Everything you NEED to memorise for A-Level Further Maths • Part 1: Core Pure Year 1 💡

I’m offering a Core Pure Year 1 Revision class for the 2023 exams - check it out and buy a ticket here www.tickettailor.com/events/b...
For all available sessions, check out the full range: buytickets.at/bicenmaths
If you’d like a blank copy to test yourself with, or the completed pdf, you can find them both on my Bicen Maths Google Drive here: drive.google.com/drive/folder...
VIDEO LINKS TO TEACH YOU ABOUT THE FORMULAE
COMPLEX NUMBERS - coming soon
SERIES
Whole Chapter: • Chapter 3: Series 🏅 (C...
- Standard Results: • Series 8 • Sums of Squ...
- Starting value not r=1: • Series 6 • When the se...
ROOTS OF POLYNOMIALS
Whole Chapter: • Chapter 4: Roots of Po...
- Sums of Roots, Pairs, etc.: • Roots of Polynomials 5...
- Sum of Squares/Cubes: • Roots of Polynomials 6...
- Transformation of Roots: • Roots of Polynomials 7...
VOLUMES OF REVOLUTION - coming soon
MATRICES - PROPERTIES - coming soon
MATRICES - INVERSES - coming soon
MATRICES - SYSTEMS OF EQUATIONS
- Overview: • Matrices 12 • Geometri...
- Checking Consistency: • Matrices 13 • Algebra ...
LINEAR TRANSFORMATIONS
Whole Chapter: • Chapter 7: Linear Tran...
- Invariant Points and Lines part 1: • Linear Transformations...
- Invariant Points and Liens part 2: • Linear Transformations...
- Area Scale Factor: • Linear Transformations...
- Successive Transformations: • Linear Transformations...
- Rotations: • Linear Transformations...
- 3D Rotations and Reflections: • Linear Transformations...
- Undoing Transformations: • Linear Transformations...
PROOF BY INDUCTION
Whole Chapter: • Chapter 8: Proof by In...
- Divisibility: • Proof by Induction 4 •...
VECTORS - DEFINITIONS
Whole Chapter: • Chapter 9: Vectors 🎯 (...
- Scalar Dot Product: • Vectors 5 • Scalar Dot...
- Vector Line Equation: • Vectors 1 • 3D and Equ...
- Cartesian Line Equation: • Vectors 2 • Cartesian ...
- Parametric Plane Equation: • Vectors 4 • Planes - P...
- Scalar Product Plane Equation: • Vectors 6 • Scalar Pro...
- Cartesian Plane Equation: • Vectors 4 • Planes - P...
VECTORS - ANGLES
Whole Chapter: • Chapter 9: Vectors 🎯 (...
- Between 2 lines: • Vectors 7 • Angles bet...
- Between 2 planes: • Vectors 7 • Angles bet...
- Between a line and plane: • Vectors 7 • Angles bet...
VECTORS - INTERSECTIONS
Whole Chapter: • Chapter 9: Vectors 🎯 (...
- 2 lines: • Vectors 9 • Intersecti...
- Line and a plane: • Vectors 10 • Intersect...
- 2 planes: • Vectors 11 • Intersect...
VECTORS - SHORTEST DISTANCES
Whole Chapter: • Chapter 9: Vectors 🎯 (...
- Point and a line: • Vectors 15 • Shortest ...
- Parallel lines: • Vectors 13 • Shortest ...
- Skew lines: • Vectors 14 • Shortest ...
- Point and a plane: • Vectors 17 • Shortest...
- 2 parallel planes: • Vectors 17 • Shortest...
VECTORS - REFLECTIONS
Whole Chapter: • Chapter 9: Vectors 🎯 (...
- Point in a plane: • Vectors 19 • Reflectin...
- Line in a plane: • Vectors 20 • Reflectin...
CONTENTS:
0:00-1:22 Why you SHOULD memorise these facts
1:22-3:35 Complex Numbers and Loci
3:35-4:44 Series
4:44-6:40 Roots of Polynomials
6:40-7:21 Volumes of Revolution
7:21-8:09 Matrices - properties
8:09-12:10 Matrices - inverses
12:10-14:33 Matrices - systems of equations
14:33-18:00 Linear Transformations
18:00-19:32 Proof by Induction
19:32-21:51 Vectors - definitions
21:51-23:20 Vectors - angles
23:20-25:12 Vectors - intersections
25:12-27:10 Vectors - shortest distances
27:10-28:28 Vectors - reflections
28:28-29:33 Outro

[@FlamefireFlash]

I beg, put my candidate number for the exam🙏🙏😭

[@therangemen8627]

Hello, I just wanted to say how much these videos are appreciated. They are fantastic and extremely helpful, especially given the current situation.

