All of Quadratics in 40 Minutes! | Chapter 2 | AS-Level Pure Maths Revision | A-Level Maths Tutor

A video revising the techniques and strategies required for all of the AS Level Pure Mathematics chapter on Quadratics that you need to achieve a grade C-A* in your A-Level Pure Maths.
These topics are the essential question styles that appear in the Quadratics Module. This however is not ALL of the question styles within the A-Level. Further videos can be found on the channel for a more in depth look at some of these topics.
👑 Everything you Need to Pass your AS Pure Maths Exam! A* | AS Pure Maths Revision | Edexcel AQA & OCR - • Everything You Need to...
See below for further links to each of these topics:
00:00 Intro
00:35 How to use the Video
01:52 Solving Quadratic Equations - • Solving Quadratic Equa...
03:40 The Quadratic Formula - • How to Use the Quadrat...
06:47 Completing the Square - • Completing the Square ...
09:53 Solving Quadratics by Completing the Square - • Solving Quadratics by ...
13:14 Negative Quadratics - • Negative Quadratics (S...
17:29 The Discriminant - • The Discriminant | Alg...
23:27 Sketching Quadratics - • Sketching Quadratics |...
29:56 Modelling with Quadratics - • Modelling with Quadrat...
44:55 Outro
See below for more chapter based revision videos:
Chapter 1 - Algebraic Expressions - • All of Algebraic Expre...
Chapter 2 - Quadratics - • All of Quadratics in 4...
Chapter 3 - Equations and Inequalities - • All of Equations and I...
Chapter 4 - Graphs and Transformations - • All of Graphs and Tran...
Chapter 5 - Straight Line Graphs - • All of Straight Line G...
Chapter 6 - Circles - • All of Circles in 25 M...
Chapter 7 - Algebraic Methods - • All of Algebraic Metho...
Chapter 8 - Binomial Expansion - • All of Binomial Expans...
Chapter 9 - Trigonometric Ratios - • All of Trigonometric R...
Chapter 10 - Trig Identities and Equations - • All of Trigonometric I...
Chapter 11 - Vectors and Magnitude - • All of Vectors and Mag...
🔹 Watch the video
🔹 Make notes
🔹 Practice the questions
🔹 Mark your work
🔹 Review what you have learnt on the exam questions
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Enjoy the video!
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[@TheGCSEMathsTutor]

If anyone would like to support the channel you can buy me a coffee here: www.buymeacoffee.com/gcsemathstutor Thank you for all of your support! 😁🙏🏼 At 6:23 I must have pressed the wrong button whilst recording as the second solution is -0.941 and not -1.59 😬 whoops!

[@dusk3315]

Thanks for notifying us!

[@text_daily]

no bro. its 4.61 and -0.94

[@ej1867]

@@text_daily bros arguing with a maths teacher 💀

[@curry42069]

@@text_daily 3 significant figures boss the 0 at the beginning doesnt count as a significant figure

[@mc3550]

14:05 hi please can u explain why we take a factor of -1

[@aarontasawer2244]

Sir, u helped me achieve a grade 8 at GCSE, and with your videos, I will hopefully do really well in my A levels. Thank you so much for posting.

[@TheGCSEMathsTutor]

Wow amazing news!!! Congratulations on your grade 8 that’s some achievement 🥳 how are you finding A-Levels so far?

[@aarontasawer2244]

@@TheGCSEMathsTutor Hey, yeah loving it with your videos it makes it more enjoyable so thank you so much for posting.

[@TheGCSEMathsTutor]

@@aarontasawer2244 So glad to hear that! Always the best kind of feedback, let me know how you’re getting on over the year! 😁🙏🏼

[@hi5294]

Long journey brother

[@nattycarey2083]

@@hi5294 tell me about it

[@scarly9674]

hey no hâte but i’m pretty sure at 6:43 its -0.941 not -1.59

[@AlishaLamba-x7p]

yeaah

[@Inkkium]

I think so too.

[@SimaKonis]

Exactly

[@CarenWilfred]

Yh. That's true.

