The 5 Hardest Indices Exam Questions | Grade 7-9 Series | GCSE Maths Tutor
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- Опубликовано: 5 фев 2025
- A video revising the techniques and strategies for completing 5 of the hardest questions on indices - Higher only (Grade 7-9)
This video is part of the Number module in GCSE maths, see my other videos below to continue with the series focussed on indices.
Useful videos to watch before this one:
Negative and Fractional Indices - Part 2 (Higher & Foundation) | GCSE Maths Tutor - • Negative and Fractiona...
Negative and Fractional Indices (Higher Only) | GCSE Maths Tutor - • Negative and Fractiona...
These are the calculators that I recommend 💎
Casio fx-83GTX Scientific Calculator, Black - amzn.to/2P2cyGG
Casio Fx-991ex Scientific Calculator Fx 991 Ex - New + 552 Function - Classwiz - amzn.to/2sw2Moz
These are the new revision guides I recommend 💡
Higher - New Grade 9-1 GCSE Maths Edexcel Student Book - Higher (with Online Edition) (CGP GCSE Maths 9-1 Revision) - amzn.to/366PltG
Foundation - New Grade 9-1 GCSE Maths Edexcel Student Book - Foundation (with Online Edition) (CGP GCSE Maths 9-1 Revision) - amzn.to/2PpbjBF
Revision videos:
The Entire GCSE in Only 2 Hours!! Higher and Foundation Revision | GCSE Maths Tutor - • Everything You Need To...
Everything for a Grade 6-9 in your GCSE Maths Exam! Higher Maths Exam Revision | GCSE Maths Tutor - • Everything for a Grade...
The 10 Hardest GCSE Maths Questions & How to Solve Them | Grade 9 Maths Series | GCSE Maths Tutor - • The 10 Hardest GCSE Ma...
More videos in the Number series:
All of Number in Less Than 1 Hour!! Foundation & Higher Grades 4-9 Maths Revision - • All of Number in Less ...
Part 1 - Multiplying Decimals - • Multiplying Decimals (...
Part 2 - Product of Prime Factors - • Product of Prime Facto...
Part 3 - Highest Common Factor (HCF) - • Highest Common Factor ...
Part 4 - Lowest Common Multiple (LCM) - • Lowest Common Multiple...
Part 5 - Laws of Indices - • Laws of Indices - Part...
Part 6 - Fractional and Negative Indices - • Negative and Fractiona...
Part 7 - Fractional and Negative Indices (Higher Only) - • Negative and Fractiona...
Part 8 - Standard Form Conversions - • Standard Form Conversi...
Part 9 - Standard Form Calculations - • Standard Form Calculat...
Part 10 - Recurring Decimals (Higher Only) - • Writing Recurring Deci...
Part 11 - Fraction Calculations with Mixed Numbers - • Fraction Calculations ...
Part 12 - The Product Rule for Counting (Higher Only) - • The Product Rule for C...
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Thank you so much. I'm really trying to turn myself around in all subjects this year. unfortunately, it's so close to my GCSE'S now, only a few months away and it's really stressful and scary since I never even tried in my previous years. I find these videos so useful, and I really appreciate what you're doing, so from the bottom of my heart, thank you so much. You're changing my life
Gabsone Saneee!! I did nothing in the previous years I regret it so bad.
@@Rafmee I personally think your in an alright position... cause i frequently see people that study 2 weeks before the exam
how coincidencial is that, im in the exact same situation :3
howd you do
@@samsolo-os9ie I did good actually, I got a 6 (I live in the UK) which is equivalent to a US grade B or something. (Idk where you live)
give this man a raise
you're saving my GCSEs! thank you.
That’s so great to hear that the channel is having a positive impact! Keep up the great work!! 😁🙏🏼
there's actually an easier way to calculate b in the last question. if you know that 9= 3^2, and square root of 3 =3^1/2, that means 3^2 x 3^1/2, then you can just add the powers to get 3^2.5
You’re right! This method is much simpler and makes much more sense ( at least to me), thought process wise.
ur a genius
wow thanks so much!
omg thats what i did
i did that too i couldn't do all the other ones by myself but i somehow did the last question onmy own
Thank u so much sir for all ur help i am year 11 and due to your awesome videos in my mocks i moved from a grade 4 to grade 7. THANK YOU
so proud of you x
Thank you so much for all the effort you’re putting into these fantastic and really helpful videos. Because of you I was able to go from a 6 in November to a 9 in the February mocks. Thank you!!!
