The 5 Hardest Vector Questions on the Maths GCSE (Including Ratios) | Grade 9+ | GCSE Maths Tutor 

You are honestly SOOO helpful..... I don’t think I will ever be able to repay you for literally saving my life and I bet hundreds of students too. Thank thank thank thank thank you SOO much. Infinite thank you’s. We really appreciate absolutely EVERYTHING you do and you are THE best. ❤️🥺 I really can’t express how grateful I am. I wish every math teacher were like you. Keep shining like the absolute star you are sir. THANK YOUUUUUUU

NOTE: (What I'm about to say is an alternative method to 10:28 and 30:16. He uses it at 19:54, so have another look with that to freshen your mind, if needed ig) Essentially: Find two different STRAIGHT lines that hit the point "X." They should both have the same scale factor, usually given as the variable, 'k.' TIP: (Make sure to apply the same rules when determining a straight line, e.g given a line 'ABC,' find the line segment AB, then AC.) find the equivalent vector equations of the two straight lines, where using another variable may be needed --- this sets up a simultaneous equation TIP: (Generally, you'll have to find a portion of one straight line, line segment AB for example in the first tip. You'll then to find another vector equation equivalent to line segment AB. Try and see if you can form one by going on a different line [look at a point, which is a midpoint to line CD or a point that has a ratio {e.g point F located 2:3 on line CD} that somehow attaches itself to point 'X.'] TIP: (think about the two lines as two linear graphs hitting the point 'X,' easier to understand when applying the skills for simultaneous equations) Match common factors in directions (put the direction 'a' as an equation, same for direction 'b') e.g 4a - 6ak + 2bk = -4bx - ax turns to: a /// 4 - 6k = -x b /// 2k = -4x Solve for k. Finally, read the question: is it asking for: A ratio of portion (of the line) : full (line)? (e.g line ABC where AB = kAC) k can be a whole number or a fraction, depending on the ratio. [portion:full] or [full:portion] OR A ratio of [bigger/smaller] partial (of the line) : [bigger/smaller] partial (of the line)? (e.g line ABC where AB = kBC) k can be a whole number or a fraction, depending on the ratio. [big:small] or [small:big] Hope this helped clear things a bit, if you're struggling. Goodluck for the paper 2 on Monday (if your doing last min revision like me lmao) (By the way, this applies to other problems where you need to find the ratios, or if a certain line segment's vector equation is given. But, you don't necessarily need this at 37:55 as that question only relies on one line. Use this if you can find two (simultaneous) lines hitting a specific point, call it 'X' as I said, or whatever the variable is thrown at you. I'd write some more examples, but I think I've yapped too much. This trick is explored more in MathsGenie's channel. Check it out if you have that teeny tiny last minute revision left lol)

This is truly a godsend! My teacher covered the basics of vectors during online school, but never really went through how to tackle the harder vector questions and so it's one of the only questions in the paper that I lose marks from for having no clue how to do it, which is very frustrating. Thank you thank you thank you!

NGL That is by far the sickest intro for a math video especially one for the hardest topic of math. Really attracts students attention. Well done.👏

Sir what tips would you give to approaching these questions because for me it seems that every question adopts a different approach so i am finding it difficult to reliably do them correctly

finally after watching this video for the 15th time I finally got all the answers right 😭😭❤ thank you so much

why they don't give you a gold award, you helped me with a lot of topics dear.God bless you. everyone here let us encourage him for he is doing what our teachers can not do for us.

Watched you for 6 months and now, day of the exam, the road ends here. Maybe I’ll see you when I start my Maths A-Level, but until then… - Thank you. You really have been the best revision channel for any of my subjects this year so thank you! ❤ 🙏

Vectors was pretty much the only hard topic for me and the second question in the video stumped me when I did it in a past paper. After seeing this, I think I'm pretty much ready for the real thing. Thanks so much

THANK YOU! this was soooo helpful, it definitely restored my confidence in vectors! you're such a good teacher, i don't think i'd ever understand vectors without you, thank you so much!! :D

Thanks man. This is exactly what I needed. you deserve way more views

Thank you so much The GCSE Maths Tutor this has really helped me.

does anybody know why '' the coefficient of a must be 6 times greater than the coefficient of b '' at 18:06

For question 1, I think calculating CD and then comparing it to OC is easier so you get c:5/2 c in k:1 format and c = k(5/2 c) so we get 1/2.5 = 0.4

thanks!! Im doing a level maths and further maths but never leant this due to covid (i was 2021 gcse year), and was really finding a level vectors difficult. this makes it easier! edit: i did q1 a slightly different way. vector CD has to be c/k. and we know vector XC is (c-a)/2. so u can just add that and make it equal to 3c-0.5a, and solve for k. thanks again for the videos!

