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

A video revising the techniques and strategies for completing questions on Vector Proofs with Ratios (Higher Only).

This video is part of the Vectors module in GCSE maths, see my other videos below to continue with the series.

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🔹 Review what you have learnt on the exam questions

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Music: Over N Over
Musician: Not The King.👑

[Sebastian]

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)

[friedfishh]

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!

[idrk]

You are honestly SOOO 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

[hasnainaya]

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.👏

[calcpost]

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

[yusrxn]

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

[em_ignite]

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! ❤ 🙏

[nathanhawey]

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.

[beananimation]

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

[aesthetic_disney_]

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

[ibraheemali]

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

[aryamrege]

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

[alicjabednarczuk]

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

[thomasstarlingcollector]

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.

[puddleduck]

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!

[isabellaheathorn]

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

[sergeiagafonov]

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

[sscomposer]

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

[AH]

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

[inffable-x]

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!