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STEP Prep Thread 2016 (Mark. II)

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Original post by ComputerMaths97
So tomorrow do I focus on 2-3 questions the whole time or shall I just poke at questions till I get stuck then move on so I get lots of partial solutions?


The recommended advice is always to focus on getting complete solutions rather than doing lots of separate parts of questions
Original post by smartalan73
The recommended advice is always to focus on getting complete solutions rather than doing lots of separate parts of questions


Even if you end up with less marks? :smile:
Original post by ComputerMaths97
Surely if f(x) = 1/x then f(f(f(x))) = 1/x ? Or do you mean something else?


Sorry, 'cyclic with period 3' is not the same thing as what I meant lol.
I meant f(f(f(x)))=xf(f(f(x)))=x.
So I guess that means cyclic with period 4.
(edited 7 years ago)
Original post by ComputerMaths97
Surely if f(x) = 1/x then f(f(f(x))) = 1/x ? Or do you mean something else?


that's period 2
Original post by sweeneyrod
f(x) = x
(possibly not what you want)


Should've mentioned, anything except f(x)=xf(x)=x.
Original post by ComputerMaths97
Even if you end up with less marks? :smile:


I think the trick is to know when you're stuck whether you're ever gonna be able to think of the solution or if it its pointless trying and would be more beneficial to move on. I think once you've got that down you've basically mastered step.
Original post by Farhan.Hanif93
The LHS of that statement is untrue - N=1 shows you that.


Yeah that's actually wrong, but don't know why the mark scheme used this statement. See attached photo
Original post by IrrationalRoot
Can anyone think of a function ff such that f(f(f(x)))=xf(f(f(x)))=x? I can't, not sure if I'm missing something obvious or what.
EDIT: I just realised there was some IMO question about iterating polynomials in this way, interesting...


f(x) = x is a solution. There might be more too. I do remember doing a step question at some point of this type. It was a bit more complex but the basic idea was the same
Original post by IrrationalRoot
Should've mentioned, anything except f(x)=xf(x)=x.


f(x) = 1 ?

(sorry, I'll stop now)
Original post by IrrationalRoot
Sorry, 'cyclic with period 3' is not the same thing as what I meant lol.
I meant f(f(f(x)))=xf(f(f(x)))=x.


Ah okay yeah I was wondering why I came up with one straight away :biggrin:

Does cheating it like f(x) = x(cos^2(x)+sin^2(x)) count? :biggrin:

Original post by gasfxekl
that's period 2


See this is why I'm never going to pass a STEP exam
Original post by sweeneyrod
f(x) = 1 ?

(sorry, I'll stop now)


...stahp.
Original post by ComputerMaths97
Ah okay yeah I was wondering why I came up with one straight away :biggrin:

Does cheating it like f(x) = x(cos^2(x)+sin^2(x)) count? :biggrin:



See this is why I'm never going to pass a STEP exam


No because that is the function f(x)=xf(x)=x! :tongue:
Writing it differently doesn't change it's mathematical meaning.
The only idea I've got for f(f(f(x)))=xf(f(f(x)))=x so far is taking ff to be a degree 2 or more polynomial and solving a bunch of ugly simultaneous equations.
Original post by Geraer100
Yeah that's actually wrong, but don't know why the mark scheme used this statement. See attached photo

Having just opened the question, it specifies that N is an integer greater than 1 and it is true that the inequality holds for N≥2.

To see this, note that N-√(N^2-1) = 1/[N+√(N^2-1)] < 1/N 1/2, which yields 2N-1/2 < N+√(N^2-1) after a little rearrangement.
Reply 1474
Original post by IrrationalRoot
Can anyone think of a function ff such that f(f(f(x)))=xf(f(f(x)))=x? I can't, not sure if I'm missing something obvious or what.
EDIT: I just realised there was some IMO question about iterating polynomials in this way, interesting...
EDIT 2: Except the trivial solutions.


Sure.

Text: f(x) = ( x + sqrt(3) ) / (1 - xsqrt(3))

LaTeX: f(x)=x+313x\displaystyle f(x) = \frac{x + \sqrt{3}}{1 - \sqrt{3}x}

Image:

Hopefully at least one format will work...
(edited 7 years ago)
When do results come in for step, same as A levels?


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Reply 1476
Original post by drandy76
When do results come in for step, same as A levels?


As soon as the clock hits midnight on the 18th of August (i.e: the end of 17th of August) you rush onto the website, frantically refresh, swear at your screen in tandem with the thousands of other candidates refreshing as the site throws up "Site error" - some furious clicks later, your continued refreshing bears fruit and your result pops up on screen, usually followed by a triumphant yell or a dive out of the window.
Original post by Zacken

Spoiler



Spoiler

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Original post by Zacken
As soon as the clock hits midnight on the 18th of August (i.e: the end of 17th of August) you rush onto the website, frantically refresh, swear at your screen in tandem with the thousands of other candidates refreshing as the site throws up "Site error" - some furious clicks later, your continued refreshing bears fruit and your result pops up on screen, usually followed by a triumphant yell or a dive out of the window.


As I dive out of the window I'll check UCAS too so I'll know it was the right call, need step so kings can ignore my woeful chemistry results


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Original post by Farhan.Hanif93
Having just opened the question, it specifies that N is an integer greater than 1 and it is true that the inequality holds for N≥2.

To see this, note that N-√(N^2-1) = 1/[N+√(N^2-1)] < 1/N 1/2, which yields 2N-1/2 < N+√(N^2-1) after a little rearrangement.


Oh I see! Thanks!

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