemes]

The factorise question should be fairly self explanatory. It’s actually under Grade 7 from MathGenie (factorising harder quadratics). If anything, the question is just a bit annoying. I do Higher Edexcel as well. 😯

[@jaxverse199]

​@@mevsmemes The Factorising and some of it I got, but anything to do with circle or complex geometry im out

[@lunadusk8590]

i'm Just glad i could follow at least half of what you did ....

[@clashgod3558]

Hi a maths fan here ….i love your approaches to these questions….i am taking further maths next year …hopefully i get into oxford and get a chance to get taught by you

[@clashgod3558]

Yeah good luck t you too

[@obiwankenobi1966]

@@imranmohammed279 same here with the further maths next year at a level. Best of luck :)

[@iTz3L1TEFUZE]

@@obiwankenobi1966 Same, although im not so sure my ability stretches to further maths a level

[@obiwankenobi1966]

@@iTz3L1TEFUZE I'm sure you can do it. Best of luck!

[@iTz3L1TEFUZE]

@@obiwankenobi1966 thank you!

[@becksfn3105]

Hi Tom, awesome video, I just wanted to mention that in the a level paper that you did, it was actually an AS paper, would you consider taking an A2 paper for a future video?? thanks alot

[@drziggyabdelmalak1439]

Your joy at getting it right is fab! Wonder how many other university-level teachers would risk doing this?! Most? None! Dr Tom...if I get it wrong...hahaha...let's have another tattoo!!!

[@complexnumbers0196]

Love your videos Tom. Could you please make a video for A-level students and how they can become a better mathematician from your experience. Sorry if you have made a video covering this already.

[@enigma7791]

Love the T shirt Tom and great video!

[@TomRocksMaths]

Thanks!

[@two697]

Next you should do an MAT or STEP paper. Even though the video would be > 2 hours, I would still watch it and find it more entertaining than just doing gcse or A level papers

[@doyourealiseiamaghost5862]

STEP papers my gosh, so much crazier than further maths, but I think a professor from a uni this prominence should try olympiad maths instead🙂

[@skrill500]

@@doyourealiseiamaghost5862 watch Timothy Gowers videos

[@MrSuspicious0]

15:05 i made the same mistake when i sat this paper in 2019. I only realised in my last 3 minutes while i was double checking my work

[@flamehaze59]

This is amazing!! You literally doing this with only a little effort, I would have a hard time 😂 Also, it's been a while since I've graduated... But yeah, great! Greetings from Germany, I'm from Bavaria, means we have the hardest exams there!

[@soham7316]

24:13 I always make that mistake of not simplying the expressions within the brackets - the second bracket (2x + 10y) could have been simplified further to 2(x + 5y). Lost 4 marks across the 3 GCSE maths papers because of this mistakes repeatedly.

[@scragar]

I think the not drawn accurately thing is just to avoid people measuring it and using the measurements as an answer. Deliberately making sure all examples are slightly wrong avoids that. Not that someone couldn't just draw it accurately themselves with a ruler, but I guess if you could draw it accurately it already demonstrates you understand it.

[@cameronweiss4044]

I swear question 8 is from the first chapter of my eighth grade geometry class, find the distance in both values in the two points and divide by 8 (3,2 5/8) then multiply by 5 and add to A but in the direction of the line

[@vimuth_04]

Love this type of videos..I recommend looking into Sri Lankan AL Combined Maths papers..they are really tough and enjoyable 😊

[@fischergriess6321]

Valeu!