[@Pillow_pill]

I got that too

[@fine-jumble2114]

bro to be honest i was avoiding your video and tried to watch other guys but you have honestly made it so easy to understand to anyone thinking of clicking of just give me a chance

[@mahjabeen5835]

Currently I have 2 months for my Cambridge AS level exam, have mock tomorrow, and I know nothing, you think this video will help??

[@nathanhawey294]

Gcse students listen to me here,I got grade 9 and not just that i got full marks in 4 papers.I don't speak much English and I got that result in one year.All I used was the gcse maths tutor.He is super, use all algebra videos trig and things everything is organised.And let's share the chanel help him as he is helping us!Thank you legend maths tutor!

[@TheGCSEMathsTutor]

Wow… I don’t even know what to say! Thank you so much for your kind words and congratulations on a phenomenal achievement, comments like this continuously remind me why I love my job, so glad that I could be a small part in your success story! Please do keep in touch 😁🙏🏼🙏🏼

[@nathanhawey294]

@@TheGCSEMathsTutor you deserve it!You did that for many of us and hopefully the UK will recognise the people like you and we can just learn on KZbin.

[@TheGCSEMathsTutor]

Thank you so much 😁🙏🏼

[@yahyaburhan339]

Damn that is amazing. Congratulations 🎉🎉 bit I'm afraid its 3years too late 😅

[@straymite707]

Thanks so much for helping me jump from a grade 5 to an 8 in maths GCSE, you really changed my life and I hope you keep uploading more a level videos because I'm doing maths at a level now and you're really good at explaining things! Keep it up

[@TheGCSEMathsTutor]

Wow that’s an incredible achievement congratulations!! Honestly it means so much to know that my channel had such a positive impact for you, thank you for commenting, comments like these really do make my day! I’ll do my best to keep up with the A-Level curriculum timings as best I can this year! Glad to hear you are doing a level maths 😁🙏🏼🙏🏼

[@straymite707]

@@TheGCSEMathsTutor Thanks

[@nicoleduplessis7256]

thank you so much for this A level content we are being blessed with

[@TheGCSEMathsTutor]

No problem at all! So glad to hear the channel is useful for you 😁🙏🏼

[@Candiceyum]

Got a high grade 8 for 2024 gcse and i climbed up from a grade 5 in year 10. Now I'm doing a level maths and further maths.

[@mochaxbear]

You read My mind…I was literally going to revise all of AS quadratics this weekend

[@TheGCSEMathsTutor]

Great news!! I hope it helps 😁🙏🏼🙏🏼

[@olismallwood9493]

You should be knighted by the Queen as Sir Maths Tutor. Thank you so much, once again, this helped ALOT.

[@GCSEALevelMaths2025]

Wow that’s such a lovely comment!! The king is proud of the GCSE maths tutor

[@kaisering]

shes dead

[@solecoffee7568]

This is what’s gonna get me through AS

[@anansii9140]

this video was amazing for my revision, made it so easy to grasp and understand. thank youu

[@xhibah]

thank u so much, u helped me get a 9 at gcse and now i'm doing maths and further maths at a level!

[@aaronennis1195]

I love this guyyyyyyyy Please don’t stop The amount of love I have for you is crazy

[@TheGCSEMathsTutor]

I won’t!! Thank you for the kind words 🙏🏼🙏🏼

[@lilomlette7923]

Greatest GCSE Maths tutor turned Greatest AS Tutor.

[@nathanhawey294]

You and bicen maths are my maths teachers.I love you dear.my Jesus bless you.