[@BicenMaths]

Thank you so much! I really appreciate your comment 😃

[@coleuk1436]

That flow diagram for systems of linear equations is amazing makes it seem so simple compared to how my teacher explains

[@f1nn203]

If you’re watching this in the morning you’re cooked should’ve watched it the night before like a normal person 😼

[@BicenMaths]

Haha, don't go scaring people, watch this video whenever you want to!

[@tomlynn27]

​@@BicenMathsthanks buddy

[@f1nn203]

@@BicenMaths don’t worry mr Bicen I was only joking 🙌, watched part 2 in the morning 😭🙏

[@drewetpa]

Hello Sir. I'm a 53 year old man. I'm in recovery from alcohol / addiction and mental illness (Anxiety and Depression). I've just received my GCSE result (Edexcel) of 203 / 240 which I was both surprised and delighted with as I dropped marks in the exams (particularly paper 1) due to anxiety. I would like to self study A Level Further Maths at a sedate pace to keep the grey matter ticking over. I've realised that I'm a Maths Nerd and actually punched the air a couple of times in the exam(s) when I knew I'd answered a harder question correctly. Your channel was reccommended to me by the chap at first class maths and it looks like an excellent resource. I would be very grateful if you could recommend good text book(s) to start learning Further Maths together with the videos on your channel. Many thanks and I look forward to spending hours scratching my head and wringing my hands over your videos.

[@BicenMaths]

Hi Phil, apologies for the delay in getting back to you, have just been busy back at work! Congratulations on your GCSE result, that’s fantastic! It’s really inspiring hearing people retuning to maths after time away from it - love to hear it. If you’d like to self study Further Maths A-Level, make sure you are also studying the regular A-Level for Maths too, as Further Maths builds on normal Maths. In terms of resources there are blank slides in my Google Drive (linked in the About section on KZbin) for you to follow along with all my videos. As for textbooks, they are all aligned with the official Pearson Edexcel textbooks. Here’s one as an example so you can see the series I am talking about - please feel free to ask any more questions! www.amazon.co.uk/Edexcel-level-Mathematics-Textbook-Further/dp/129218339X/ref=nodl_?dplnkId=c9740d47-ed49-4074-bdaf-3e1e94cd15d6 Good luck!

[@dylansimpson2322]

Just clicked the video, can already tell this is just what I needed, cheers!

[@finnleybland2301]

We are cooked

[@jackgreenfield2749]

Trust me

[@nosir1479]

Hhahahah 😂 we’ll be fine

[@francaisdeuxbaguetteiii7316]

Speak for yourself

[@FlamefireFlash]

Truly.

[@vqrtex4910]

@@FlamefireFlash cooked

[@casparclark9933]

All of these videos are so incredibly useful, thank you so much for taking the time to make them. A levels are about 2 and a half months away, I can't describe how thankful I am for such a resource

[@BicenMaths]

I appreciate the comment - thank you!

[@jamescoulthard2989]

This has helped me so much with revision. Thanks!

[@theversatiletrader18]

Extremely useful video, making revision way easier!

[@cheesesammich9233]

Mr Bicen, Thank you, so incredibly much for this video!!!!

[@ml8911]

I really appreciate the concise summary that you've made. It is (presumably) meant to be a revision video but i find it equally useful for students who want to pre-learn further maths lol

[@pierscarr6298]

Potentially the most useful video ive ever watched. thanks

[@MinecraftCurios]

yes very good video

[@livelydodo]

Thank you so much. you are a life saver. This is exactly what i needed for the upcoming exam in two days. i hope you reach over a million subscribers and be able to help more students in need, like me, with your channel. 😄

[@BicenMaths]

Thank you! Wishing you the best of luck for your exam! 😃

[@brendamiriamlam5074]

You are amazing amazing! Thank you soooooo much.