[@jf5419]

I've got a wild idea- how about attempting papers of subjects you're not super familiar with? It'd be cool to see you attempt them 😁

[@Infinium]

Great video as always! :)

[@IAmWood_]

I hope at some point he tries the Australia HSC Extension 2 Exam

[@ykeongchee]

I can't check all comments to see got user give the correction on Q10, your answer still can factorise 2 out from 2x+10y. Q10 final answer: 1(3x-2y)(x+5y)

[@NZC_Meow]

21:52 I did middle term. Where did I go wrong? 6 * 20 = 120 26 = 30 - 4 6x² + 20xy -20y² => 6x² + 30xy -4xy - 20y² => 6x (x + 5y) -4y (x + 5y) My answer is: (x + 5y) (6x - 4y) Edit: Nevermind it's the same thing Edit 2: oh no the 2

[@JudeAndTrains]

You should do the igcse further pure maths, it’s certainly harder than aqa

[@devondevon4366]

55:39. Well, those preparing for this test or preparing students for it, will now realize what they expect when students are asked to factorize 55:59

[@dileepkumarpydi27]

Your teaching level is fantastic.... 💕 ur teaching From india !😍

[@evandrofilipe1526]

This makes me sad cuz If I knew there was such a gcse I would've taken it in an instant. But sadly I found out months before my exams.

[@avoriginal9342]

If it is delta y over delta x why at min 15:07 it’s the other way around? EDIT: nvm at 16:36 it gets rectified

[@swldnsstory9843]

We need a GCSE Statistics Video!!!!

[@AndrewRoberts11]

Have a go at the 1979, standard, Oxford and Cambridge O-Level maths paper.

[@nepaliman9027]

I am sitting my first GCSE Maths paper on the 20th May. I need a Grade-7 at least for A-Level Maths and I am already really nervous and my confidence is really low.

[@R4qayyah]

Wishing you all the best! Just have confidence in yourself more times than not you’ll be right.

[@nepaliman9027]

@@R4qayyah thank you so much for the advice it will help me.

[@human-kg8nu]

Same here although I only need 6 for my courses but I want to aim higher I suggest using maths genie and youtube videos by gcse maths tutor

[@nepaliman9027]

@@human-kg8nu Thank you good luck in your GCSE as well.

[@human-kg8nu]

@@nepaliman9027 thanks . Good luck to you too :)

[@julianrisos2365]

Another Paper that would be interesting to see is A level mechanics papers.

[@PureExile]

24:10 I reckon that should be 2(3x-2y)(x+5y).

[@PureExile]

Ah, ok, you mark it at the end. Cool. 2 is a factor so you definitely deserve a dropped point there.

[@selcuk2649]

@@PureExile how to solve

[@peterbenoit5886]

On question 10, for full factorization, you should have factored out the common monomial from each term to begin. For question 9, there is a much easier way. Now to restart the video and continue.,

[@dd6240]

Hey could you do a further maths aqa AS level paper please 🙏, I have my AS exam coming up and it would be great to watch something productive and entertaining on KZbin like your exam videos

[@julianrisos2365]

He already did an AS paper for further maths so I doubt he's going to do another one specifically for AQA is what I'm guessing.

[@dd6240]

@@julianrisos2365 no he did A level not AS

[@julianrisos2365]

kzbin.info/www/bejne/eWnSYamchsqSbKM you can check in the video again if you want. It says Pearson Edexcel AS Paper core mathematics 2018

[@mohannedabdulaziz1862]

Hello. Dr. Tom Crawford. I would like to know if you could make a video of you doing IB Furthur Mathematics or AA HL, AI HL papers. That would be amazing.

[@htrxmtrx]

Agree with this --- would be an interesting watch!

[@matthieu_fulhaber]

For Question 17, can you not just simply do 2x +46 =2(127-3x) and then solve for x giving x= 26 degrees based upon curcle theorem where angle at centre is twitce angle at circumference instead of having to go and find each angle in the triangle and work to solve x? 😊

[@matthieu_fulhaber]

@dnomyarakunawik38bro 😭 ofc it is. Look at it Icl 😂

[@ammarahmed8268]

Hey Tom, a big fan of your channel and I'm from India. Why don't you try to take a CBSE(Central board of secondary education) mathematics exam it would be so cool to see you solve a board exam from another country.

[@stormflame829]

You make this look so easy :( I wish I was as smart xD

[@Lou_Snuts]

Elegant solutions! For the part of the exam that allows calculation aids, how about using a "slide rule" instead of an electronic calculator. Both are calculation aids. How about it?

