Remainder Theorem for higher level maths?

damienricefan

I can't find it in my text book anywhere so can somebody link me to a proof or somewhere in past exams where t'was asked?

It's a possibilty on paper one not two right?

Regards

likely_lass

there is no remainder thoerem proof??????????

damienricefan

likely_lass wrote: »

there is no remainder thoerem proof??????????

really?

my grinds teacher told me to learn it!! maybe he's go mad :pac:

alan4cult

It's not on the syllabus.
It says it here

http://www.education.ie/servlet/blobservlet/lc_maths_sy.pdf?language=EN

Use of Remainder theorem not required.

damienricefan

alan4cult wrote: »

It's not on the syllabus.
It says it here

http://www.education.ie/servlet/blobservlet/lc_maths_sy.pdf?language=EN

Use of Remainder theorem not required.

oohh right , thanks everyone!!!

DJ Hafez

Any website that has all the proofs?

awhir

ya really stuck on what proofs there are for paper 1 ..

likely_lass

factor thoerem
de moivre & de moivre for -n (which could come up even though the + part was on last year)
First principals - (u+v) (uv) (u/v) (x^n) ..(x^2) (x^3) (1/x) (sq root of x) (sin x) (cos x)

trig identities cos (a+B) is overdue



how nice am i ?

Yah, it's not on the syllabus. It's a pity it isn't, because there's a nice proof of the Factor Theorem using it.

As for the proofs on the syllabus: give a search back through the the last few pages, because there was a full list posted about a week ago.

zodac

likely_lass wrote: »

factor thoerem
de moivre & de moivre for -n (which could come up even though the + part was on last year)
First principals - (u+v) (uv) (u/v) (x^n) ..(x^2) (x^3) (1/x) (sq root of x) (sin x) (cos x)

trig identities cos (a+B) is overdue



how nice am i ?

trig identities rnt on paper 1 are they? Im pretty sure theyre on p2. Also the differential rule by induction is a proof for p1 and it hasnt been asked recently.
Most r expecting quotient and/or product rule proofs for diff and maybe sinx from first principles;)

RayCarley

zodac wrote: »

trig identities rnt on paper 1 are they? Im pretty sure theyre on p2. Also the differential rule by induction is a proof for p1 and it hasnt been asked recently.
Most r expecting quotient and/or product rule proofs for diff and maybe sinx from first principles;)

No, trig equations are on Paper 2, so no need to worry about them for tomorrow.


Don't forget about proving the Volume of a cone and sphere in Q8-Intergration

If proof of the quotient rule comes up, do people think it would be "safe" to just prove the product rule from first principles, and then rearrange it algebraically to get the quotient rule? It's far less time consuming than proving the quotient rule straight out. And, you're still basing your quotient rule derivation technically on first principles (as you've proved the product rule that way).

I'm ignoring the natural log method for the moment, I think it's too risky.

Thoughts?

aisling.laura

I only know the natural log method, we were never taught another way and its the only method in my book...

why is it risky?

alan4cult

aisling.laura wrote: »

I only know the natural log method, we were never taught another way and its the only method in my book...

why is it risky?

It ain't from first principles because you're assuming ln(x) differentiates to 1/x.

aisling.laura

alan4cult wrote: »

It ain't from first principles because you're assuming ln(x) differentiates to 1/x.

aaahh gotcha.
thanks.

well i'm a bit screwed if that one comes up then!

As far as I know, they're accepting the natural log method until the next syllabus change.

rcaz

Can the induction proofs come up outside the induction question?

I'm not gonna do any induction tomorrow, can they ask an induction proof in a calculus question?

Got my first principals DOWN though

aisling.laura

-JammyDodger- wrote: »

As far as I know, they're accepting the natural log method until the next syllabus change.

phew!
hope your right.
i'm sure they'll throw me a few attempt marks if i do that one right anyways...

Fringe

El Pr0n wrote: »

Can the induction proofs come up outside the induction question?

I'm not gonna do any induction tomorrow, can they ask an induction proof in a calculus question?

Got my first principals DOWN though

There's the induction proof for the differentiation rule.

rcaz

Fringe wrote: »

There's the induction proof for the differentiation rule.

I know that. I'm asking do they put that in Q5, or in Q6/7.

El Pr0n

El Pr0n wrote: »

I know that. I'm asking do they put that in Q5, or in Q6/7.

I've never seen it in question 6 or 7, and I highly doubt they would put it there. Questions 6 and 7 are for differentiation only (as far as I'm aware); the proof of the differentiation rule using induction isn't differentiation.

P.S. Anyone know if the only volumes they can ask are of the cone and the sphere? Or can they give spin-offs of those two?

rcaz

-JammyDodger- wrote: »

I've never seen it in question 6 or 7, and I highly doubt they would put it there. Questions 6 and 7 are for differentiation only (as far as I'm aware); the proof of the differentiation rule using induction isn't differentiation.

P.S. Anyone know if the only volumes they can ask are of the cone and the sphere? Or can they give spin-offs of those two?

Well, they're the only two we were told to learn off. Can't they do random curves like an area question? So you just stick in (pi)|y^2dx?

zodac

El Pr0n wrote: »

Well, they're the only two we were told to learn off. Can't they do random curves like an area question? So you just stick in (pi)|y^2dx?

Yeah, the only specific volumes we need to learn are sphere and cone. The vol of a cone came up in 2005 so a sphere is due. They could also ask the area between a curve and a line.

aisling.laura

2006 Q6 (c) was the proof of the differential rule by induction.

so yup they do put it in there!

xOxSinéadxOx

aisling.laura wrote: »

2006 Q6 (c) was the proof of the differential rule by induction.

so yup they do put it in there!

it's bad that I don't know what this is isn't it?
we never did proof by induction/binomial thereom and all that stuff

Crap. Going to have to go over that now.

SligoBrewer

-JammyDodger- wrote: »

Crap. Going to have to go over that now.

Just did it. It's fairly simple.

And DeMoivre came up last year in Q3 so..