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The 2012 STEP Results Discussion Thread

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Avatar for gff
gff
5
Original post by twig
The intended method I think (someone has probably posted this already, I have not checked):

Spoiler



Original post by GreenLantern1
How would you show a modular arithmetic proof of this problem? I am not quite sure :|


It all amounts to the same thing.

Spoiler

I've seen STEP and STEP Past Papers sections on the MEI integral website. I was wondering if integral did extra step work. Despite I will not be taking the exams I have been rigorously preparing for them as I only came to decision after I found there were multiple clashes within my exam time table.
Original post by GreenLantern1
How would you show a modular arithmetic proof of this problem? I am not quite sure :|

EDIT: And can you use modular arithmetic in STEP, since it isn't on the A Level course?

If it holds for 0,1,2 then it holds for all n as (3n+k)^3 = k^3 mod 3, 7(3n+k) = 7k mod 3 for any n. (and any integer can be written as 3n + k where k is 0, 1 or 2)
I have a question. Does the statement that if a certain number is a zero of a polynomial and has a n multiplicity then it is a zero of all derivatives of this polynomial up to (n-1)th need to be proved or can it be taken for granted? While doing a STEP question of course..

Thanks for help :smile:
Original post by zuzia.kru
I have a question. Does the statement that if a certain number is a zero of a polynomial and has a n multiplicity then it is a zero of all derivatives of this polynomial up to (n-1)th need to be proved or can it be taken for granted? While doing a STEP question of course..

Thanks for help :smile:


Which question? (I only ask because I remember a question which effectively asks you to prove it).
Original post by shamika
Which question? (I only ask because I remember a question which effectively asks you to prove it).


Question 2 in STEP II from 1994
It says 'explain'...
Original post by zuzia.kru
I have a question. Does the statement that if a certain number is a zero of a polynomial and has a n multiplicity then it is a zero of all derivatives of this polynomial up to (n-1)th need to be proved or can it be taken for granted? While doing a STEP question of course..

Thanks for help :smile:


Just curious, what does it mean?
And, do you want to say that if some number A is a zero of f(x), than the value of f''''''''(derivative)(A)=0?
Original post by zuzia.kru
Question 2 in STEP II from 1994
It says 'explain'...


I would...

Spoiler

Original post by zuzia.kru
Question 2 in STEP II from 1994
It says 'explain'...


As it says "explain", you can probably go for something like -

"if f(x) = p(x)(x-a)^n for some integer n, polynomial p, then

f'(x) = np(x)(x-a)^(n-1) + p'(x)(x-a)^n.

so a is a zero of f' with multiplicity n-1.

Applying this result to f, then f', ... f^(n-1) shows us a is a zero of f^(n-1)"

If it asked you to prove it, it'd probably be easiest to replace the last line of that with an induction argument.
Original post by shamika
I would...

Spoiler




Original post by matt2k8
As it says "explain", you can probably go for something like -

"if f(x) = p(x)(x-a)^n for some integer n, polynomial p, then

f'(x) = np(x)(x-a)^(n-1) + p'(x)(x-a)^n.

so a is a zero of f' with multiplicity n-1.

Applying this result to f, then f', ... f^(n-1) shows us a is a zero of f^(n-1)"

If it asked you to prove it, it'd probably be easiest to replace the last line of that with an induction argument.



Thank you both...I will now know how to deal with 'explain' :smile:



Original post by Dog4444
Just curious, what does it mean?
And, do you want to say that if some number A is a zero of f(x), than the value of f''''''''(derivative)(A)=0?


If a zero of polynomial has a certain multiplicity it means that that polynomial is divisible by (x−a)n(x-a)^n where n is the multiplicity of that zero.....this also means that on the graph in the point (a,0) the graph crosses the axis when n is odd and it "turns around" when n is even.

I hope I explained it well.... anyway, here is the link to another explanation : http://www.mathwords.com/m/multiplicity.htm
I always use that website when I don't know what something means, because I'm not a native english speaker, and I found it very helpful :smile:
Reply 1510
Avatar for gff
gff
5
Original post by zuzia.kru

I always use that website when I don't know what something means, because I'm not a native english speaker, and I found it very helpful :smile:


A bit more legitimate one.
What would constitute an acceptable answer to "describe the subsequent motion" for the last bit of STEP III 1994 Q9? I did the following:

Spoiler



Is that enough for "describe" or would they be looking for a more mathematical explanation?
Original post by zuzia.kru
I have a question. Does the statement that if a certain number is a zero of a polynomial and has a n multiplicity then it is a zero of all derivatives of this polynomial up to (n-1)th need to be proved or can it be taken for granted? While doing a STEP question of course..

