Marking schemes!!!

JC 2K3

Ah, I actually did a lot better in App Maths than I thought, having looked at that marking scheme. My A2 was justified it seems. Question 2 let me down. I think I was fairly close to getting 1(b)(ii) - I thought I was miles off.

Papers will be interesting to see on Saturday..

EDIT: Ha! Physics Q3 - what was all that bs about having to have the line cutting the X and Y axises about?

ZorbaTehZ

I thought that they were extremely fair with Physics tbh, if you look at the graph on question 3 and 4 they accepted a lot of things that I thought they wouldn't, and look at that question that everyone was kicking a fuss up about on question 2 where they did the same. Another question they were very fair on was the Charges question (think it was Q7?).

Tech Drawing - PII question 1 didn't get heavily adjusted as I thought. The roads question, they were very fair with too.

Haven't really looked at any others yet except maths, which was ok I thought.

carlowboy

JC 2K3 wrote:

Ah, I actually did a lot better in App Maths than I thought, having looked at that marking scheme. My A2 was justified it seems. Question 2 let me down. I think I was fairly close to getting 1(b)(ii) - I thought I was miles off.

Papers will be interesting to see on Saturday..

EDIT: Ha! Physics Q3 - what was all that bs about having to have the line cutting the X and Y axises about?

It's that 1/f = the point where it cuts the axis.

JC 2K3

Yup, but the marking scheme says you can jst get the average value.

carlowboy

Yeah, probably because the SEC only checked the syllabus after sending out the exam!

Gangsta

JC 2K3 wrote:

Yup, but the marking scheme says you can jst get the average value.

There are usually alternate answers which are quite acceptable.

sd123 wrote:

No, Keep walking

me challenges you to a maths test!:D

Aoibheann Brady wrote:

Join the club!

Hey, post your support for an RCSI forum:) http://www.boards.ie/vbulletin/showthread.php?t=2055138705

sd123

Gangsta wrote:

me challenges you to a maths test!:D

Bring it on BITCH....:cool:
Lets find out what % you got in maths when you know :rolleyes:

JC 2K3

I'll set the first question:

Find the value of the square root of 2 using a MacLaurin series.

ZorbaTehZ

Omg such nerds ...

(I'm putting my money on sd123 mwahaha :cool:)

Aoibheann

Gangsta wrote:

Hey, post your support for an RCSI forum:) http://www.boards.ie/vbulletin/showthread.php?t=2055138705

Done! *crosses fingers that it works*

sd123

ZorbaTehZ wrote:

Omg such nerds ...

yea, pretty nerdy, believe it or not, i know the answer to 9 decimal places off by heart, but no way of proving it here

(I'm putting my money on sd123 mwahaha :cool:)

is that my reward for saying that YOU were the best at maths:)

off i go to try to remember how to do maclaurin seres. answer to come soon hopefully:rolleyes:

ZorbaTehZ

Gangsta wrote:

Hey, post your support for an RCSI forum:) http://www.boards.ie/vbulletin/showthread.php?t=2055138705

Ghey.

Gangsta

ZorbaTehZ wrote:

Ghey.

What?

sd123

JC 2K3 wrote:

I'll set the first question:

Find the value of the square root of 2 using a MacLaurin series.

Ok, if anyone remotely cares, i went as far as (x^12)/12! and got 1.420916804.

v--2 = 1.414213562 on a calculator

JC 2K3

No, not accurate enough I'm afraid.

(lol, the only reason I asked that was because root2 is something like 150 digits long )

Thomas_S_Hunterson

JC 2K3 wrote:

(lol, the only reason I asked that was because root2 is something like 150 digits long )

It's irrational, it goes on forever

dan719

JC 2K3 wrote:

No, not accurate enough I'm afraid.

