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# STEP Prep Thread 2016 (Mark. II)

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1. (Original post by EnglishMuon)
I mean i cant imagine mentioning bolzanos theorem would get u any more credit especially as you are not required to know it and it is just the same as saying there is only 1 root if u dont give proof.
At least one root not one root.
Also you are not required to write the name of the theorem but I can remember from a-levels that sign change in continuous functions means a root in that interval so I guess you can use it and since it's an established result , wouldn't it be better ?
2. (Original post by Vesniep)
At least one root not one root.
Also you are not required to write the name of the theorem but I can remember from a-levels that sign change in continuous functions means a root in that interval so I guess you can use it and since it's an established result , wouldn't it be better ?
Question is 1 root not atleast. English muons idea is the best I feel, I would write it like this,
the curve is strictly increasing hence does not turn and come back for another root.
-infinity to infinity so it crosses atleast once, since it is strictly increasing it crosses exactly once.
For the atleast once root you can just say complex solutions come in pairs hence atleast one real root.

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3. (Original post by physicsmaths)
Question is 1 root not atleast. English muons idea is the best I feel, I would write it like this,
the curve is strictly increasing hence does not turn and come back for another root.
-infinity to infinity so it crosses atleast once, since it is strictly increasing it crosses exactly once.
For the atleast once root you can just say complex solutions come in pairs hence atleast one real root.

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I said that you use bolzano's theorem with the fact that the function is strictly increasing thus 1-1.
Edit: actually what I said was your second solution just in a more formalistic way.
4. (Original post by physicsmaths)
Question is 1 root not atleast. English muons idea is the best I feel, I would write it like this,
the curve is strictly increasing hence does not turn and come back for another root.
-infinity to infinity so it crosses atleast once, since it is strictly increasing it crosses exactly once.
For the atleast once root you can just say complex solutions come in pairs hence atleast one real root.

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(Original post by Vesniep)
I said that you use bolzano's theorem with the fact that the function is strictly increasing thus 1-1.
Edit: actually what I said was your second solution just in a more formalistic way.
5. A question about STEP III 2015
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Q4 (i). I just argued that coefficients all real nonreal roots come in conjugate pairs, so either 0 or 2 nonreal roots and hence either 1 or 3 real roots at least one real root. (Fundamental Theorem of Algebra tells us that there are 3 roots.)
Would this be an acceptable answer?

I guess you could also argue as and cubic is continuous so at least one real root by the IVT.
6. (Original post by IrrationalRoot)
A question about STEP III 2015
Spoiler:
Show
Q4 (i). I just argued that coefficients all real nonreal roots come in conjugate pairs, so either 0 or 2 nonreal roots and hence either 1 or 3 real roots at least one real root. (Fundamental Theorem of Algebra tells us that there are 3 roots.)
Would this be an acceptable answer?

I guess you could also argue as and cubic is continuous so at least one real root by the IVT.
perfectly fine. I actually said this a few posts ago although for a different question.
7. (Original post by ComputerMaths97)
Thanks for the words of hope mate

What did he get in his A levels?
He did get 3A*s so that may have contributed, not sure. His step score wasn't good though I know that, he was certain he hadn't got in when he got his step results (they come out a few hours before A-Level/UCAS)

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8. (Original post by Vesniep)
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Q3 was very easy btw .
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I am usually torn by these sorts of questions. They are either nice and easy, or I spend ages working out what is going on. I decided not to do it in this case.
9. (Original post by 16Characters....)
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I am usually torn by these sorts of questions. They are either nice and easy, or I spend ages working out what is going on. I decided not to do it in this case.
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In this case, it was definitely nice and easy. The counting part was easy, and the induction wasn't very algebraic.
10. (Original post by sweeneyrod)
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In this case, it was definitely nice and easy. The counting part was easy, and the induction wasn't very algebraic.
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Ah well. I hope II 2016 has some nice and easy questions too.
11. (Original post by 16Characters....)
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I am usually torn by these sorts of questions. They are either nice and easy, or I spend ages working out what is going on. I decided not to do it in this case.
Didn't do it as well , for the same reason.
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Q2 was easy as well . Now I have to ask myself why did I choose a difficult stats question instead of one of these two trivial Qs and why did you choose the geometry of Q7 rather than of Q2?
Perhaps our choices were not the best .....
12. (Original post by Vesniep)
Didn't do it as well , for the same reason.
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Q2 was easy as well . Now I have to ask myself why did I choose a difficult stats question instead of one of these two trivial Qs and why did you choose the geometry of Q7 rather than of Q2?
Perhaps our choices were not the best .....
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Q7 was mostly just algebra with a bit of Pythagoras thrown in. It was not much more geometric than Q5 really. Not tried Q2 yet but it looked like it contained more "proper" geometry and trig.
13. (Original post by jjsnyder)
He did get 3A*s so that may have contributed, not sure. His step score wasn't good though I know that, he was certain he hadn't got in when he got his step results (they come out a few hours before A-Level/UCAS)

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dont they update at 12 midnight on results day morning same as ucas track?
14. (Original post by Number Nine)
1,2,3,5,7,8
Well done.

I did STEP III 2015 yesterday, feel like I did quite well, finishing 5 questions and doing the first part from a sixth. But I'm scared to look at the mark scheme.
15. Anyone have advice for binomial expansion questions? As in finding general terms when two expansions are divided etc

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16. (Original post by Number Nine)
dont they update at 12 midnight on results day morning same as ucas track?
Na, step is out at 12, UCAS updates at 8am.

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17. (Original post by fa991)
Anyone have advice for binomial expansion questions? As in finding general terms when two expansions are divided etc

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I guess it really does just come down to case work tbh.

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18. (Original post by physicsmaths)
I guess it really does just come down to case work tbh.

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Ah I see, I think I just assumed there were neat tricks but I suppose case work isn't too bad

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19. Has anyone come across any interesting/challenging qs from the older papers now theyve finished the new ones? I just had a look at I '98 and some of the qs couldve come straight from an A level paper.
20. (Original post by Number Nine)
dont they update at 12 midnight on results day morning same as ucas track?
I remember he got his STEP at midnight, but UCAS didn't come until later for some reason. They closed it as they had problems with too much traffic I think. Which I've heard happens quite regularly.

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