[@TheGCSEMathsTutor]

So glad to hear it! 😁🙏🏼🙏🏼

[@syuennilim298]

I believe at 6:21 there is a mistake. The negative value is supposed to be -0.9405 but other than that amazing videos👏👏

[@McAi-xe9di]

yes

[@mrkhoabane8903]

The first part of solving quadratics I got -0.9254

[@mrkhoabane8903]

@6:45

[@lusci0usss]

same

[@RennesPuffs10]

Yea i think he got it wrong

[@kay1127]

Omg you are back. Thanks to you I got 7 in GCSE and now I am doing a level math so this videos will be useful

[@TheGCSEMathsTutor]

Amazing news congratulations on your GCSE grade! 👏🏼 so glad to hear you have decided to carry on with A-Level maths it’s a fantastic subject 😁

[@Wolfiewyd]

What did u end up getting

[@kay1127]

@@Wolfiewyd A now doing computer science degree

[@Wolfiewyd]

@@kay1127 good on you. What other resources did u use for A level maths I’m kinda struggling

[@kay1127]

@@Wolfiewyd thank you! I was also struggling at maths to the point where i got Ds and Cs in the trial exams. I used to do a lot of past papers from different exam boards and would watch tl maths on all the topics i was struggling with. I also used physics and maths tutor for questions on specific topics and followed along videos of Mr Astbury who records solutions to hard maths alevel questions. i hope that helps. Best wishes!

[@mujahiduddin8249]

Keep them coming ☺️

[@TheGCSEMathsTutor]

I absolutely will! 😁🙏🏼

[@lamiyakhokon890]

we are literally blessed with your existence :)

[@TheGCSEMathsTutor]

Haha thank you so much for your kind words 😁🙏🏼🙏🏼

[@amadif1793]

Very helpful! I have a test on this coming up

[@TheGCSEMathsTutor]

Hope it goes ok! Are you feeling confident? 😁🤞🏼🤞🏼

[@amadif1793]

@@TheGCSEMathsTutor Yes I understand it well as it's mostly similar to GCSE, I just have to do some more exam questions to get it nailed down

[@TheGCSEMathsTutor]

@@amadif1793 amazing news and yes absolutely! The more exam practice the better! Glad to hear this ones helped you 😁🙏🏼

[@amadif1793]

6 months later and I'm back watching this video for revision! I've finished the whole AS course and I'm very confident for mocks thanks to your videos. Keep it up!!

[@amadif1793]

Another 8 months later... revising for my Y13 mock 😅

[@a.a1061]

my god thank you so much. i was actually clueless in class this past month. why are my alevel teachers so crap 😭

[@ellasorchid]

how is it?

[@some-hc9pg]

Hi I did my gcses this year and achieved a grade 8 after watching lots of your videos which were very helpful and easy to undrerstand. I hope you will make a level videos and would appreciate if you make AS maths videos but in more detail of each topic.

[@Fawad_Ahmed598]

love the pfp

[@Maryam4726-l9p]

This is so helpful. I can't even explain how this video has saved me ....

[@nathanhawey294]

smashed it. hopefully graph inequality soon. next week is October exam

[@TheGCSEMathsTutor]

Thank you!! That’s one of the next on my list! 😁🤞🏼🤞🏼

[@yuriandcats]

thank you so much i have a test tomorrow on quadratics this really helped

[@ms12earth]

I have a semester exam in 4 days and this really helped, thank you soo much

[@TheGCSEMathsTutor]

So glad to hear it 😁🙏🏼🙏🏼

[@aguy165]

Hello sir, good to have you back, can you please post videos on the following topics: Trigonometry ( trigonometric equations and identities) and the other 3 trigonometric functions Permutations and combinations Circular measure More videos on vectors (vector geometry, constant velocity problems involving vectors) More calculus videos (optimization problems, the chain rule, product rule, quotient rule, rates of change, integration by substitution, integration by parts, integration by trigonometric substitution, and application of calculus in kinematics) Solving cubics if you haven’t posted a video about it already Solving equations of the type |ax-b|=|cx-d| Geometric and arithmetic progressions, and infinite geometric progressions Converting from a non linear equation to linear form, converting linear equations into non linear form and finding relationships from data. And some videos on complex numbers and more on calculus. Thank you.

[@TheGCSEMathsTutor]

They’re all coming! Some I have done such as solving cubics, this can be found within the factor theorem video in the a-level playlist here: kzbin.info/www/bejne/rJ-UmYd3asadlc0 I’ll do my best with all of them! Keep an eye out 😁🙏🏼

[@jbjxc]

hi sir you made me go from a grade 3 to 8 in gcses thank you!!

