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Year 13 Maths Help Thread

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Reply 40
Avatar for B_9710
B_9710
18
Original post by Palette
UK Senior Mathematics Challenge held annually to Year 12 and Year 13 students.


Oh, it's not really talked about much on here so I've never seen it abbreviated. I'm not really sure what you're expected to know and what you're not tbh.
Original post by Ano123
I'll get the ball rolling. If anyone is out there who has done some trigonometry and want to put their knowledge to the test, here's a tough question they can try if they want to. (Probably not many for another few months at least). I made it up a while ago.
Sin 3.png
For the solving the equation the question should really state that 0<x<90.


:eek::eek::eek:
Reply 42
Avatar for Ano123
Ano123
15
Original post by ODES_PDES
:eek::eek::eek:


Nice question?
Original post by Ano123
Nice question?


Looks very hard
Original post by Ano123
Nice question?


Might want to spoiler it. Might make the new Y13's run away from the thread :wink:
Reply 45
Avatar for Ano123
Ano123
15
Original post by ODES_PDES
Looks very hard


It's alright actually. Plenty of guidance. I did that so people wouldn't just lose interest when seeing an expression like that.
Reply 46
Avatar for B_9710
B_9710
18
Original post by Palette
This is an SMC problem which I solved, but I want to know if there is a way of solving it non-manually:

Let f(x)=x−1x+1 f(x)= \frac{x-1}{x+1}. Calculate f6(x) f^6(x).


I think actually that they are using the notation that fn=fff⋯f⏟n \displaystyle f^n= \underbrace{ fff\cdots f}_{n} . So it would just be composing the function with itself 5 times for f6 f^6 .
(edited 7 years ago)
Reply 47
Avatar for Palette
Palette
OP
14
Original post by B_9710
I think actually that they are using the notation that fn=fff⋯f⏟n \displaystyle f^n= \underbrace{ fff\cdots f}_{n} . So it would just be composing the function with itself 5 times for f6 f^6 .


Is there any rigorous shortcut that enables one to solve the question quickly? I deduced manually that for fn(x) f^n(x) from n=1n=1 to n=4n=4, fn+2(x)=−1fn(x)f^{n+2}(x)=-\frac{1}{f^n(x)} but I can't actually prove it for all n.
Reply 48
Avatar for B_9710
B_9710
18
Original post by Palette
Is there any rigorous shortcut that enables one to solve the question quickly? I deduced manually that for fn(x) f^n(x) from n=1n=1 to n=4n=4, fn+2(x)=−1fn(x)f^{n+2}(x)=-\frac{1}{f^n(x)} but I can't actually prove it for all n.


I'll have a proper look later, but perhaps it may be useful to see if this pattern holds for a few more and if it does use induction to prove the result (if it is true). Can be much easier than a direct proof, maybe so in this case.
Reply 49
Avatar for B_9710
B_9710
18
Original post by Palette
Is there any rigorous shortcut that enables one to solve the question quickly? I deduced manually that for fn(x) f^n(x) from n=1n=1 to n=4n=4, fn+2(x)=−1fn(x)f^{n+2}(x)=-\frac{1}{f^n(x)} but I can't actually prove it for all n.


If you consider f5(x) f^5(x) it will become very clear that you can write a general expression for fn(x) f^n(x) explicitly, and it's very easy to just define fn(x) f^n(x) in more than 1 way.
(edited 7 years ago)
Reply 50
Avatar for Zacken
Zacken
22
Original post by Palette
This is an SMC problem which I solved, but I want to know if there is a way of solving it non-manually:

Let f(x)=x−1x+1 f(x)= \frac{x-1}{x+1}. Calculate f6(x) f^6(x).


Sure.

f(x)=x−1x+1⇒f2(x)=−1x⇒f3(x)=−1f(x)⇒f5(x)=f(x)⇒f6(x)=f2(x)=−1xf(x) = \frac{x-1}{x+1} \Rightarrow f^2(x) = \frac{-1}{x} \Rightarrow f^3(x) = -\frac{1}{f(x)} \Rightarrow f^5(x) = f(x) \Rightarrow f^6(x) = f^2(x) = -\frac{1}{x}
Hello, friends. I'm just curious! Have you ever used online homework help services like https://assignment.essayshark.com/math-help.html to do your math assignments? Did they work fine for you? I'm considering giving it a try.
Original post by jessback
Hello, friends. I'm just curious! Have you ever used online homework help services like https://assignment.essayshark.com/math-help.html to do your math assignments? Did they work fine for you? I'm considering giving it a try.


Homework help services? I've never went to lengths of that for homework lol. Just post some problems, or ideas you dont understand, here.
Reply 53
Avatar for Ayman!
Ayman!
15
Original post by SeanFM
My D2 textbook has arrived :excited: I feel like a 6th former again. :moon:


Reminds me - I should buy M4 and M5. :tongue:

Spoiler

I'll be working on M3, D2 and S3 this year. Perhaps M4, 5 and S4 depending on whether I find them too insane.
Original post by Ayman!
Reminds me - I should buy M4 and M5. :tongue:

Spoiler


Spoiler

Silly question but is this thread for maths alone or can FM students use it as well?
Original post by Imperion
Silly question but is this thread for maths alone or can FM students use it as well?


FM as well.
Reply 58
Avatar for Ayman!
Ayman!
15
Original post by Imperion

Spoiler



Better not post it here - the TSR police will arrest me. :mob:

Check your PM soon, I'm looking for the link :lol:
Reply 59
Avatar for B_9710
B_9710
18
Original post by Ayman!
Better not post it here - the TSR police will arrest me. :mob:

Check your PM soon, I'm looking for the link :lol:


I wouldn't mind...the links.. You know !:wink:

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