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STEP Prep Thread 2016 (Mark. II)

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If anybody would like to explain how in STEP III 2009 Q7 ii that after proving Pn(X) is a polynomial of degree n that I prove that the coefficients are non zero I will be forever in your servitude
Original post by Number Nine
If anybody would like to explain how in STEP III 2009 Q7 ii that after proving Pn(X) is a polynomial of degree n that I prove that the coefficients are non zero I will be forever in your servitude


You just need to show the leading term is non zero.


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(edited 7 years ago)
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Original post by drandy76
I imagine the wait until 9 is like the count down to summer in high school musical 2


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:rofl:

Pretty much. :tongue:

Original post by Gwenuin
...


Please remove your post.
Any Last minute advice for step 2 and 3 such as key areas to learn /go over?
Feels like I'm getting worse at STEP and highly unprepared.
Original post by Number Nine
If anybody would like to explain how in STEP III 2009 Q7 ii that after proving Pn(X) is a polynomial of degree n that I prove that the coefficients are non zero I will be forever in your servitude

Strictly speaking, you haven't proven that P_n(x) is a polynomial of degree n until you've proven that the leading coefficient is non-zero. But anyway, you use the inductive relation, P_(n+1) = (1+x^2)(P_n)' - 2(n+1)xP_n.

If you assume that that P_n is a poly of degree n i.e.

P_n(x) = ax^n + ..., where a≠0

Then you can show that:

P_(n+1)(x) = -(n+2)ax^(n+1) + ...,

by finding the coefficient of x^(k+1) from substitution into the RHS of the above relation. Then by induction, we're done.

(Obviously, with the "..." terms representing polynomial terms of a lower degree - LaTeX is not cooperating)
(edited 7 years ago)
In the Paper II, 2015, Q9 why the distance AD is the distance of the Centre of Mass from A in this solution? Shouldn't the centre of mass be somewhere along AD, but not at D?:smile:
Solution attached.
Step2015Paper2Question9 (1) (1).pdf62.6KB
Original post by Geraer100
In the Paper II, 2015, Q9 why the distance AD is the distance of the Centre of Mass from A in this solution? Shouldn't the centre of mass be somewhere along AD, but not at D?:smile:
Solution attached.

All of the mass in the system is found at B and C so, given that the rods are all light, we expect the COM to lie on BC.
Could you guys use pencil to write the solutions? My invigilator said "maybe"..wtf
At what time do you sit the STEP II in England?
Original post by krishdesai7
At what time do you sit the STEP II in England?


9 am GMT
Original post by Farhan.Hanif93
Strictly speaking, you haven't proven that P_n(x) is a polynomial of degree n until you've proven that the leading coefficient is non-zero. But anyway, you use the inductive relation, P_(n+1) = (1+x^2)(P_n)' - 2(n+1)xP_n.

If you assume that that P_n is a poly of degree n i.e.

P_n(x) = ax^n + ..., where a≠0

Then you can show that:

P_(n+1)(x) = -(n+2)ax^(n+1) + ...,

by finding the coefficient of x^(k+1) from substitution into the RHS of the above relation. Then by induction, we're done.

(Obviously, with the "..." terms representing polynomial terms of a lower degree - LaTeX is not cooperating)


You're an absolute lad, thank you very much

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Are we allowed to upload solutions to step 1 at 9am UK time, or will there be a separate thread for solutions?

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Original post by mpaterson
9 am GMT


Nope - 9am BST (GMT+1).
Original post by nitromeguy
Are we allowed to upload solutions to step 1 at 9am UK time, or will there be a separate thread for solutions?

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There's usually a separate thread but in general, yes you're allowed to upload solutions. If someone uploads the paper that'd be great, I can then give a proper assessment of its difficulty.

Not long to go: remember 9:00 UK time (35 minutes from now).
Original post by shamika
There's usually a separate thread but in general, yes you're allowed to upload solutions. If someone uploads the paper that'd be great, I can then give a proper assessment of its difficulty.

Not long to go: remember 9:00 UK time (35 minutes from now).


I can get my hands on the paper later today if no one else can :smile:

Is someone going to create a solutions thread?

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(edited 7 years ago)
So how we doing this lads?


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It's 9:01 according to my time. Anyone going to start off?
8. (1-x-x^2)^-1
Beautiful question!
Solution to Step 1 2016 Q2
2016STEP I Q2.pdf308.8KB
Original post by jjsnyder
I can get my hands on the paper later today if no one else can :smile:

Is someone going to create a solutions thread?

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Anyone can make one but it should be someone active so that the OP gets updated.

Hope the paper went well for everyone who took it!

EDIT: if someone can let me know when the paper has been uploaded that'd be great
(edited 7 years ago)

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