[@omacc11]

Thank you got a test tomorrow and wasn’t feeling confident

[@rosegold2072]

You are amazing, thanks for all the content 😁

[@TheGCSEMathsTutor]

Thank you so much! Glad you like it, any topics in particular you’d like to see next? 😁

[@GCSEALevelMaths2025]

Very helpful sir good job!!

[@TheGCSEMathsTutor]

Thank you 😁🙏🏼

[@indiebreez5265]

I love you I love you so much you are the best teacher no emphasis you really know how to do your job you inspire me in many ways thank u for a level content squeezes you

[@TheGCSEMathsTutor]

So glad to hear that! Thank you so much for the kind words, are you currently doing your as level? How are you finding it? 😁🙏🏼

[@indiebreez5265]

@@TheGCSEMathsTutor GRRRRRR I HAVE AN EXAM ON QUADRATICS TOMORROW CRAMMING LAST MOMENT BUT GHHHHHH I JUST LOVE U I FOUND U WHILE DOINGS MY IGCSES AND HAVENT SHUT UP ABOUT U EVER SINCE SO SWAGGY OF YOU ON GOD

[@TheGCSEMathsTutor]

@@indiebreez5265 aaaaaah I hope your exam went well? 🤞🏼 so glad to hear the channel has helped and thanks for sharing it and telling others it’s really appreciated 😁🙏🏼🙏🏼

[@QuaternionPhysics1]

Could you make a video on stretching graphs? Thank you so much for your help! :)

[@TheGCSEMathsTutor]

Graph transformations I’ve done here: kzbin.info/www/bejne/sJOwoHeBi8-ti68 or are you looking for more advanced questions? 😁🙏🏼

[@QuaternionPhysics1]

@@TheGCSEMathsTutor yes, mainly questions where you are given a graph y = f(x) which is a cubic or quartic, and to sketch the graph y = 2f(x) and y = f(3x) and sometimes both scale factors for x and y :)

[@thearmchairanarchist9403]

Thank you so much sir,for your wonderful videos. Please keep uploading,you make everything seem easier and understandable!!! I'm sorry but at 6:23 ,11- the square root of 277 divided by 6.I got the answer -0.94.

[@TheGCSEMathsTutor]

Thank you so much for the kind words and well spotted! I must have pressed the wrong butting whilst I was recording, serves me right for answering questions live and not doing them first 🤣🤦🏽

[@thearmchairanarchist9403]

@@TheGCSEMathsTutor No problem, sir.It is easily done.I really infinitely appreciate your effort and time you put into making these videos as they are wonderful. My stress levels always decrease when I watch your videos.

[@abdulraheemhabeeb6921]

Nice! Circles is a bit tricky as well hopefully you cover them

[@TheGCSEMathsTutor]

I’ll be covering everything this year so keep an eye out 😁👍🏼

[@Mathspaperks1ks2]

Great job

[@TheGCSEMathsTutor]

Thank you 😁🙏🏼🙏🏼

[@johnkhan9579]

I really lovc these videos. You explain the steps so well, I was just wondering about the answers (timestamp 6:00), where the question asks for 3 significant figures, as opposed to rounded. So, the solutions would be 4.60 and 1.58. Or maybe I am wrong.

[@musa2908]

its -0.941 for the second value

[@isit6193]

Could you cover the whole of the AQA spec for year 1 A level maths😅your vids are the only thing saving my grades🙏🙏🙏Have you done a vid on straight line graphs and surds etc?

[@TheGCSEMathsTutor]

I will be doing them all as fast as I possibly can!! 🙏🏼🙏🏼 I’ve covered both of those topics at GCSE level right up to to what’s needed at A-Level, for example surds here: kzbin.info/www/bejne/n6mmnYl7g9aNbK8 and SLG’s here: kzbin.info/www/bejne/hZaWnIupoJiJjdk 😁🙏🏼

[@najeebaamin]

Thank you 🌹🌹🌹🌹🌹

[@TheGCSEMathsTutor]

My pleasure 😁🙏🏼🙏🏼

[@kings-Rex]

Thanks! Really handy

[@Yamesy]

Thank you !

