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

2 жыл бұрын

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

@morzee94

2 жыл бұрын

@@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

2 жыл бұрын

@@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.

@vantage224

2 жыл бұрын

@@morzee94 Loci segue into A-Level further maths with the 'loci in the argand diagram' topic.

@rogorix4991

2 жыл бұрын

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

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

@chrisi359

2 жыл бұрын

Would love to see that

@jakoolaboo

2 жыл бұрын

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

@georgezhang865

2 жыл бұрын

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

2 жыл бұрын

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

2 жыл бұрын

@@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.

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

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

@TomRocksMaths

Жыл бұрын

Happy to help!

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

9 ай бұрын

Yea I think he overcomplicated it

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

2 жыл бұрын

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

2 жыл бұрын

@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

2 жыл бұрын

@@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

2 жыл бұрын

@@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

2 жыл бұрын

@@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.

Your genuine excitement for getting math questions correct is wholesome.

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

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

@TomRocksMaths

Жыл бұрын

Any time!

@przemeklisicki8741

Жыл бұрын

​​@@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.

Great video as always! :)

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

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

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

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

@TomRocksMaths

Жыл бұрын

how did it go?

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.

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

2 жыл бұрын

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

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

@stevembanaso2817

2 жыл бұрын

Same

@samdowning6641

2 жыл бұрын

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

@samleman

2 жыл бұрын

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

@dunzomemes

2 жыл бұрын

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

2 жыл бұрын

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

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!!!

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

2 жыл бұрын

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

2 жыл бұрын

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

2 жыл бұрын

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

@juliusteo

2 жыл бұрын

@@createyourownfuture5410 kzread.info/dash/bejne/h2dnuqqLacnHhag.html

@timothyaugustine7093

2 жыл бұрын

@@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.

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

Love the T shirt Tom and great video!

@TomRocksMaths

Жыл бұрын

Thanks!

Man your the best math Oxford professor ever

@TomRocksMaths

Жыл бұрын

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

2 жыл бұрын

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🙂

@sudhansh6998

2 жыл бұрын

@@doyourealiseiamaghost5862 watch Timothy Gowers videos

Nice. Gonna be there

It's too great 🤗🤗🤗

Great video!

@TomRocksMaths

Жыл бұрын

Glad you enjoyed it

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

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

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

2 жыл бұрын

Yeah good luck t you too

@obiwankenobi1966

2 жыл бұрын

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

@iTz3L1TEFUZE

2 жыл бұрын

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

@obiwankenobi1966

2 жыл бұрын

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

@iTz3L1TEFUZE

2 жыл бұрын

@@obiwankenobi1966 thank you!

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

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

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.

@htrx1380

2 жыл бұрын

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

Really want to see you do some bulgarian uni maths.

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

@michaelchicken472

2 жыл бұрын

rip

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

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!

@tyrahuntr

8 ай бұрын

try the chinese gaokao and you will know what a hard exam is lol

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

We need a GCSE Statistics Video!!!!

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

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

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

This video gonna be lit!!

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

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

Valeu!

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.

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

Can you try a Scottish advanced higher mathematics paper? 👍

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.

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 KZread like your exam videos

@julianrisos2365

2 жыл бұрын

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

2 жыл бұрын

@@julianrisos2365 no he did A level not AS

@julianrisos2365

2 жыл бұрын

kzread.info/dash/bejne/dWyjktifgcjFZqQ.html you can check in the video again if you want. It says Pearson Edexcel AS Paper core mathematics 2018

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

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

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)

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

2 жыл бұрын

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

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

2 жыл бұрын

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

2 жыл бұрын

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)

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

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

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

This is crazy!!!

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.

hey, could you do Indian JEE Adnavced paper

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

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.

Your approach to #8 was interesting 🤔🧐

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

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.

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

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

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.,

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 😁

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.

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

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

Жыл бұрын

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

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

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?

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.

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

2 жыл бұрын

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

@nepaliman9027

2 жыл бұрын

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

@human-kg8nu

2 жыл бұрын

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

2 жыл бұрын

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

@human-kg8nu

2 жыл бұрын

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

Question 10. Why not factor out 2 first?

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

nice...

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

@PureExile

2 жыл бұрын

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

@selcuk2649

2 жыл бұрын

@@PureExile how to solve

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

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

PLEASE DO IGCSE FURTHER MATHS

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

2 жыл бұрын

This further maths is learnt for children aged 15-16

@hyuyu3799

7 ай бұрын

@@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

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

@TomRocksMaths

2 жыл бұрын

I’ve already done one!

@multiarray2320

2 жыл бұрын

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

Please do an IB HL Math AA (or Further Maths) paper 1 or paper 2 next 😂

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.

Yessir

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

Do a different subject paper English then we can c if you r clever or not?

52:39 for marking

Bài toán về số nguyên tố phải không bạn ?

@amritlohia8240

2 жыл бұрын

None of the problems in this exam were about prime numbers.

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

2 жыл бұрын

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

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

2 жыл бұрын

At what age do people take that test?

make an ib exam. could be great

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

f(3) = 20/27?

as an edexcel student this looks a lot easier

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.