[@adlinaky2821]

Btw,, THANKUUUU SO MUCH FOR ALL YOUR VIDEOS AND NOTES!!! IM SITTING FOR MY CAIE ALEVELS NEXT WEEK!! U R DA BEST!!

[@finnpea]

Thanks for all these resources 🙌🙌

[@soham5381]

thank you sooooo much was such a great video

[@sammossop2047]

Great video thanks sir!

[@thomashall4683]

I just recommended this video to my further maths class as we have a mock tomorrow!!

[@shindedh]

Extremely useful for last minute revision.👍👍

[@khan99ish]

Thank you for this summary video As exam tomorrow nice way to summarise a years worth of content cheers

[@miabramble4193]

Thank you so much this is super helpful!!!!

[@BicenMaths]

You’re welcome! 😃

[@dheeraj5343]

Thank you so much! So nervous for the AS exams as I've been self teaching myself and your videos have been amazing!

[@BicenMaths]

Ah thank you! Let me know if there’s anything you need guidance/help with 👍🏼

[@hiper_tops]

just what i was looking for :)

[@ArifulIslam-ti3ch]

Really great video sir. It's so useful and so easy to understand>

[@flocierplays6289]

wow. Thank you so much.

[@nathanhawey294]

This is going to help me alot.

[@m4dalex828]

Super useful video, thank you Sir

[@iqbalmatics824]

very good effort ...go on

[@finnpea]

You are the man

[@thefishoftruth235]

Your channel is criminally underrated. Thanks so much for making these

[@BicenMaths]

Thank you! 👍🏼

[@nadiaally7235]

Got the further maths exam today... just wanted to say thank you!!! Been following you since the start of the course and you’ve made learning further maths as easy as it could ever be :)

[@BicenMaths]

Good luck! I’m really pleased you’ve found my content helpful - thanks for sharing this with me. Let me know how it goes! 🤞🏼

[@baldoggie]

What did you get

[@nadiaally7235]

@@baldoggie Nearly full marks! An A* :)

[@lav9sh]

@@nadiaally7235any tips?

[@zohaibgulawan9070]

@@nadiaally7235 in final a level?

[@flamingash3809]

Awesome video!

[@BicenMaths]

Thanks!

[@jessielulu277]

This is amazing for a last minute check that you know what you're doing as well as to make a revision list from!

[@BicenMaths]

The pdf, including the blank version, is available in my Bicen Maths Google Drive. Link in description if you want it 👍🏼

[@jessielulu277]

@@BicenMaths that's great thanks!

[@MegabyteMusician]

Watching this as I try to fall asleep the night before the exam 😌😌

[@yellowmoss271]

lol same

[@easondu9236]

BICEN IS THE KING!!!!!!!!!!

[@clement_jacob]

so good

[@LU-dm7kj]

thanks

[@ricy4059]

Hi, really love this and it helps so much! Thank you so much for making these. Will there be a part 2 for further mechanics anytime soon? Because that would be very useful for me :) thank you!

[@BicenMaths]

The one for FM1 is complete, it's just one single video that covers the whole module (Year 1 and 2). Here is a link to it: kzbin.info/www/bejne/mJDTZnd8h5qqsKM

[@joebloggs2782]

great video

[@BicenMaths]

Thanks!

[@spectrum4real208]

These summary videos are amazing to rejog memory of key points. Could you do videos like these for Decison 1 and Decision 2?

[@BicenMaths]

These are coming later this year!

[@JJFHNREHJEDK]

Week 2 of a-levels and I have 3 FM exams in a week 😭 Thanks for this

[@snookyloopy]

Fantastic resource - thaks for sharing! My students are asking if you have any plans to a similar one for CP2 and FP1?