[@nabilshahfiee3618]

Thank you sir!

[@Imnotjia.1]

The second solution to the first quadratic formula question I believe is incorrect, it should be -0.94 not 1.59 😊

[@Deadman2DX]

I was so confused when I worked it out I thought my calculator was on the wrong setting 😂

[@Sami-vd3co]

great video, please correct me if im wrong but i believe the answer to question 2 is wrong 3x^2 - 11x - 13 = 0 x = 4.61 or -0.91 ( NOT -1.59 )

[@Deadman2DX]

Yh that’s correct maybe he missclicked

[@cassie0736]

isnt it suppose to be -0.94 for the minus part 6:47

[@muhammadabdulhakeem7152]

@TheGCSEMathsTutor At 6:23 I must have pressed the wrong button whilst recording as the second solution is -0.941 and not -1.59 😬 whoops!

[@Charlotte-zi1fd]

Thanks this is really helpful

[@dusk3315]

Hi Sir. Thankyou very much for this amazing video. Very well explained, great job! However, I was wondering if you could make a video re. examples of the Quadratic formula where you do the working out to show the answer. I have noticed that no tutors explain as well as you do. And, rectangle word problems with area and quadratic equations is something I'm struggling with at the moment. For example, A rectangular field is 15m longer than it is wide. The area of the field is 800m². Work out the length of the field. Give your answer to 1 decimal place. If it is possible, would you be able to help me out with this? Thank you Sir for your time. 🙂🙏👍

[@TheGCSEMathsTutor]

Aaaah yes forming and solving quadratic equations would certainly be a good one! I’ve just added it to the list for you 😁 what do you mean by the first one? Where you show the working out, do you mean doing the quadratic formula without a calculator and leaving it in surd form? 😁🙏🏼

[@dusk3315]

@@TheGCSEMathsTutor Thanks for your reply Sir and thank you very much for considering this. I mean that perhaps you could solve some word problems in the video so we can see how you do it and then have a go too. Preferably, exam style questions and if possible, at GCSE level since I haven't yet reached A level studies. Thanks again for your reply. Great to know we have the best Maths tutor to help us out! 😃👍

[@shainyshafi8024]

Amazing!!!!

[@antisocialbarbie1587]

Please start uploading p3 and p4 from this year

[@eth9293]

i am loving this a level content, will set notation be soon?

[@TheGCSEMathsTutor]

Amazing news I’m glad you like it! It’s not part of my next chapter of videos but I can add it onto my to-do list as I like to do a few different ones when I can find some spare time 😁🙏🏼

[@eth9293]

@@TheGCSEMathsTutor my teacher explained it but i am still unconfident so a video would be great! thank you so much 😊

[@asmaa1853]

Thank you

[@ewanjoseph5187]

Just curious, at 25:44 you write that p=-2, however, I though you would do x-2=0, and actually find p=2. Have I made an error in this case?

[@airplanevibes9475]

Sir thankyou for the amazing video. Can u also share the link to the video about quadratic inequalities topic since they are not in this vid, thankyou very much

[@AwesomeJL]

thank you very much for this, can i ask what app you use to make these videos and draw your solutions over the questions?

[@TheGCSEMathsTutor]

Thank you for the kind words! I use notability 😁🙏🏼🙏🏼

[@izzya9807]

How is the answer for number 2 on the quadratics equation bit -1.59 it’s coming up on my calculator as -0.94

[@rifannizar8629]

can you please explain how you sketched the graph

[@Ghost-fh3lg]

23:45 imma come back to this whenever ig

[@mubinaabdullah9405]

At 23:19 can you explain how the circled areas in the graph are related to the square root of eight

[@ramens]

Thanks a lot

[@AditiGupta-k9f]

very useful !! thank you but no hate - completing square could have been explained more clearer but really helpful ;)

[@paawanjotkaur1901]

👍🔥

[@TheGCSEMathsTutor]

😁😁

[@BobBob-uv9fq]

Not taught scenarios ,but then there are questions in the exam

[@hbrarianf1853]

This is a level? I’m doing this in year 11 ?!