Tom WOW that is spectacular!!! That is serious progress well done! 🙏🏼 make sure you keep up the great work now to maintain it but hats off to you that is incredible! Thank you for the kind words 😁🙏🏼
how did you revise please help!
i wish i'd have revised more from november to now so I could've improved more
I always got these wrong on tests but I finally get them!!! These are still really difficult though 😬 Thank you again for another brilliant video
James Chester Great news! These are certainly very difficult questions though! Keep up the great work 😁🙏🏼
mol da
Thanks for this sir I went from a 5 in September to getting 8s in a lot of my tests now
what did u get in ur gcses
@@dilpreetnagra8097 lol good question
well done im proud of you
nah if my teacher gives us these questions in my maths test on monday im gonna CRY. congrats on 60.5k subscribers by the way!!
The really low and calm piano in the background actually helps a lot
Really love the calm intro and overall explanation can not be underestimated.
Keep it up!!!
Amazing I’m glad you like it as it took me ages to make!! Great to hear it’s all working out so well for you! I will do my best 😁🙏🏼
@@TheGCSEMathsTutor who doesn't love that intro?
I think the whole approach of calmness is a part of the key. It says - "Look Sticky Question coming up - these are the tools to crack it open and have it gurgling happily on your lap. It's just like changing nappies!" Thank you TGMT
17:45
for anyone who doesn't understand his method of finding out b, i know an easier way.
since we know that sqrt(3) is the same as 3^1/2 and 9 si the same as 3^2, we can write it as 3^b= 3^2 * 3^1/2
now its much eaasier since we can just cut out the two 3's and add the powers and we get 2+1/2 which equals 5/2
so the answer would be b=5/2
well I hope this helped. have a good day
how does 2 + 1/2 = 5/2 or have u just done 2 denominator times by the 2 and then added 1?
@@anyonymous9145 idk
you are a literal lifesaver thank you so much for this video
My pleasure! Just glad it’s helpful 😁🙏🏼
Because of you I survived my maths exams, amazing videos keep it up!
You made a meal of that last question. I converted 9 to (3 to the power of 2) then x (3 to the power of 1/2) , so add indices to get 2+ 1/2, therefore b = 5/2. Thanks for your clear instructions on the rules to enable me to do that 😀
rewatched this 2 times first was to understand, second to practise the question. i have a test for mock preparation tomorrow
This channel could give me the grades I want for maths as I struggle with it a lot thank you so much 🤝🤝
Khan channel Fantastic! I certainly hope it will 😁🙏🏼
@@TheGCSEMathsTutor also Maths tutor i would also like to ask what other way should I revsie for maths other than using your marvellous videos
Khan channel I would focus on past papers, identify topics you don’t know yet and then target these with the videos, and when you do watch a video, make a revision card, keep your notes in order with titles, keep them filed, make a revision pack from them! There is so much you can do using a video beyond just watching them that will benefit you to no end! I may try and make a video on this soon 😁🙏🏼
@@TheGCSEMathsTutor thank you ever so much for this advice means a lot if I have any questions may I put it on here sir🤝🤝
Khan channel Absolutely! I will always do my best to help 😁🙏🏼
this man is a genius
Haha thank you for the kind words 😁🙏🏼
@@TheGCSEMathsTutor please you deserve it you've literally been a saviour for so many students around the world!! I just wanted to ask if you'll start making videos for further math content?
@@oliviaaa2324 thank you so much I’m so glad to hear that! I’m just finishing the last few videos for the GCSE course and then I’ll be moving onto the next stages of the AS pure content 🙏🏼🙏🏼
thank you Olivia
@@parthjain29 ur welcome parth
I love everything about the format of your videos. Your subtle explanations, the gentle justifications of your answers and to mention.. the peaceful music in the background.
i remember getting the question at 14:05 on a practice paper, it hurt my head so much lmao, i thought it was meant to be an easy one, but realised its actually quite annoying for others as well.
and all i needed was the methods you taught in the video, which was like 2 minutes of my time. Thank you very much sir!
