The 5 Hardest Surds Questions | Grade 7-9 Maths Series | GCSE Maths Tutor

A video revising the techniques and strategies for answering some of the hardest surds questions. (Higher Only)
Don’t forget to check out the rest of the surds series below!
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🔹 Watch the video
🔹 Make notes
🔹 Practice the questions
🔹 Mark your work
🔹 Review what you have learnt on the exam questions
Part 1 - Simplifying Surds - kzbin.info/www/bejne/qHmsk52Mdqqeq9E
Part 2 - Adding and Subtracting Surds - kzbin.info/www/bejne/gIPSnJKmp8xgbdk
Part 3 - Multiplying Surds - kzbin.info/www/bejne/n5zdmqWnotNnnMU
Part 4 - Expanding Double Brackets - kzbin.info/www/bejne/n5i7h5uuoJJ8e68
Part 5 - Rationalising the Denominator 1 - kzbin.info/www/bejne/h4ebhZmAiNamjJo
Part 6 - Rationalising the Denominator 2 - kzbin.info/www/bejne/n6mmnYl7g9aNbK8
Part 7 - The 5 Hardest Surds Exam Questions - kzbin.info/www/bejne/qYDUo3-nZsh5eJY
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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! 😁🙏🏼

[@loveyourself8458]

@Justin Takehara LOL

[@fatimaahmad3681]

@Justin Takehara why are these comments everywhere

[@mfz2856]

if i somehow get a 7 then okay

[@3mkmedo176]

Ight bro lemme get a 7 or 8 first

[@5kinz]

if i get an 8 then ill buy u 10 coffees

[@KK-mk8xb]

these type of videos are the best ones! love the 7-9 maths series, so helpful

[@TheGCSEMathsTutor]

That’s so great to hear! I will try and do at least one of these per week for you 😁🙏🏼

[@rottinqangel]

these questions humbled me💀

[@wishcom69]

I don't care

[@rottinqangel]

@@wishcom69 i dont care that u dont care

[@nadiyai7092]

Same 😂

[@al3j_ndr053]

@@wishcom69wrd

[@AppleApple-ux1be]

It’s the fun part of maths whilst simultaneously scaring me because I can’t do it.

[@tpr1808]

With this guy I don't think we can call these questions hard anymore

[@TheGCSEMathsTutor]

Thanks for the kind words 😁🙏🏼

[@AppleApple-ux1be]

@@TheGCSEMathsTutor I have to disagree. Obviously your videos are great but the more I watch, the more I realise how less I know. They sure do help though.

[@adhalex4778]

This man has helped me so much. I can’t thank you enough. My grades have skyrocketed as a result of this channel. You are incredible!!

[@idrk1507]

Could you do Grade 9+ videos? I.e. Questions that are so hard they’re borderline Maths A Level stuff. I say this because when you’re thrown in the deep end, the once-difficult stuff isn’t as difficult anymore

[@jamsi1066]

have you found videos like this ?

[@idrk1507]

@@jamsi1066 Oops I can’t copy-paste the TSR link. I’ll just write it now. Write on Google “TSR Grade 9 Maths Paper GCSE (and other difficult GCSE questions)- 2018 thread”

[@idrk1507]

@@jamsi1066 Bro I wrote you a massive paragraph of everything yet it disappeared 🗿

[@jamsi1066]

@@idrk1507 thank you so much !! and dw i think i can still see it is it the tsr grade 9 maths paper one ?

[@idrk1507]

@@jamsi1066 My pleasure! And no it was much longer, maybe 40 lines. I’ll rewrite it again today :)

[@sahnafthehumble7252]

Your brain is enormous

[@TheGCSEMathsTutor]

ALPHACONIC Haha thank you! 😂😂😂

[@geetikagupta315]

i really needed practice with surds so thank you so much for this

[@juliethmoreno9251]

I got the last one correct at first try and it gave me the confidence for next week exam, THANK YOU

[@hettysinclair9393]

this has saved me for tomorrow thank you sir

[@i4TheWinN]

This is great, thank you sir!