[@TheGCSEMathsTutor]

Some of it crosses over with the GCSE 😁👍🏼

[@isit6193]

It's Right at the beginning of a level maths where you cover GCSE content just a bit more in depth u think

[@EricLee0217]

Hello, sir, may i ask you a question that the examples in the video are the most basic ones or as difficult as the questions in the exam

[@JamieKing-wn1qm]

Hey, one thing im a bit unsure of is am i allowed to just type in the quadratic into my calculator to solve rarther than using the quadratic formula?

[@EmpoliBridget]

Sir help me in solving equations by quadratic equation

[@II_official448]

hello sir PLEASE PLEASE DO STATISTICS AND MECHANICS FOR A LEVEL IM BEGGING YOU PLEASE FIND SOME TIME TO MAKE THEM I DONT WANT TO FAIL PLSSSSSSSS YOUR SUCH A GOOD TEACHER

[@tejeshvararunkumar9411]

How do you make your own quadratic equation when it gives you the values for the roots and the turning point? I can't find the answer for this anywhere

[@TheGCSEMathsTutor]

If you were given the roots - say x=3 and x=-2 then you know the factorised form would be (x-3)(x+2)=0 expand and simplify and there you go 😁👍🏼

[@haroldchukwurah9199]

How come our turning point is +2 when it's minus in the bracket

[@TheGCSEMathsTutor]

My video on completing the square in the algebra GCSE playlist would explain this better than a comment! It’s somewhat similar to the sign reversal when solving quadratics if that helps 😁🙏🏼

[@AshBeastFPS]

hey, are functions included?

[@TheGCSEMathsTutor]

Only in their notation! 😁🙏🏼

[@aishajamal1307]

how are you supposed to know when to complete the square or use quadratic formula?

[@Chad4Life]

Specified in question, or else u have a choice.

[@AlishaLamba-x7p]

great vid! answer at 6:21 is wrong though

[@mallikaamarasekara7844]

Sir how did you get the negative answer for the 2nd question?please explain it. 6:38

[@Deadman2DX]

I doubt he would reply but to answer that you probs forgot the brackets around -11 which means you did 11 squared; so 11 times 11 then made it negative - rather than -11 times -11 which would change your whole answer 👍

[@rifannizar8629]

cant we just to differentiation to find the turning points

[@mariafarah7688]

is this for CIE?

[@Pillow_pill]

I really don’t understand where did the 12 come from in the 11:06 i am confused

[@zzuww]

bc when u move the 24 to the other side, the brackets is being multiplied by 2, so to get the brackets on its on, u do the opposite and divide the 2 onto the other side, so the 24 becomes 12

[@Pillow_pill]

@@zzuww oh i got it thanks

[@Oscar-jt5rq]

that quiet background music carried my attention for some reason

[@TheGCSEMathsTutor]

Very interesting! Some people really disliked it and I’ve since removed it, I always find it helps with my concentration but others seemed to disagree!

[@nathanhawey294]

First

[@TheGCSEMathsTutor]

Legend 🥇🥇🥇

[@TheGCSEMathsTutor]

👑 Everything you Need to Pass your AS Pure Maths Exam! A* | AS Pure Maths Revision | Edexcel AQA & OCR - kzbin.info/www/bejne/i5quh3Wpna6CrJY

[@thedoorofspirituality1210]

I think the negative answer for 6:35 is wrong

[@aswinkrishna9297]

Dear Sir, Your 2nd Questions answer is incorrect! the value is -0.94055 [-0.941 (3 s.f)] Please do check on it!

[@Yamesy]

he did, pinned comment

[@BukharinStan]

wow i am COOKED for a level

[@Deadman2DX]

A lot of time still

[@bilqisazwa]

24:07

[@lindsaygabrielle3218]

16:44

[@undercaffeine]

13:15

[@BobBob-uv9fq]

Still think the owl should be smiling

[@mohammedk2054]

i failed bcs of you

[@Wolfiewyd]

Wym

[@anotidachigwada9315]

thank you