There is a quicker solution to question at 19 minutes. Note that 3^(a+b+c) is the result of the multiplication of the three given terms. When you multiply the 3 terms they all cancel so 3^(a+b+c) =1. Hence a+b+c = 0 (because 3^0 = 1)
Very well spotted and you’re absolutely right, I wonder how complex this would be however if they didn’t sum to 1. The method I’ve applied here would ensure marks were collected on an exam paper no matter the numbers in question but you’re method is definitely a viable alternative! Also, very well explained via a RUclips comment so I take my hat off to you 😁👏🏼👏🏼
Looking at these questions hurts my head
Last question can be done more simpler using formula
3 power a * 3 power b * 3 power c = 3 power a+b+c
3 power a * 3 power b * 3 power c = 1/9 * 9*sqrt(3) * 1/sqrt(3)
=> 3 power a+b+c = 1
=> 3 power a+b+c = 3 power 0
=> a+b+c=0
There's a much easier way to find what b is on the last question. Separate the 9 and sqrt(3) and make them both 3 to the power of something. So 3^1/2 = sqrt(3) and 3^3 = 9. They are both multiplying together so (3^1/2 x 3^2). Then add the powers and you get 3^5/2 so b =5/2.
Love it! 😁🙏🏼🙏🏼
tyyy!!
thank u smm
i moved up a set because of you. Thanks
i am now top set!!!!
Wow!!! Fully smashed it 👏🏼👏🏼 well done!! Keep it up now that’s amazing news 🥳
@@TheGCSEMathsTutor thanks
thank you soo much im aiming for an 8 at igcse and youve helped go from a 5 to a 7/8. Thanks you
penois spagetti
for the question on 10:36 can you 3-n = 1/3n which equals 0.2 and 0.2 is 2/10 which is 1/5 so then u flip 1/5 to get 5 which gets of the negative?
Omg I would struggle so much with these questions in my mocks u made it soo easy thanks so much !
mok
how did your exams go in the end ? :)
mok wok mok
mok wok
wok mok
The second last one was way harder than the last. Working in powers of root3 made it way more complicated than necessary. Still great video as always
Glad to hear you found the last one ok! Always like to hear different methods did you do it in a different way? 😁🙏🏼
TO BE HONEST YOU GOT A BEST TEACHING SKILLS EVER! THANK YOU SO MUCH MY BESTFRIEND AND I HOPE I'LL GET A 1ST RANK BY WATCHING YOUR VEDIOS IN'SHA'AALAH😁🦋
So glad to hear I could help 😁🙏🏼
Many thanks. With the last question, I thought it was just testing your knowledge of indices rules, i.e 3a x 3b x 3c = 3a+b+c. So you multiply the 3 together and as the 9s and root 3 cancel, it works out as 1. And if 3 a+b+c = 1, then a + b - c must = 0 because any number to the power of 0 =1
the last question is very funny.....after all that working and get 0
i hate when that happens it feels like i wasted my time 😭
Thank you so much for the video please keep uploading you make my study life so much easier please upload more i really appreciate it like it makes so much easier for me to understand then learning from my teacher
Amazing to hear! I will do my best for you and thank you for the kind words, it’s great to hear that the channel is working out so well for you! 😁🙏🏼
All ques were easy thank u
Well done! 😁💪🏼
i cant seem to find any practice worksheets online for this. can you make some or let me know if there are any? found this video very useful!!!!!!
thanks
quite handy stuff
So glad it helped! 😁🙏🏼
at 9:15 it says 2 to the powr of blah multiply 2 to power of blah but its rearranged itno addition? i thpught that if you were to rearrange it itd be division
wow i actually understood something in maths, that felt strange!
The last one was much easier than I think but it was tricky rather than difficult
I got all 5 right!!!! Anyway thanks for the somewhat challenging questions, this is a definite exam booster prep for my next week End Of Years
When u relies this man can teach better then ur teacher
I'm starting to find these easy thank you very much
isis is bad 123456789
10 moth a go a fly losd
I did all of them easily but the last was interesting. BTW, what are you using to write?
