HARDEST Circle Question?? | Tricky A-Level Maths Question #56

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[@Ace__Matic]

good luck tomorrow everyone 😁

[@Jiten-pm5lz]

Thanks. I do AQA but this still looks like an awkward synoptic style concept that can be added to many contexts

[@Chakamatics]

​@@Jiten-pm5lz bro are you ready?

[@Jiten-pm5lz]

@@Chakamatics you can never be truly ready but I completed the 2023 paper and got 86 on it so I think I should be ok

[@Chakamatics]

@@Jiten-pm5lz where did u get the paper bro congrats hope it's like that in the real thing too

[@Jiten-pm5lz]

@@Chakamatics I have the password for it. The AQA 2023 A level Maths past paper. It's unreleased to the public. But it's actually a sweet paper.

[@radicaledward4717]

you and tlmaths are a deadly combo

[@03FRK]

I did my first maths A Level back in 2022 and I didn’t know about this channel. Last year I did a resit and I found this channel the day before Paper 3 and realised how good of a channel it was (albeit too late). I’m doing maths for the third time and from day one I’ve been waiting for these uploads, the teaching is almost like that in a classroom which makes it so much easier to learn. Thank you Mr. Astbury!

[@HamzaElsharkawy-rb2nc]

im gonna pray specifically for you in my night time prayers

[@03FRK]

@@HamzaElsharkawy-rb2nc I will likewise pray for you during Qiyamul Layl 😄 We’ll regroup once again and evaluate after tomorrow I guess 😎

[@itazuraja9921]

This is dedication man! All the veryy best. Insh'Allah u will get A*.

[@HO-xi9em]

do ur best bro get those grades inshallah

[@zarinuddin]

im also resitting this year. i sat my first maths alevel last year 2023. hope u get that A/A * insha'allah

[@eugeniafernandes7956]

Thank you so much for taking the time to make this playlist. I found your explanations really helpful. I am looking forward to a video on predicted paper 2! :)

[@Oliver-zj4sh]

No way, you were my maths teacher when I was maybe 9 years old? I am now 21 studying Engineering so thanks for the help. I just randomly stumbled across this video.

[@stardreamix786]

Thanks so much! - nice question! - good luck everyone tomorrow lets cook

[@MrAstburyMaths]

Good luck!

[@isashyo773]

Thanks for the blessings love the content

[@itzhena5301]

please do the tricky question tomorrow on pure before our paper 1sir! maybe some trig modelling? differential modelling? whatever you think is best

[@sultanamjed3641]

its the big day tomorrow ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

[@MrAstburyMaths]

Let’s go!

[@txb_6713]

loved this question, circles are always so fun to do, thank you sir for all your work! good luck everyone!

[@MrAstburyMaths]

My pleasure!

[@bennyx9x347]

Mr Astbury you are the goat. I can only dream of solving circle equations like this. So dam talented!

[@miamoos6566]

good luck everyone for tomorrow! - maths a level ocr a student

[@aa-gn6zn]

Don’t see many people doing ocr, how u feeling?

[@madeleine-wc1gx]

Why do you do tan(2theta) rather than 2(tan(theta)) as the triangles are similar so surely you can just double the value of 1/2?

[@spencergee6948]

Just see if tan 60 is twice tan 30.

[@ShubhkarmanSinghNijjar-xq1cq]

You can also use vectors to find the angle between them and then you can see cos x = 3/5 and make a triangle you get tan x = 4/3!

[@OzeCovers]

Love this question

[@best_mate456]

That should be worth like 12 marks

[@gangstaflower2262]

lets go !

[@darrenloroy3011]

The last part I just noticed that the gradients are the tan of the angles we can work tanAPB =(3-1/3)/(1+3x1/3)=(8/3)/2=4/3

[@sampanchung1234]

With the power of Mr Astbury, I will win

[@davidworley5254]

cant you just do tan(arctan(3)-arctan(1/3))? it gives the right answer

[@daveyboi6675]

That paper was blessed

[@moistmoist5279]

Truly heaven sent

[@markhughes4617]

for the last part, if the angle PA makes with x axis is a, and the angle PB makes with the x axis is b then the angle APB is a - b. so tan APB is simply tan(a-b) and we know tan a and tan b as they are the two gradients, 3 and 1/3. Simply sub into the double angle formula in the data book and voila. Might be a smidgeon quicker but obviously both approaches work.

[@MrAstburyMaths]

Fantastic 👌

[@davidjenner5665]

Definitely the preferred option, and a(i) should've been done by just substituting y=mx+2 into the equation of the circle then expanding and simplifying to give the answer required. The mark allocation suggests that this was all that was needed.

[@user-fr5tt3fn2l]

why do we sometimes substitute the equation of a line in the equation of a circle and other times into the main equation that is provided ?

[@ho-lq6nd]

the equation of a circle is obtained from the main equation, so theyre essentially the same thing. Its up to personal preference tbh, for some people its easier to sub in values into the main equation or the completed the square ver. Either will work. Good luck tom

[@user-fr5tt3fn2l]

@@ho-lq6nd that’s makes sense, thank you !! Good luck as well

[@thomasdie7689]

Hello, did anyone else's exams feel easier than they thought. Did they lower the grade boundariesm

[@eugeniafernandes7956]

No one knows what the grade boundaries for 2024 are yet since the exams aren’t done yet. But if many people found it easy then it’s likely that the grade boundaries will be higher this year or roughly the same as 2023, since I thought the 2023 paper wasn’t too hard.

[@AS-rq6tr]

Firsttttttt

[@ccccccccccccccccccccccc684]

wow this is actually relally hard

[@michaelswahla4927]

why is the first question 2 marks bro, should be 3 ngl

[@madeleine-wc1gx]

Why do you do tan(2theta) rather than 2(tan(theta)) as the triangles are similar so surely you can just double the value of 1/2?

[@hazelwi]

It's the tan of the angles between APB which is 2theta so it's tan2theta

[@hazelwi]

You could solve for theta multiply it by two and then find the tan of the new angle after, if that helps!

[@madeleine-wc1gx]

Why do you do tan(2theta) rather than 2(tan(theta)) as the triangles are similar so surely you can just double the value of 1/2?

[@eugeniafernandes7956]

Because you've found the value of tan(1/2APB). So, to find the value of tan(APB) you do tan(2x1/2APB) which is basically tan(2theta). You find the value of tan(2theta) using the double angle formula. I'm sorry if I haven't explained this well.

[@madeleine-wc1gx]

@@eugeniafernandes7956 ah thank you so much, that does make sense yes!

[@wesh10748]

@@eugeniafernandes7956 So if tan(1/2APB) = 1/2, why can't you do (arctan(1/2))/(1/2)