[@TheGCSEMathsTutor]

Great to hear!! Thank you 😁🙏🏼

[@cat-crewplayz952]

honestly quickfired ur surds videos watched them in 10 mins attempted these grade 9 questions gottem right thanks man

[@Kamile7899]

My only regret is not finding your channel earlier 😢

[@user-gv5rr4ds2x]

For the last question you can work out the value of x using simultaneous equations if you do the following: y = the multiplier between each term y(rootx-1)=1 and y=rootx+1 Solve via substitution and you get x=2. Then for the second part you can work out an equation for the nth term as we know the value of x we would do: (root2 +1) which is the value of y(the multiplier between terms) so nth term = n(root2 +1) +2 as you add 2 to (root2-1) to get (root2+1)

[@Mathspaperks1ks2]

Very useful sir good job keep up your amazing work sir. Thank you for your time.

[@amlanbhowmik]

For question 3, couldn't you just multiply it by 2-√2/2-√2 and get the answer by just simplifying?

[@glider5253]

That last one got me but i understood in the end, just need to recap geometric sequences

[@adili2405]

Why did you use 2 root 2 +2 instead of 2 root 2 -2 on the first question at 3.05?

[@axeleli6845]

u reverse + or - if it's more than just a surd in the denominator

[@ameliaroberts9921]

on question 2, when you rationailized it you put 11+6 root 2, but i thought it would have been timsing the numerator and denominator by -11 -6 root 2

[@user-sc6in4lm4d]

I feel relieved now sir😅.I thought surds were difficult to solve.Thank you very much

[@millazigangirova2418]

(Im gonna use / as root) I’m a bit confused on why you added ( onto the 2/2 - 2 ) 2/2 + 2 can you please explain? Also at the end you got 16/2 + 16, why did you change it to 16( 1 + /2) where did the other 16 go?

[@MAN59724]

At 9:22 , can't you multiply by 49 to get rid of the fraction so it matches the way they want it written? So can the answer be 1127+833root2 ?

[@user-we8ly2ns6c]

u could only do that if it was equal to something, when getting rid of the denominator u have to multiply on both sides of an equation

[@edenhines]

I wonder if 5b can be done using the geometric sequence formula... otherwise great video! I'm trying to revise a lot of topics in a short period of time so this video helped me a lot!

[@azrilhilmi952]

you will get in decimal ans

[@michaelmwesigwa8499]

@@azrilhilmi952 It can be done using the Geometric formula and would give the proper answer albeit it's a fairly harder method.

[@user-ot1hc8qo9t]

hi i just wanted to ask if you could write decimals instead of fractions for question 2 final answer.

[@beomgyusberry5773]

for the first question, why did you simplify the 16 down to a 1?

[@TheGCSEMathsTutor]

I was factorising 16 out to get it in the format the question wanted. So dividing them both by 16 essentially 😁🙏🏼

[@trpp9586]

I had the first question in my mock exam, it was only 3 marks..

[@robbolewis6878]

At 3:03 why do you rationalise the denominator by multiplying it by 2root2 +2 instead of 2root2 -2 like it is previously in the question. How do I know what I should be multiplying the denominator by.

[@aaron-rs8kz]

Hi in the second question how come you only did 11 x 11 and 6 root 2 x minus 6 root 2 and not 11 x 6 root 2?

[@15kcx34]

For the first question I got confused how you factorised 16root2 + 16 can anyone explain the steps ?

[@TheGCSEMathsTutor]

The same way you would factorise 16x+6=16(x+1) 😁🙏🏼

[@abcdefghijklmnopqrstuvwyxz102]

Pull out the 16, remove 16 from 16 root 2 and u get root 2. Remove 16 from 16 and u get 1. And j put them in the brackets

[@Cricketbolton]

I don’t understand at 8:55 why you don’t multiply by 49 and instead choose to split the fraction.

[@sourthakjackmcober29]

Well I am an Indian ICSE 9th grader who solved all... Maybe it's just a matter of country syllabus that I thought these questions were included in my last year's syllabus

[@ayushhongkong]

at 3.52 dont you have to multiply both terms in the bracket?

[@farah-vb4ti]

Would any of these except the first one and maybe the second one actually come up in the papers?

[@TheGCSEMathsTutor]

tia 72 No reason why not! Just depends what grade of surds question the exams decide on! 😁🙏🏼

[@farah-vb4ti]

@@TheGCSEMathsTutor thanks sir

[@adityashijikumar1131]

I had the last question come up in an assessment I did a few weeks ago so there's definitely a chance.

