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# STEP Prep Thread 2016 (Mark. II)

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1. (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)
2. 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?
Solution attached.
Attached Images
3. Step2015Paper2Question9 (1) (1).pdf (61.1 KB, 16 views)
4. (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?
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.
5. Could you guys use pencil to write the solutions? My invigilator said "maybe"..wtf
6. At what time do you sit the STEP II in England?
7. (Original post by krishdesai7)
At what time do you sit the STEP II in England?
9 am GMT
8. (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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9. 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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10. (Original post by mpaterson)
9 am GMT
Nope - 9am BST (GMT+1).
11. (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).
12. (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

Is someone going to create a solutions thread?

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13. So how we doing this lads?

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14. It's 9:01 according to my time. Anyone going to start off?
15. 8. (1-x-x^2)^-1
Beautiful question!
16. Solution to Step 1 2016 Q2
Attached Images
17. 2016STEP I Q2.pdf (301.6 KB, 91 views)
18. (Original post by jjsnyder)
I can get my hands on the paper later today if no one else can

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
19. (Original post by nitromeguy)
Solution to Step 1 2016 Q2
Yay thats what I got! used different values of a,b,c,d,e but am sure that won't matter
20. So for the graph sketching question, I drew vertical lines between my horizontal lines, do you think this will be ok?
21. I have a solution to Q4 which is somewhat legible and working on one to Q7. Don't really have faith in myself to get STEP right, still bloody hard a year later, but I suppose if they're a load of crap I can be told lol
22. (Original post by shamika)
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
Yeah I agree, I have other exams to focus on and am not that active so I won't, anyone want to do one?

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