Thanks for help :smile:


2000 STEP II Q2

I think you need to prove this result whenever you use it.
Reply 1513
Avatar for TSong
TSong
Q15 STEP III 1988
Is it possible to do this question even if you know nothing about random process?
(edited 12 years ago)
Original post by Ree69
I just emailed [email protected], confirming that we're allowed to do the exam in pencil.

She said no. Answers must be written in black or ball point pen.

I feel so heartbroken. :emo:


you got told wrong....Siklos today just confirmed you can use anything as long it aint red :tongue:

lots of posts to catch up on :colone:
Reply 1515
Avatar for Ree69
Ree69
14
Original post by Rahul.S
you got told wrong....Siklos today just confirmed you can use anything as long it aint red :tongue:

lots of posts to catch up on :colone:


Really?! In the email I received I was told you can't use pencil and that they'll soon ammend the FAQs on the STEP section of the Cambridge Assessment website.
Original post by Ree69
Really?! In the email I received I was told you can't use pencil and that they'll soon ammend the FAQs on the STEP section of the Cambridge Assessment website.


you can use anything as long PREFERABLY it aint red. Siklos said that today :tongue: so if you want to use pencil......then use it. the actual paper scripts are marked btw; thats why it doesnt really matter as long the writing is legible.
Reply 1517
Avatar for Ree69
Ree69
14
Original post by Rahul.S
you can use anything as long PREFERABLY it aint red. Siklos said that today :tongue: so if you want to use pencil......then use it. the actual paper scripts are marked btw; thats why it doesnt really matter as long the writing is legible.


Yeah I know they're manually marked and not scanned in or anything (unlike A-Levels) but this damn woman said I still have to use pen!

Let me show you the email:

Hi ******

I have now spoken to our Head of Assessment and have a definitive answer. The correct answer is that you should use a black ink or ball point pen and NOT a pencil.

The reason for this is that the markers like to be able to see your working out towards a solution. No marks are deducted for what you might perceive to be silly working out. Marks can be awarded for the method you use in working towards a solution. The markers want to be able to see your working out and don't want candidates rubbing anything out. Hence, why you are asked to put all the questions you attempted on the front grid of the answer booklet. even if you start a question and then score it out and never go back to it.

I will see that the use of the pencil is taken out from the FAQ section.

Thank you very much for bringing this is to our attention adn make sure you have a black pen on the day. No correction fluid though!

Good luck!

Best wishes

Annie


I then pleaded with her that some of my best work is done in pencil. This was then followed by:

Dear ******

It will be better if you do use a ball point pen to complete the STEP papers, ball point ink does tend to dry quickly and will not smodge. As my colleague said (below) you should not use any correction fluid or erase any of your work - any errors should simply have a line drawn through them and the answer continued below it. This is because even if the answer is wrong, the markers will still give you points for correct method. So you could lose points if you erase an incorrect answer.

best wishes,
Sandi Spence
Admissions Testing Service
Cambridge Assessment www.atsts.org.uk/


...bastards. :cool:
Original post by Ree69
Yeah I know they're manually marked and not scanned in or anything (unlike A-Levels) but this damn woman said I still have to use pen!

Let me show you the email:



I then pleaded with her that some of my best work is done in pencil. This was then followed by:



...bastards. :cool:


ignore it...if you REALLY want to use pencil...you can. although I like my maths in pen :colone:
Original post by Ree69
...


Original post by Rahul.S
ignore it...if you REALLY want to use pencil...you can. although I like my maths in pen :colone:


No, don't ignore it. (Surely you use pen for your A-Levels anyway?)

It sounds like the examining team gave your request some thought, and gave you (well, at least I thought it was) a reasoned explanation for why they want you to use a pen.

Rule number one: don't antagonise the person marking your script. But there's an even more basic reason for not using a pencil - it rubs and fades easily, meaning there is a danger your hard work is illegible by the time someone gets to mark it.

I know it must be annoying, and you don't want to have to forget old habits for the sake of an exam, but I would use a pen unless there is a very good reason not to.

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