Glad to hear it! I use an Apple Pencil or another stylus depending on which device I’m using 😁🙏🏼
I regret not doing anything in the past years because it’s my exam year now and I can’t pull myself back up in lesson cos of corona and now where I live they are doing teacher assessed grades and all my teachers think I’m dumb. No hope, honestly. :p
hahaa what exams.. other than the boat load of topic tests they're giving us instead now... what exams??😁😂😂
@@khadija2625 I just did a set of mock exams and doing another set in 2 weeks
@@ytfresh4741 ouch
woah, i get through this video and realized indices is really that hard omg
Hope you’ve managed to figure it all out 😁🙏🏽
Sir just wondering for the last question and for calculating b what are the indications that show we need to keep multiplying the root 3's because I dont understand how you would realise to use that in an exam
These videos are excellent ....on this one you may find an easier way to think about it to be.....write the product of the rhs of each equation to be equal to 3 to power x...simplify to give 1 equals 3 to power x.....or, alternatively, write each term as base 3 and solve the equation of the powers by adding
Just think it this way 9=3^2
And √3=3^1/2 the base is same so when u multiply the base u add the powers hence 3^2+1/2=3^5/2
does 13:33 come up in a calc paper or non calc?
16:54 what the hell are you doing, there is a much easier way, 9√3 = 3^2 x 3^1/2 = 3^5/2 from adding powers
kinda off topic but what ipad do you use because i want a similar one with good value for note taking
also thanks for ending my procrastination as soon as i saw this vid i grabbed my textbook and started practicing
Amazing news! Glad this video gave you that last kick you needed 👏🏼 I use both an iPad Air and an iPad Pro, I’d say the air is perfectly fine for note taking but I teach all my lessons in the classroom via an iPad Pro and it’s far superior to the air for intensive use, hope that helps 😁🙏🏼
@@TheGCSEMathsTutor yeah if I get a lot of 9s in gcss inshallah parents will get me ipad pro as I heard its helpful for medical school and a levels
And it just looks so satisfying that I can literally go through a past paper without printing (correct me if I'm wrong)
@@cali5635 it’s so useful for that! You can’t beat it.. now you just need to get those 9’s 😁🤞🏼🤞🏼
Thanks for making these mate, they help me so much considering I have a mock on Monday and another at some point in the week. Do you recommend any ways to remember certain things/ any revision strategies?
Active recall for sciences and any humanity. What i mean by this is take a look at your specification and then make the requirements into questions for you flashcards (i recommend anki its WAYY better then quizlet and it uses active recall!) for example students must know the definition of active transport. using bbc bitesize or a revision book (both are great tbh) make an answer to that question and revise that deck of flashcards for 7 days after that search up topic questions (gcse biology movement in cells or gcse physics energy past paper questions) and some lovely people on the internet would have already compiled it for you!
For maths i would recommend doing questions from a topic like algebra from corbett maths or maths genie and then the questions you got wrong or werent able to get at all just search it up on youtube like fractional indices gcse maths and you will get lots of vids doing examples and giving you questions to do at the end. Hopes this helps xx
Great video
Thank you! These were tough… how did you find them? 😁
@@TheGCSEMathsTutor yeah they were difficult so I hope they don't come on my test. But I will watch again and understand it better each time. Thanks!
@@skykingtenz1232 great idea! And then you’ll be hoping it does come up on the test… hopefully! 🙏🏼🙏🏼
is there an easier method to find c in the last question? i'm still a bit confused
Holyyy these are hard 😅😅 but practise makes perfect
Is there anywhere to practice these questions online?
Do you have any practice questions similar to these so we can practice further our understanding?
I did it this way before I saw your answer - does it still work?
3^2x=1/81
3^2x=1/3^4
3^2x=3^-4
(cancel out 3's)
2x=-4
x=-2
Do you do any other subjects apart from maths?
for the last one, just treat the 9root3 as two separate terms so 9 times root three
That zero though
Idk why, but I found the last one quite easy
Always a nice moment when you get the hardest one right? 😁👍🏼👍🏼
hi, what year do you aim these videos at? i'm year 9 and i was wondering if these are the sort of questions that i should be aiming to be at already?