(lol, the only reason I asked that was because root2 is something like 150 digits long )

*Cough* Root 2 is irrational so it cannot be written down*cough*

JC 2K3

hmmm... where did I hear it was 150 digits then?

meh.

genericgoon

I assume they were looking for an approximate value in the question.

dan719

You can prove that it's irrational using the method of infinite descent.(a particular case of proof by contradiction)
Assume root two can be written as a fraction
E.g p/q
But this must be divisible by two (because p/q all to be squared is equal to two)
Therefore root two is equal to p/2x and this can be repeated ad infinitum. But we cannot simplify fractions for ever- therefore this is a contradiction, therefore root two can't be written as a fraction and is irrational.
p.S I don't know if it was Fermat who proved the irrationality of root two but it was he who turned the method of infinite descent into such a powerful tool.

rjt

dan719 wrote:

You can prove that it's irrational using the method of infinite descent.(a particular case of proof by contradiction)
Assume root two can be written as a fraction
E.g p/q
But this must be divisible by two (because p/q all to be squared is equal to two)
Therefore root two is equal to p/2x and this can be repeated ad infinitum. But we cannot simplify fractions for ever- therefore this is a contradiction, therefore root two can't be written as a fraction and is irrational.
p.S I don't know if it was Fermat who proved the irrationality of root two but it was he who turned the method of infinite descent into such a powerful tool.

Supposedly this was discovered by one of Pythagoras' students (who was subsequently thrown in a river and drowned by Pythagoras, for questioning the belief that all numbers were rational). The proof via infinite descent is generally attributed to Euclid I believe (although IIRC it's not kown if Euclid proved these things himself or if he was simply the first to write them all down).

The same method can be used to show that root(p) is irrational for all primes p (and with a little more work it can be shown that root(n) is irrational for all n that are not the square of a natural number).

<pedantic>
"But this must be divisible by 2..." - How is a fraction divisible by 2?
</pedantic>

dan719

p/q all to be squared equals 2
therefore p/2q all to be squared=1
therefore p/2q=1
I just allowed 2q=x

Sorry for not being explicit.
Ah yes I forgot the Pythagoras story, it was a huge secret because it disagreed with his philosophy that number was perfect.

sd123

JC 2K3 wrote:

No, not accurate enough I'm afraid.

(lol, the only reason I asked that was because root2 is something like 150 digits long )

Even if you were right about root2 being 150 digits long, did you really expect someone to ACTUALLY do out 150 derivatives??? Also, even if i did, is it not true that it would probably never be exactly correct using this method anyway?

dan719

Btw sd123 are you doing medicine or TP?

MathsManiac

dan719 wrote:

p/q all to be squared equals 2
therefore p/2q all to be squared=1
therefore p/2q=1
I just allowed 2q=x

Sorry for not being explicit.
Ah yes I forgot the Pythagoras story, it was a huge secret because it disagreed with his philosophy that number was perfect.

Dan, your proof is all over the place - no wonder rjt queried it. What you've given above doesn't stand up either. (For example, the second line doesn't follow from the first.)

The standard proof goes as follows:
Suppose sqrt(2) can be written as a fraction. Then it can be written as a fraction in simplest form. That is, can be written as p/q, where p and q are integers that do not share a common factor.

Now, p/q = sqrt(2) implies p^2 = 2(q^2).
Since 2 is a factor of the right hand side, it must a factor of the left hand side.
Since 2 divides p^2 then it must divide p, (because 2 is a prime number and, by definition, if a prime number divides a product ab, it must divide a or b).
So now we know that p is even, we can write p=2t, where t is an integer.
Therefore, p^2 = 4(t^2)
That is, 4(t^2) = 2(q^2)
So 2(t^2) = q^2.
So, we now know that 2 divides q^2 and must therefore divide q.
We've now established a contradiction, (by showing that 2 is a common factor of p and q, which were supposed not to have a common factor.)
Therefore, the initial assumption is false, and sqrt(2) cannot be written as a fraction of integers.

dan719

yeah what he said, knew I had messed it up.

I may really go brush up on some maths before college.

rjt

MathsManiac: What course are you doing? It seems that all the maths people are doing TP or CS.

sd123

dan719 wrote:

Btw sd123 are you doing medicine or TP?

I'm doing TP, for now at least! Turned out that med was 580* in trinity on 2nd round and i never got offered it. I'm getting chem remarked so if that goes up i'll have 590. Dunno if I'll even take med now if i'm offered it... Can't wait for TP

dan719

*High five*. Yeah I can't wait either, even if mathsmaniac did just absolutely whoop my ass.:D Should be 'interesting' anyway. If not particularly conjuicive to a social life.

rjt

dan719 wrote:

*High five*. Yeah I can't wait either, even if mathsmaniac did just absolutely whoop my ass.:D Should be 'interesting' anyway. If not particularly conjuicive to a social life.

Grr, traitors! :P

Yeah, clearly Mathematics is the course you should've done if you're looking for an active social life