[@gregorwarren9118]

Can you try a Scottish advanced higher mathematics paper? 👍

[@tpthpt5973]

Great video!

[@TomRocksMaths]

Glad you enjoyed it

[@chrisi359]

Nice. Gonna be there

[@ahmedjawad6580]

Hey nice video. You might want to solve a Cambridge A level Further Pure Maths paper they are very difficult.

[@soham7316]

How did he just end up doing that paper in 50 mins wow

[@julianrisos2365]

Would Love to see a Further Pure 2 or 3 exam. I'm, taking Futher A Level Maths this year!

[@michaelchicken472]

rip

[@fknzz6]

12:30am, here i am 'revising' for the fm paper tmr😅

[@MrPlaiedes]

Imagine taking a maths exam with Tom... Woo ... woo ... woo ... Woo

[@imogenfleming-yates5996]

52:39 for marking

[@golammorshed7260]

I suggest you try the IGCSE papers for Edexcel and Cambridge. They have Further Pure Maths which are much harder. Edexcel has less topics + depth than Cambridge but I personally find Edexcel's questions interesting and trickier.

[@chaitanyachoudhari5934]

hey, could you do Indian JEE Adnavced paper

[@baggysimandoff1193]

Really want to see you do some bulgarian uni maths.

[@Zee-hd1yr]

For Q8 we got the same answer and I did it in a way that took about 2 mins. We still got the same answer though.

[@sharvilpatel1651]

It's too great 🤗🤗🤗

[@Boba_green_tea_yakult]

I guess using section formula in Q8 will be extremely easy to do

[@star.759]

I remember last Year doing my further maths exam and funny enough regular maths in my opinion was so much harder to no reason. But then again the edexcel regular test had that devil circle question lmao. I'm saying the further maths test was easier as I completed that test in like 45 minutes and in paper 1 I cried during that last question because my head wasn't computing what to do for an hr lol.

[@James_Anderson_]

If you try one of the Scottish exam past papers do the 2015 Higher one

[@JamesJones77980]

looking back on this a few years after getting a level 6 and i literally could not answer 1 question 💀

[@samuelgabor7521]

Too much coke, professor? Just kidding! Nothing wrong with blowing your nose. Love your videos!

[@warmpianist]

5:28 x > -18/5 but not x > -18/5 > -3. But still yeah

[@engineeringjoe]

can someone pleas explain how he did the 4.? What is o(x) an O(i)?? woudn't it be right to solve the euation by putting al x ank k one one site?

[@VenkataB123]

I'm not sure either what that "o" is supposed to mean, but what he did was this: He compared the coefficients of x on both sides. So, that gave p+6=4. Then, he compared everything else (-p+2k=8), because -p and 2 are also some constant values. I don't see the point of taking x and k on separate sides. It would be better to reform the LHS according to the RHS (like (p+6)x + (2k-p) = (4)x + (8)) and then simply compare. Moreover, when you have three unknowns here, best not to transpose stuff across the equals sign

[@deekoei]

the o is "order" - as in the size of the power of x o(ax^2) being 2 and o(ax^5) being 5 etc etc the order of the constant term being 0 as x^0 is 1 (edited to correct my wording)

[@abdullahferoz8248]

I'd advise u to do the A level further mathematics pure papers Pure 1 or pure 2 Mechanics paper is considered to be the hardest tho

[@Hope4thebest6969]

This video gonna be lit!!

[@physicsman3788]

Would you mind to take the Chinese Higher Education Entrance Maths Exam in science aspect this year? It's considered to be extremely hard and notably one of the hardest Uni-entrance exams in the world that national average score is 53/150.

[@overlordprincekhan]

1:00:30 That's a nice marks!

[@rygerety8384]

As an GCSE maths student (not further), I could do all of them apart from the matrix questions and I shouldn't be able to do the derivative question either but can :). Just shows there isn't a whole lot of difference at GCSE between the exams Edit: can't spell further 😭

[@CaoNiMaBi]

Differentiation is in regular GCSE maths so you SHOULD actually be able to do it.