Year 9 onwards! I mean.. a lot of year 9 students may not see questions this tough, but I'd teach these for the first time to year 9 and revisit them again in year 11!
@@TheGCSEMathsTutor Thank you!
All right only last one a liitle tine mjsyake
I do wish you put the amount of marks each question would be worth. I there any chance you Could put their marks in the description ??
It’s unlikely I’ll have time and unless they are from an exact paper any marks would only be estimates of which they will all be 2-3 marks! I don’t tend to teach using marks in a classroom so it’s not something I’d probably plan to incorporate into a video 😁🙏🏼
Can you please help me solve this question step by step. 9( to the power of minus one half)= 27(to the power of one fourth) divided by 3(to the power of x+1)
9^-1/2 is equal to 3^-1. 27^1/4 is equal to 3^3/4. Because 27^1/4 is being divided on the right side, we multiply it on both sides.
9^-1/2 x 27^1/4 = 3^x+1
However we know what 9 and 27 is to the base of 3 so we rewrite it as,
3^-1 x 3^3/4 = 3^x+1
Its multiplication so the powers add to x+1,
-1 + 3/4 = x+1
-1/4 = x+1
x = -5/4
would these be on a non-calc? - thanks
It could be on either 😁🙏🏼
Very useful sir great job!! I’m nearly at 1000 subscribers!!
INCredibke thast very ainm pressuve!!!
iamn bvery jeouloyus
the math is mathing a bit too much
hello, I have been trying to find out this question 9260=5nx7x11
find the value of n
Any Help
thats really easy..
u do 9260/77=120.26 and then 120.26/5=n = 24.05 i think...
you multiply 5n x 7 x 11 = 385n. Then you divide 385n/385 = 1n and on the other side 9260385 = 24.05 THEREFORE n = 24.05. hope this helped
@@irc7504 🥇
can any1 please tell me which paper did the last one come in. like which year
thank you
For the last question I just did 3^2 x 3^1/2, which is just 2 + 0.5
Sup 2023 gang
dose anyone know where to find practice questions about this topic?
Hi how do you know if it’s a negative or not could you please explain?
Could you explain further? Possibly time stamp the moment you are referring to 😁🙏🏼
for the first question, could I use the log button on my calculator and still get full marks?
How would you do that x
I didn't understand why it is 3 to the power of - 4 2:41
I need more explanation on this
when ur video ends its so saddening :( no more challenging questions
Ahhh glad to hear you enjoy them! Lots more in the series though 😁🤞🏼🤞🏼
are GCSE cancelled or just delayed ?
At the moment it’s very uncertain and I don’t want to speculate, I will update on the channel when we have concrete information 🙏🏼🙏🏼
Nice video
Turbiyo Thank you 😁🙏🏼
how many marks is the last one?
I’m confused by the second one. With your workings out you got 300 but double checking this on a calculator it says the answer is 360,000
👌
.2=2/10then next step which equals to 5 so we cross multiply in this equation so we get 3^n=5😅
👍🏽👍🏽👍🏽👍🏽
aaron janjuha 😁🙏🏼🙏🏼🙏🏼
10:25
lol i have to learn this in grade 6
I will never understand that
why isnt b= 9/2, why 5/2- HELP
He did it by seeing how many times you need to multiply it in order to get sqrt(-3) * 9.
But you can also just do 3^1/2 * 3^2 and get 2.5,
This is super difficult 😓
try to be more clear in your speaking and explanation. Not everyone is capable of understanding a British accent
Sorry that you are struggling to understand my accent. This is the first comment that has ever mentioned this out of tens of thousands of comments so I’m quite shocked as my clarity of speaking is one of my primary goals on the channel, but my only advice to fix this would be to turn on the captions so that you have subtitles, I hope this helps! 😁🙏🏼
i already did my gcses but reviewing these for a levels. these suck
Bruh
The 2nd is disgusting.
I'm living in an Asian country and it's both funny and heartbreaking that he's calling those easy questions nasty 🥲🥲🥲 feels like our maths is over complicated...