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#11226 2013-06-06 06:17:45

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

So far I did Q1, Q2, Q3, and am about to finish Q5 when I start under mock exam conditions again.

#11227 2013-06-06 06:22:32

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

That is very good!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11228 2013-06-06 06:23:32

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Thanks -- do you agree that those are the easiest?

#11229 2013-06-06 06:25:51

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

I hope not, I have not looked at the others yet.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11230 2013-06-06 06:27:15

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

You are writing solutions to them?

#11231 2013-06-06 06:30:14

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

Nope, I am wondering how to do them.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11232 2013-06-06 06:31:08

anonimnystefy
Real Member

Offline

Re: Linear Interpolation FP1 Formula

Hi zf.

Do you have a link to the exam paper?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#11233 2013-06-06 06:32:28

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

maths helper . co . uk / oxb . htm (remove spaces)

Please don't post solutions or spoilers to any (yet) as I want to finish them under exam conditions.

#11234 2013-06-06 06:38:35

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

That is a better link , I can download it.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11235 2013-06-06 06:39:09

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Yeah it's the best link to use, although some of the links stopped working recently...

#11236 2013-06-06 06:47:27

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

I am looking at 1.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11237 2013-06-06 06:49:59

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I thought you might like that question, it is similar to some GF problems we did...

#11238 2013-06-06 06:52:19

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

That is what I am doing with it. It is a partition problem actually. We can look at it when you are done, if you like.

There are a few others that are mean. I am going shopping see you when I get back and good luck.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11239 2013-06-06 07:06:04

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Sure, that would be great.

Okay, see you later.

#11240 2013-06-06 07:28:12

anonimnystefy
Real Member

Offline

Re: Linear Interpolation FP1 Formula

You are doing STEP II, year 2012?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#11241 2013-06-06 08:17:40

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Yes, I just finished that one, haven't checked my answers yet though. Thought it was quite a nice paper, lots of accessible questions not requiring that much work. Hopefully the mark scheme will not be harsh.

#11242 2013-06-06 08:32:01

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Just done marking... lots and lots of silly errors but definitely a solid 1 or possibly a low S if I got a generous examiner. Happy times! I am just glad I did not embarrass myself.

I did Q1-5 and 13. The cyclic quadrilateral one looked like it would take a long time to manipulate algebraically so I skipped that and did a shorter question so I could spend the last 5 minutes or so checking over.

#11243 2013-06-06 11:17:16

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

That is very good.

I was looking at Q12 also. Seemed like a nice problem.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11244 2013-06-06 11:18:43

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

The probability one?

#11245 2013-06-06 11:30:12

bobbym
Administrator

Offline

Re: Linear Interpolation FP1 Formula

Yes, I have not looked at it because I just got back home. It was like 110 or something over there.

Did you want to go over the coefficient problem or you are comfortable with the solution you have?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11246 2013-06-06 19:47:58

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I am interested in seeing how you did it -- given that they asked for the co-efficient of x^k for (relatively) small k, I just used arithmetic.

#11247 2013-06-06 19:56:16

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

Hope I can remember it offhand. Correct me if I make some silly mistake.

We are interested in the coefficient of x^24 of



is that correct?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11248 2013-06-06 19:59:26

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I think so. And the answer was 15?

#11249 2013-06-06 20:18:10

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

If we think of this as a partition problem then that has the polynomial representation of.



This is the generating polynomial for the number of ways you can form a sum using sixes and threes. We can now enumerate the possibilities by filling in the 3 polynomials.

You can have

(4 sixes)(0 threes) 1 way
(0 threes)(4 sixes) 1 way
(3 sixes)(1 six)(0 threes) 1 way
(1 six)(3 sixes)(0 threes) 1 way
(2 sixes)(2 sixes)(0 threes) 1 way

(2 sixes)(1 sixes)(2 threes) 1 way
(1 sixes)(2 sixes)(2 threes) 1 way
(3 sixes)(0 sixes)(2 threes) 1 way
(0 sixes)(3 sixes)(2 threes) 1 way

(1 sixes)(1 sixes)(4 threes) 1 way
(2 sixes)(0 sixes)(4 threes) 1 way
(0 sixes)(2 sixes)(4 threes) 1 way

(1 sixes)(0 sixes)(6 threes) 1 way
(0 sixes)(1 sixes)(6 threes) 1 way

(0 sixes)(0 sixes)(8 threes) 1 way

total ways 15.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11250 2013-06-06 20:27:35

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Oh I see, so you treated (1 - x^6)^(-2) as the square of a geometric series. That looks pretty neat. The binomial expansion of it has the triangular numbers as co-efficients (and then I used the same method as you, pairing up the exponents).

You did the same thing for the last part?

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