Hello, you see at 33:04 how you did n lots of FM, wouldnt it be n/n+1 lots of FM because it's in a ratio?

sir, In question 20 don't we need to multiply FM by n/n+1 to get FX

Great video but in the second question I don't get the part about how coefficient of a in MN is 6 times that of b in MP. a and b are different variables so why are those being compared

33:04 Why are you able to multiply it by n, when it should be multiplied by n over n+1?

watching your videos always gives me that extra confidence that I'll be able to reach the higher grades. I appreciate your work :)

I'm a bit confused with your answer 19:45 on that question. Before factorisation we have a - ka + kb - 1/2b. I chose to factorise this to a(1-k) + b(k-1/2) and you chose to do it as a(1-k) - b(1/2 - k) but when you equate the coefficients you made 1/2 positive and left behind the minus sign. I ended up with an answer of 7/4 but you got 2/5. Why did you leave behind the minus sign?

For question 20 surely you should multiply FM by n/n+1 instead of just n

so i understand the 2nd last question, but may you tell me why you do AN=xAP, is it so that you can compare the coefficient x with k? as its basically comparing coefficient of AN

Hello Sir. I am confused why for FX = it's n(2a-1/2b). I thought it had to be 1/n+1 instead of just n as you find only the part of FM? Thank you

hi! for question 4, would it be possible to find two ways of expressing FX using two different coefficients, say k and n, and then comparing the coefficients of a and b for both the expressions? for example, FX= 2ak - 1/2bk [basically k times FM], and FX also = a-b + n(a+b); then you say that 2k= 1+n [1+n is what you get after expanding n(a+b) then simplifying] and -1/2k = n - 1. Then you solve the equations simultaneously to find n and k, and then sub it back into either of your original expressions for FX. After this you can subtract your answer from FM to find what XM is. I tried this method but it doesn't work for some reason, as both n and k come out to be 1. Is there any reason why this doesn't work? I'm super confused

Hi sir, for the first question, when you find OD, would you not add 'a' aswell since it would be OA to AX to XD, so it would be a+1/2a+1/2c+3c-1/2a= a+3 1/2c. Does that make sense? I'm not sure why you didn't include OA. Thank you :)

How do you know which coefficients to compare?

Personally find grade 7+ Vectors one of the hardest, any1 agree??

hi, may i know how to solve for the question where for example in question 24 of your video, Area of OPZ is given. Find area of ORZ? I'm working on a mock exam question and cant seem to solve it. It's also in 4MB0/02/2017/May Q10, couldn't understand the marking scheme as well. Appreciate your help!

Have these questions actually been on gcse papers THEYRE SO HARD

17:31, I'm sure I must be not properly conceptualizing something here. Why use - b( 1/2 - k) instead of +b(-1/2 +k) ? I understand the values inside the brackets are not the same, but how do I know which one is correct? Thanks, great video!

Went from avg. grade 6 to avg. grade 9 with your help, thx

The fact that these sorts of questions even have a chance to appear on the exam is quite frankly shocking. The amount of work you have to do for 4 marks is unreal. Either these questions be scrapped completely or there’s a bit more incentive to actually doing them. If I come across this in my exam I’m skipping it and moving to the next one. Not doing that for 4 measly marks.

YEAHHHHHHH. i felt so happy when i got the first question right straight away. u should win the global teacher prize

For question 4 isn't FX = n/(n+1) lots of FM? because I got n= 2 (so one part is 2/3 and the other being 1/3)... but I did a different method.

Is it possible to explain why the co efficients of a and b are equal?

does lots of vector questions appear on our exam paper? or just 1 or 2 and what could be the marks?

Thank you, sir, you've made a hard topic much easier. my only question was at 36:05 why are 2n-1 and 1-1/2n equal to each other

I have a doubt- at 18:30 you've mentioned that b is 6 lots of a, however in the equation given above, b was a negative integer, so shouldn't you substitute it as -6 instead?

sir i got 4:1 on the question 20 becuase i used mass point theorem and showed almost no working needed. do you think they will allow this in the exam like will i get marks for it or do you have to use this type like what u used

29:36 could you leave the ratio with fractions or would you lose a mark for not converting them into integers

For question 2, I don't understand the part where the 'coefficients have to be the same' 15:45

The music at the start makes my day

Urgent request Please could you help me on the following question : a swimmer jumps from a board 2m above the level of water. How fast is she moving when she hits the water ( the acceleration due to gravity is 10m/s squared, and you can ignore the affect of air resistance) I REALLY NEED HELP PLEASE

i dont get the equating coefficient part that you did in the second question. As why was one 6x bigger than the other

What advice do u have if I want to go from a 7 to a 9. Also if I'm currently working at a 7, do u think I will struggle if I do maths for a level.

i think i’ve just ascended to a higher level of being after doing these questions, they take so long but when you get them its brilliant, thank you so much!

Since FM is a full vector and n is just a fraction, won't FX be 'n/(n+1)FM' .My answer for 'n' is 3.