[@BicenMaths]

Thank you! I’m currently working through these as my next project - I’ll be doing Mechanics and Statistics from Maths, then Core Pure 2, Further Mechanics 1, and eventually Further Pure 1, although I’ve not been teaching FP1 for a year so will take a bit longer. They take some time to put together, but pleased they are of use! Make sure you check out the pdf versions linked in the description, and more generally my whole channel for video tutorials. Thanks for the support 👍🏼

[@dompatterson609]

the goat

[@gddanielk8491]

So helpful!

[@rubenkovacic7988]

Hey Mr Bicen, are you planning on doing an Everything you need to know for FP1? It would be much appreciated.

[@BicenMaths]

Hopefully will be coming at some point… got a lot of things I need to do!

[@francescalee4693]

This is very helpful! Just wondered if you would ever do a D1 video, as that would be greatly appreciated :)

[@BicenMaths]

Probably not for a long while, D1 isn’t something I currently teach, sorry!

[@francescalee4693]

@@BicenMaths That's ok! No worries. It's just your videos are so useful.

[@BicenMaths]

Ahhh thank you!

[@ashdragontamer1222]

Watching this before I go into my as further maths exam this afternoon. Let’s hope it sticks

[@lexie3039]

me too bro

[@BicenMaths]

Good luck to you both! I'm interested to hear what are they hard questions this year... let me know

[@aymqnoo9291]

This year was relatively easier

[@aymqnoo9291]

12 marker on finding roots and the a b and c in the equation (idk if u get what i mean)

[@hvh6368]

@@aymqnoo9291 questions this year were so calmmm only hard one for me was the magnitude of Z^10 question

[@AJMaths]

Surely the proof by induction for a recurrence relation in the Core Pure mock is a mistake? I know it was part of the old FP1 spec but proof by induction is part of chapter 4 on the official Pearson textbook for Further Pure 2, It's always in AS Papers as well or it seems that way when going through it with students.

[@BicenMaths]

I agree with you - but an email directly from Edexcel said it was not a mistake, as it technically builds on knowledge from Maths A-Level Sequences and Series. Utterly terrible on their part, but it’s what was emailed to me after several teachers complained! So I add it in to deepen understanding and show it has other uses too.

[@AJMaths]

@@BicenMaths That's surprising to say the least, I mean it makes sense given the introduction to recurrence relations in sequences and series but it seems to be rather inconsistent with textbooks/their own exams. Cheers for the heads up though!

[@BicenMaths]

I was so surprised they didn’t back down from it! Mad!

[@dylanpi]

Do you think you’ll ever do one of these for FP1? Thanks so much for these videos, they’re lifesavers!

[@BicenMaths]

Yes, I will do! I’m going to be working on FP1 videos in the coming months, so a memory page will also be created. Might not be until after this exam season though…

[@rozhakram1084]

Excellent one, Will you have one for CP2 anytime soon? (Sorry if I’ve asked this before) do you do 1-to-1 tutoring for further maths?if not, do you know anyone that you could please recommend? It’s incredibly difficult to find an experienced tutor for further maths online

[@BicenMaths]

Sorry this has taken me a while to respond! I will be doing one for CP2 soon, but am taking a bit of a break over the holidays. Should be there in a couple of weeks! As for tutoring, if you could email me it’s easier to discuss directly. You can find my business email in the About section when viewing my channel from a laptop/desktop (not sure why it can’t be seen on mobile). Thanks!

[@Voltanaut]

I always wondered about doing FM when I was an A Level student. This video reassured me that not doing FM was the right choice. This stuff is bonkers. I also flubbed my regular maths exams and only got a C, so dodged that bullet.

[@morienrobertson9743]

These are great. Any chance of an all you can memorise for FP1?

[@BicenMaths]

Probably not until next year!

[@GreyJaguar725]

​@@BicenMaths Will that be before the summer of 2024 as that's when I will take my Further Maths exams? Also Will there be one for FP2?

[@liangchen4679]

I'm cooked

[@stevieb7695]

real

[@beanie2571]

as exam is in like two weeks not exactly slaying rn 🙏

[@hvh6368]

How did you find it? I thought it was quite easy

[@beanie2571]

@@hvh6368 yeah it was easier than i expected

[@hvh6368]

@@beanie2571 did you figure out the magnitude of Z^10 one?