[@magicalbabylullabies1192]

Don't EVER second guess what questions come up!!! That is a formula for failure!!! This guy gives you all principles / rules to pass with 9 everytime. Learn the principles!! Then the exam is super easy!!

[@cheese-hf3jz]

thank you

[@INFINITY_meZza]

Great video keep it up

[@TheGCSEMathsTutor]

Thank you! I’ll do my best 😁🙏🏼

[@winger_om]

Make video about solving √(8-(√3)-(√2)+√(6+2(√3+√2+√6)))

[@mdrobinbhuiyan8824]

Thank you

[@JosephIgwe-ig8gn]

So!! Brilliant

[@sanjanakamath3655]

Thank you so much for this video! At 10:43, why do you decide to rational the fraction using just 'root 2' rather than '1+1/root 2'?

[@TheGCSEMathsTutor]

You could do either methods, the second method you mention really over complicated something that can be rationalised in a much simpler way though, this is a very unique question which is why I highlighted it in this video 😁🙏🏼🙏🏼

[@user-bq1rj8vy9g]

Last minute vibes Mock tmr 😂

[@bilalshelmani2486]

9:29 could I not just do the actual sum for this answer so actually divide 23 by 49 and divide 17 by 49 and get the answer of 0.5 + 0.35root2?

[@garrybeck216]

No, 23/49 is not 0.5

[@Gmoney-Matthew7verse21]

sir i have a question for the first surd question will you still get the correct answer even if you simplify the root 18

[@safiyyahbland553]

yeah I simplified it and still got 32 for that part

[@ELLIPTICALWR]

Hello, i dont understand the 3:50 bit sir i thought we was supposed to do the 2root2 bit times the +2 but we did +2x-2 for -4 at the end

[@yourlocalpostman]

he did a shortcut, the reason why is because if you multiply the 2root2 by the +2 and vice versa for the -2 then they cancel each other out. But of course, do expand them if you're not comfortable with doing shortcuts during an exam

[@mariamasanneh6918]

is this calc or non calc?

[@diegomandragora4327]

What is the rule to simplify a fraction which has an integer as denominator and an addition or subtraction in the numerator? Until now I thought it would only possible to simplify using a common factor if we have multiplication. It was at 5:14 btw. 🤔

[@5kinz]

rationalise

[@Salwa88324]

Which exam board is this please?

[@Ss-bt4to]

There we go, there we are!! No need to be a child!

[@amanmirza2002]

Would these types of questions be non-calculator ?

[@TheGCSEMathsTutor]

King M these are usually always non-calculator 😁🙏🏼

[@user-ok2fj1pl5s]

for the last question when he got to the fractions: 1/√ x - 1 = √ x - 1/ 1 can someone explain why he multiplied the fractions like that? timestamp of this is 8:55 and he refers to it as cross multiplying

[@Alkalosis]

for the first one I got 8(2+ square root. 2)

[@jakewatkins5202]

can you do 3d pythagoras and trigonometry?

[@TheGCSEMathsTutor]

jake watkins I have done a selection of some of the hardest questions here - kzbin.info/www/bejne/hIXCf4OLrZZplaM I am also planning on doing a few slightly slower paced videos but this should help 😁🙏🏼

[@mathsmadefun6484]

@@TheGCSEMathsTutor could you send the link to the slower paced video`s

[@imene7322]

Hi sir, I’m the first question why do we rationalise the number by multiplying it by +2 and not -2 ( 3:19 ) Thank you!

[@gtee5843]

Because with roots you have 2 answers, for example root 25 can be either -5 x -5 or 5x5. So multiplying it by the opposite sign accounts for that

[@hosamsameh3726]

17:18 why you cant simplify 8 to 2 root 2

[@bradysmudge]

thanks!

[@TheGCSEMathsTutor]

My pleasure! 😁🙏🏼

[@chefpepe283]

cant believe i was doing this in year 8..

[@williamjones1869]

will these questions be on a calculator or non-calculator test

[@MikolajSycz]

both

[@asmaa1853]

this is very useful

[@TheGCSEMathsTutor]

Glad it was helpful! 😁😁

[@maureensalama2390]

3:14 why was it 2 root 2 plus two and not minus ?