Hi sir for the first question at the answer where does the vector c go when u divide CD to get 1 . Would i write 2/5 C

Could you explain why for vectors on the same line the coefficients of A and B have to be equal? Thanks

Does anyone know how to figure out what vectors you need to answer the question cus the patterns or they vectors they use to find the answer is different every question

for question 2,how did you kno w that the coefficient of b is six times greater than coefficient of x?

hi, thanks for this video, im just confused as to where 6x greater came from in the 2nd question

hey, where did the 7c come from in 7:42

Hi can you create a pdf with these questions like you did for the 10 hardest GCSE questions? Also you mentioned in that video in the description that there were 20 questions to choose from - what were the other ones not mentioned in that video? Thanks

For the third question, why did you find AP?

Sir on average what percentage of the country gets full marks on this question?? love your videos btw : )

THANK YOU SO MUCH!! IVE BEEN STUCK ON THIS TOPIC FOR AGES AND YOU EXPLAINED IT SO ELOQUENTLY!! nvm im confused again...

Yh, I still don't get it

i did all these correctly first try, except one, where i incorrectly labelled my own diagram at the start what grade would you consider that to be at roughly?

For the last one, surely it would be easier to deduce that triangle ZRY and ORP are similar.

These are definitely challenging problems. I have a 1st class maths degree and the 2nd problem you did still took me about 20 - 25 mins to solve. I did the last part differently though. I used the fact that MPN is a straight line to write MP= rMN for some other constant r. Then set this equal to the other vector expression you had written with the factored components involving k. Then you can set both the x-components and y-components equal which gives you a 2x2 set of simultaneous equations you can solve for r and k. From this you find r = 1/5 and k = 2/5. So this also tells you that MP = (1/5)*MN. I'm currently teaching GCSE maths in an F.E college and find all your videos really helpful. Thanks for making them all!

19:18 why use MP even though it does not equal MN? or do they?

at 37:01 does anyone know why FX isnt multiplied by n/n+1 cause when I did that I got a rlly strange answer that doesn't look right

Sir at 30:21 shouldnt they give use a ratio for CX and XE ?

sir i have a question for the trapezium vector question when you solved n as 4/5 wouldnt the ratio of 4/5 : 1 be the same as the ratio a 4/5 : 5/5 which is 4:5?

Hey there, just wanted to point out that on your website the free booklets and past papers, that stuff never actually gets to my inbox so could you please look into that... Otherwise really love ur content. Really helpful for getting a grasp of new topics.

Can you solve the 2nd question using the topic of similar triangles?

Yea I'm done👍 My dad wants a grade 8 in Maths and I'm at a grade 6 rn and I can't even manage whatever in god's hell these questions are.

Hey, I did the first question a bit differently and it worked out, but I was wondering if this would be "okey"... What I did is give OC a midpoint, and called it Z, as this is a parallelogram, Z to X, will be the same as 1/2 of O to A (so 1/2 a), after that you can do X to Z, which would be -1/2a, and from there on I bet you will understand how I did it. I think its a great method and it worked out perfectly, so I just need to know if it would be "legal" in the exam haha, thanks, great video and keep up these hgiher tier vids.

Is there anyway you recommend at getting very good at vectors like these as when I ask my teacher they don’t even know themselves

Thanks man your teaching is soo good

sir what level would these questions be on an A level maths or further maths paper ?

love this channel, thanks so much I now understand how to answer these questions every time!

18:30 - Why is coefficient A, 6 times coefficient B?

whats crazy is that this guy's just cooking these up like nothing

THANK YOU SIR. the last question I was going to do with my class but I didn't understand it. But you explained it properly

in 17:56 please could you explain why we multiply the coefficient by 6

could you please make a video on matrices, matrix transformations and identity matrix :)) they're all part of GCSE math

Thank you so much for this! I'm just proud of getting the last question right :P

Hello gcse maths tutor, thanks so much for this vid. But for question 21, why did you assume that the coefficient of a must be 6 times greater than the b coefficient?, im still confused on that

Can someone please tell why in question one you looked at O to X and X to D Why do you not do C To D = C to X + X to D surely that’s easier

these questions are rediculous lol. no way this is gcse level. i think A level students would stuggle with this. are these difficoult vector questions likely to come up in exams do you think?

That’s a nice intro

You are real life hero! you're beautiful, hats off to you sir. Thank you. appreciation😃

Are vectors likely to show up for GCSE 2020?

Hi GCSE Maths Tutor. Could you please do videos on Loci and Construction and Bearings?

what paper and year is this from and is this 0607 math?

Got the first one on my own with a little hint from the vid using much less working out.

Do you have any video on matrix translation?

Great video! Thank you soooo much and many blessings!!!

True nature of vectors

so if CXE is a straight line, CX=CE?

PLEASE REPLY AND LISTEN PLEASE Grade 6/7 playlist please really need to request this please please

Why do coefficients of vectors have to match? Pls help

why does the coefficient of a have to be six times the coefficient of of b

Amazing! Thank you very much:)

why does the coefficient of a have to be 6 times greater than b???? - for the second question

I got only 2 right😂😂other half way (2,3,4) was actually hard ones

In relation to the first question there's also another, potentially quicker way. Work out AC (c-a) then XC as 1/2(c-a). We already know XD as 3c-1/2a. So the distance C to D can be found by subtracting XC from XD which is 2 1/2c. From here the ratio can be found.