[@beanie2571]

@@hvh6368 nah did you get it?

[@hvh6368]

@@beanie2571 nah only one I think I got wrong

[@mrfreerunners1]

hey would you do this for D1 ?

[@scrtpawrd]

Please make a further pure video🙏

[@BicenMaths]

It’ll be coming soon, but not before the exam this summer I’m afraid!

[@nadimali101]

At 15:44, shouldn't the area scale factor be the modulus value of the determinant of the matrix?

[@BicenMaths]

That is correct! Thanks for pointing this out.

[@s.hjb0]

vectors better not come up as I haven't revised them as they came up in paper 1

[@mh.1.]

_Thats my worry fr_

[@lbz5910]

what the sigma

[@chesster5981]

1:53 They come in conjugate pairs only when the coefficients are all real.

[@hvh6368]

Did you do AS paper 1 today?

[@a-history-nerd]

Would flashcards be a good way to revise content, along with practice questions?

[@BicenMaths]

I think so! I personally don’t use flash cards, but I can see them working well for you to check a formula - but don’t rely on them, make sure you try and pull it from your memory first!

[@adlinaky2821]

25:08 dont mind me, putting my revision timestamp reminder

[@Ron7008]

Any chance you can make one of these for stats?

[@BicenMaths]

If you mean further statistics 1, I don’t currently teach this so won’t be making one right now. But if you mean regular stats, here’s a link to the video! kzbin.info/www/bejne/jajZh6iGbpuLoMU

[@mateenabdul4593]

For finding the intersection of 2 planes in the vectors section, can’t we just use matrices?

[@BicenMaths]

Yes, you could do this too - how would you propose going about it?

[@winlarter4235]

Hi Mr Bicen I’m thinking of self teaching Further maths where can I get the spec from do I need the book you think also what advice would you give me ? I love a level maths and I want to further maths now haha crazy but why not when there’s the lovely Mr Bicen‘ after resources

[@BicenMaths]

That’s great! 🤩 You should definitely purchase the official Pearson textbooks that I refer to in all my videos - you can buy them cheaply on ebay usually! I would also make sure you practice lots and lots from the exercises, not just using the videos. In the Bicen Maths Google Drive there are blank versions of all the slides I use, so if you like you could print these and take notes alongside the videos. Good luck! 😃

[@winlarter4235]

@@BicenMaths thank you and one last question how is Edexcel further maths structured please

[@BicenMaths]

There’s 2 compulsory modules - Core Pure Year 1 and Core Pure Year 2 - and then you can pick two optional modules. I recommend Further Mechanics 1 for one of them, and usually recommend either Further Statistics 1 or Further Pure 1 as the other. Each module is a 90 minute exam. I hope that helps!

[@winlarter4235]

@@BicenMaths thank you !!! Mr Bicen

[@frankiestark1577]

Ive got my a levels coming up soon. I’m really good at normal maths but i get really bad grades on further maths because my confidence is incredibly low and i end up panicking. Any advice?

[@BicenMaths]

Pick a topic, revise it thoroughly, then practise, practise, practise. Once you realise that you can do a topic, you’re confidence will increase, and you’ll be less likely to panic. Don’t think about trying to do the whole course all at once, just start small and you’ll feel better in no time. There are tutorial playlists for every chapter - check them out on my homepage. Good luck!

[@kayleigh8069]

Hi, do you generally have to use unit vectors in exam questions as i've gone through every question in the book and not one refers to a unit vector? Thanks :)

[@BicenMaths]

Unit vectors aren’t really used in Core Pure - but they do come up in Pure for regular maths A-Level, and also come up in Further Pure 1. I also can’t think of any Core Pure questions that involve unit vectors, but make sure you know them as they sometimes appear in the normal maths A-Level!

[@kayleigh8069]

@@BicenMaths Okay thank you! i have a chapter test for vectors tomorrow and wasn’t sure if it would come up, would anything to do with distance between planes or intersection of two planes come up either?