[@QuaternionPhysics1]

because you’re rationalising the denominator

[@Khaldoon.Arshad10]

Thanks

[@TheGCSEMathsTutor]

No problem 😁

[@asmaa1853]

amazing

[@TheGCSEMathsTutor]

Glad you enjoyed it! 😁🙏🏼

[@xiao7744]

Can someone explain what happened at 3:03

[@averageplayer6495]

Rationalizing... I think you should search it up on online

[@khadija2625]

who in their right mind would dislike this?!

[@saaimnaqvi8106]

Thanks for the vid, I especially enjoyed trying to work out the geometric sequence one (it was quite tough😅😂), just one question though: At 17:44, could it also just be c = a^2 d = 8 + 4a Instead of c = a^2 + 8 and d = 4a

[@samm9849]

no because a^2+(8+4a) root 2 is not the same as (a^2+8)+4a root 2. because (8+4a)root 2 = (8 root 2 +4a root 2) therefor (a^2 +8 root 2 +4 root2) is not the same as (a^2+8+4a root 2). PS. this reminds me of the questions which goes like: Saaim says "another answer is C= a^2 and D=8+4a" explain one reason Saaim could be wrong (2 marks) lol

[@nathanhawey294]

24:00 3+2 how did you get the 2

[@nathanhawey294]

i got it sorry there is always 1 before the roots

[@akirayuki5738]

Um.. okay so the second question when you had your answer the first fraction can actually cancel out leaving your answer to be um... 11÷23 + 17÷23√2

[@lilyclarke]

1:52 why is it 36?

[@adili2405]

root 18 multiplied by root 2 is root 36

[@bonnisikhag.choudhury7991]

Hey... You can use (a-b)^2 and (a+b)^2 formula... But you are just going to long multiplication ... 🙄

[@Raf-pv7mp]

Sir do these questions come often in exams? Thanks

[@TheGCSEMathsTutor]

XxUniquecornxX Quite often I’d say! But the new GCSE has only been running for a few years so we don’t have much past data to go by 😁🙏🏼

[@Raf-pv7mp]

@@TheGCSEMathsTutor Thank you sir! Someone got the virus in our school, what do you think will happen to our gcses?

[@TheGCSEMathsTutor]

XxUniquecornxX I believe they will go ahead as planned 😁🙏🏼

[@aurixiaispreppy7454]

@@Raf-pv7mp someone in my year got the virus so we had to self-isolate. at the way things are going maybe they'll get cancelled but we have mocks soon

[@nanakwame5688]

Pls I had a squared +8+8a root 2

[@quickmathswithjesse3553]

Good

[@calcpost3641]

9:32 that one was nasty

[@Mathspaperks1ks2]

This was a difficult question.

[@AjayiIsrael-th3xt]

I last question, I don't actually understand the part b

[@mustafaefe6695]

Last question💀

[@TheGCSEMathsTutor]

😬😬😬

[@akikabanu5885]

anyone got any answers to why 2 root 2 times root 2 is 4? shouldnt it be 8? since it becomes 2 root 4 then 2 times 4 is 8?

[@magicalbabylullabies1192]

No because it is 2 X root 4 (which is 2) , not 2 times 4 like you say

[@ameliaroberts9921]

i might be wrong but i think you rationalized the second question wrong

[@marvelousgamingverse7302]

Can't you say some hard questions these all are very easy

[@tanzela6366]

why is the fifth question so hard :(

[@osmani3481]

Im not sure if that question will come up but it Very crucial you know how to do it as it will 155% help when answering surds questions plus you never know exams are unpredictable at times so it good to be absoloutley prepeard.

[@ninaluv1]

Just watched one of ur other videos n this waa so easy peasy. Thank you for ur servise, truly grateful 🫡

[@safabintmd]

Many of your videos are really helpful, but it would be really helpful if you broke down the steps instead of directly writing a "simplifying" way of it. I really struggled with you directly moving on to a step instead of explaining it. Otherwise, the videos are good.

[@MikolajSycz]

watch the previous videos before going to this one as thats when he goes over the basics

[@SuperiourFNXbox]

That wasn't that bad

[@mariahoque2644]

Too hard

[@oscargodard5803]

this video makes no sense to me, he isnt even explaining why hes doing things he just doing them and expecting people to understand

[@toxicstorm5924]

Well maybe you are just a bit thick

[@iliketrainzes6522]

These ARE quoted as grade 7-9 and these are more for students that understand the topic and seek to practice or push themselves to a higher grade. If you dint understand the key concepts he has videos for them.

[@vm1429]

love gangy free ysl