[@rygerety8384]

@@CaoNiMaBi nope not in the course I'm doing... my maths teacher explicitly said it was a-level

[@ajrafkabir]

Igcse additional mathematics 0606 is much harder than this. So maybe you can do that one next

[@robmiller2811]

Your approach to #8 was interesting 🤔🧐

[@topilinkala1594]

There was a mistake of marking question 18. You marked that A = sqr(2)is correct when A does not correspond anything on you diagram and the same with y. Using your own definitions for line segments can be a problem when you erase the references. Use only the given names. In this case A=AB and y=DE. Btw. Congratulations on the profesorhood.

[@adamknight1001]

I’m taking this exam in like a month and I don’t really understand most the stuff in it, my teacher has been more focused on normal maths GCSE. Anyone got any tips?

[@VenkataB123]

Good luck for your exam!!😃 And I'd be glad to explain some stuff if you wanna get the hang of it

[@j.sgames5829]

What do you mean with further maths? Here in Greece we learn those things in 2nd and 3rd grade of high school (age 17-18) in addition with many proofs and proof theorems like Fermat's, Bolzano's, Rolle's, Mean Values Theorem,Calculus II and many other nice stuff😂

[@hiow2298]

This further maths is learnt for children aged 15-16

[@hyuyu3799]

@@hiow2298 in America we do this maths in like 8th grade, precalc in 9th grade and then we do calc 1 and 2 in 10th grade. Why is England so behind with maths

[@Pinekones.]

​@@hyuyu3799ur exams are all multiple choice, we actually have to work out are answers and not just make an educated guess

[@christianmiranda331]

Do CSEC Additional Mathematics next (Caribbean Version of GCSE) 🤗

[@scnt]

One day, hopefully, I'll also be a math professor 😊

[@krishanmenon420]

Hey sir, could you possibly share your expirience on getting into oxford?

[@ksmyth999]

Question 10. Why not factor out 2 first?

[@marybethperdomo5323]

I barely made it out of Algebra II without serious scars. What the hell am I doing here? 😅😅

[@NewtonMD]

High school student from Cameroon, Africa. The Cameroon GCE Further Maths exams make this looks like elementary level. I can link a paper on Google docs if anyone needs

[@alexanderg7951]

At what age do people take that test?

[@art3mis02]

Hey, maybe you could take an A-level core maths paper next?

[@TomRocksMaths]

I’ve already done one!

[@multiarray2320]

@@TomRocksMaths what about a math exam from an elementary school?

[@alxna._]

where and how do you write on the test? just want to know since I've been looking for a while

[@marklondon9004]

Your mistakes and actually more instructive, as I think they are representative of how good students lose marks.

[@Fahim1738]

PLEASE DO IGCSE FURTHER MATHS

[@nomanpathan9435]

pls try jee advanced, one of the toughest exams in India

[@stanx0176]

as an edexcel student this looks a lot easier

[@Ehzgnimeh]

Bruuuuuuh all these questions are basically my math exam questions in a week 🤔🤔😭😭😭(other than the matrix one, which I have not learnt) I’m only secondary 3.

[@khailequang9613]

So gcse Further math is just igcse math (0580) normal math, they even give you a bunch of equation and trigonometry identity for Further math what?

[@ibrahimmassab3903]

This is way easier than our olevels add math

[@hyuyu3799]

I have a stack of olevel papers from my dad and they were piss fucking easy, no wonder ur generation is so shit at maths

[@filippoabbattista9189]

Do an LSE MA100 exam

[@babyelian77]

Problem 17 is easier if you simply know that angles on a circumference are always half of that on the center (btw, it' s why a triangle inscribed in a circle with the hypotenuse on the diameter is a right triangle). Thus, angle BCA = half of BOC = x + 23°, so 90° + x + 23° - 37° + 3*x = 180°, or 4*x = 104°, x = 26°. Just to speak...

[@CaoNiMaBi]

You don’t even need that theorem to solve this one. There’s a much faster way.