[@BicenMaths]

Yes, this definitely could - distance between planes you change the question to distance between a point and a plane (just pick any point on one of the planes), and for intersection of two planes watch this to check you understand: kzbin.info/www/bejne/h4rLcoWEjauLpLM Good luck! 🍀

[@kayleigh8069]

@@BicenMaths Ah thank you! i need to go over that and reflections and hopefully should be all good :)

[@kayleigh8069]

@@BicenMaths Got 100%!!

[@mrfreerunners1]

could you do a pdf of the all you need to memorise for D1

[@BicenMaths]

Very unlikely, as I don’t teach D1 and so would take me a looooong time. Sorry!

[@mrfreerunners1]

@@BicenMaths that's totally fine dude!, I am enjoying your tutorial videos for further maths as I am private candidate at the age of 24 taking 3 a levels aha

[@BicenMaths]

Amazing! Let me know if there’s anything I can help with - drop a comment on a video if you have any specific questions about what I explain! Good luck 👍🏼

[@KiranPatel-wl9jz]

Sorry Mr Bicen I know you are busy, but to find the line of intersection of two (or three) planes, we can let z = 0 then solve two simul. eqs. How do we do this if the line of intersection is parallel to one of the axis? It would be difficult to tell I think e.g. if the line of intersection is parallel to z = 0 we can't let z = 0

[@BicenMaths]

You'd have to think through which you could set to 0 carefully I'm afraid!

[@lbz5910]

@@BicenMathswhy are you afraid? dont be scared sir!

[@BicenMaths]

Very funny 👏🏼

[@KiranPatel-wl9jz]

Good luck sir!

[@lakisananratnarajah8787]

at 26:55, shouldn't the numerator for the equation for distance be n1x+n2y+n3z-d instead of plus d

[@BicenMaths]

No, it is as I have it written - see the bottom of page 14 qualifications.pearson.com/content/dam/pdf/A%20Level/Mathematics/2017/specification-and-sample-assesment/Pearson_Edexcel_A_Level_GCE_in_Mathematics_Formulae_Book.pdf This is because (annoyingly) they are using d when ax+by+cz+d=0 even though most people write ax+by+cz=d, so just be careful of the form of the plane that you have!

[@lakisananratnarajah8787]

@@BicenMaths thank you

[@angelkapur]

Hi, do you have the pdf version of the FM1 book ? Will extremely appreciate!!

[@angelkapur]

i found it nvm! but what does the yellow dots mean next to the topics?

[@angelkapur]

if i am doing AS i wouldnt need to know the topics that have a yellow dot? sorry for asking as i am self studying fm1 for a test .

[@BicenMaths]

Yep that’s correct! The yellow dot corresponds to topics for Year 2. I think there’s a key on the contents page!

[@jessicaschoolacc291]

6:16

[@simstar9364]

for the equation of the shortest distance from a point to the plane, i thought it is minus d?

[@BicenMaths]

It depends on how d is defined - I use the version from the formula book where the constant of the plane equation is on the same side as the x y and z, so it’s equal to 0. So annoying that the formula book does it this way!

[@simstar9364]

@@BicenMaths oh ok, so doing minus d is correct anyway? thanks for fast reply, exam is tomorrow

[@BicenMaths]

Definitely check your formula booklet as then you can be sure exactly how it looks! Just Google it and it should come up. Good luck for tomorrow 👍🏼

[@simstar9364]

@@BicenMaths thanks so much sir

[@darenkaulsay8076]

Can this be used for CIE further maths as well?

[@BicenMaths]

As far as I’m aware, essentially, yes - it’s possible there are a couple of minor differences, but if the same topics are in the specification, the maths will be the same! Sorry I don’t have a definitive answer for you 👍🏼

[@shehz]

Will we get a statistic one?

[@BicenMaths]

kzbin.info/www/bejne/jajZh6iGbpuLoMU This is for A-Level Maths Statistics 👍🏼

[@ayeshakashif6757]

Hello, for which year's syllabus is this?

[@BicenMaths]

This is the new specification for A-Level Further Maths, Edexcel (2017)

[@qch0918]

will there be a further stats version of this?

[@BicenMaths]

Yes eventually!

[@qch0918]

@@BicenMaths Thank you! The series has already helped alot for my current alevels!