Math Proof Predictions(Higher).

BLARG

I've been told that the factor theorem is quite likely. Anything else I should cram in?

~Candy~

yay, the factor one..

i d be watching sin and cos from first principle:D

Product and quotient rules from first principles.

Prowetod

-JammyDodger- wrote: »

Product and quotient rules from first principles.

This question has probably been asked a thousand times already but still not sure.
Can you use logs to prove them or do you have to use first principles?

BLARG

eoccork wrote: »

This question has probably been asked a thousand times already but still not sure.
Can you use logs to prove them or do you have to use first principles?

If it says in the question to use first principles, then you have to use first principles.

TanG411

I'd learn all the proff by 1st principals because 1 nearly always comes up. And they're easy aswell.

The 1st principals also includes the product, quotient rule etc.

eoccork

eoccork wrote: »

This question has probably been asked a thousand times already but still not sure.
Can you use logs to prove them or do you have to use first principles?

There has been a bit of talk about this - read the report that was posted in a thread a few pages back - and, in 2007 anyway, you were allowed to use logs to prove both rules.

xOxSinéadxOx

what is this logs method you speak of? I hope the factor theorem comes up. only proof I know

rcaz

Haven't they never asked the Quotient rule ever? My teacher reckons they never will ask it.

xOxSinéadxOx

xOxSinéadxOx wrote: »

what is this logs method you speak of? I hope the factor theorem comes up. only proof I know

It's given in the wiki article on both the product and quotient rules. Here: http://en.wikipedia.org/wiki/Product_rule#Alternative_proof:_using_logarithms

Same goes with the quotient rule.

El Pr0n wrote: »

Haven't they never asked the Quotient rule ever? My teacher reckons they never will ask it.

No it hasn't ever been up as far as I'm aware. It's tedious to prove using first principles, anyway.

If it comes up, prove the product rule first, then, instead of using uv in the product rule, use u.v^-1 (that's just u/v). If you do that, and do your algebra correctly, the quotient rule pops out. Far far easier than doing it the other way.

MathsManiac

-JammyDodger- wrote: »

If it comes up, prove the product rule first, then, instead of using uv in the product rule, use u.v^-1 (that's just u/v). If you do that, and do your algebra correctly, the quotient rule pops out. Far far easier than doing it the other way.

Surely you wouldn't need to prove the product rule first - since it's listed earlier in the syllabus, is it not a fair starting point?

But intriguingly, you need to use the chain rule also, which doesn't appear in the syllabus until AFTER the quotient rule. So would one not have to first prove the chain rule first, so as to demonstrate it's legitimacy in advance of the quotient rule?

timmywex

Any method is perfectly acceptable for product/quotient proof, they cant specifically ask by first principles. Yes they did a few years ago but they changed it now; See this letter

http://maths.slss.ie/resources/Reply%20to%20Query.doc

MathsManiac

timmywex wrote: »

Any method is perfectly acceptable for product/quotient proof, they cant specifically ask by first principles. Yes they did a few years ago but they changed it now; See this letter

http://maths.slss.ie/resources/Reply%20to%20Query.doc

That letter indicates that the log method is ok for the exam, not that any method is acceptable. The letter makes the point that the derivative of the log function is mentioned before the quotient rule in the syllabus, so I still have my doubts about whether the use of the chain rule is fair game.

Des23

Does the proof of the differentiation rule, x^n -> nx^n-1, by induction come up in Q5 or Q6 & Q7 or can it some up in both?

HQvhs

The last two times it came up it was in question 5 and 6. I assume it could be in question 7 also. So yeah, it seems as if it could appear in any of those questions.

Des23

I was just wondering since I'm not too fond of Q5, it's an easy proof anyway just a bit of first principles.

Slightly off topic but isn't Sequences and Series a lovely question?
They are after making it so easy the past few years... I wasn't planning on doing it because it was the last thing we did in school but I said I'd have a look at the exam questions and they are just delicious!:D
It's kind of fun aswell cos it is a bit of a departure from the other questions.

MathsManiac

MathsManiac wrote: »

Surely you wouldn't need to prove the product rule first - since it's listed earlier in the syllabus, is it not a fair starting point?

But intriguingly, you need to use the chain rule also, which doesn't appear in the syllabus until AFTER the quotient rule. So would one not have to first prove the chain rule first, so as to demonstrate it's legitimacy in advance of the quotient rule?

Damn it, you're right. I've never thought of that; I didn't really pay any notice to the chain rule coming in half way through. There goes that idea, as I doubt they'd accept a proof of the chain rule (a bit too long anyway).

It's pretty quick and simple to derive the quotient rule from the product rule, though. Just a minute or two of rearranging the formula. So, you think that since the the product rule comes earlier, it would be acceptable to assume that it's true for the sake of proving the quotient rule?

Also, what's your stance on the natural logarithm method, MathsManiac?

MathsManiac

-JammyDodger- wrote: »

So, you think that since the the product rule comes earlier, it would be acceptable to assume that it's true for the sake of proving the quotient rule?

Don't know, really. But that's the rationale used in the trig proofs, so it's hard to see how one could object.

-JammyDodger- wrote: »

Also, what's your stance on the natural logarithm method, MathsManiac?

Well, it's a bit of a cheat really, when you consider how complicated it is to establish the necessary properties of the ln function. But hey, if they're not going to penalise it...

MathsManiac

MathsManiac wrote: »

Don't know, really. But that's the rationale used in the trig proofs, so it's hard to see how one could object.

Might be a bit risky to do it that way then. Still, I think it's quicker to prove the product rule and then to rearrange it than it is to prove the quotient rule from scratch.

Well, it's a bit of a cheat really, when you consider how complicated it is to establish the necessary properties of the ln function. But hey, if they're not going to penalise it...

Yah, it is I suppose. The report the Chief Examiner gave was an interesting read. Still, I think it would be dangerous to do it that way, who knows when they'll start penalising it.

Just another question, I'll post it here other than starting a new thread.

Does anybody know if it's possible for the binomial theorem and induction can come up in question one and two? I know they're typically confined to question five, but, I'd just like to make sure.

MathsManiac

-JammyDodger- wrote: »

Yah, it is I suppose. The report the Chief Examiner gave was an interesting read. Still, I think it would be dangerous to do it that way, who knows when they'll start penalising it.

I think it was pretty clear that they would not require first principles until the next syllabus change.

MathsManiac

MathsManiac wrote: »

I think it was pretty clear that they would not require first principles until the next syllabus change.

Oh, really? I didn't realise that from reading it at all; I thought it would just have been more of a subtle change in the marking scheme or something. Looks like I'll be doing it that way if one comes up, so.

aine-maire

Have you guys picked what questions you're doing already?

I'm kinda planning on doing more than 6 (if there's a really sticky part c)........

The only thing I've ruled out is vectors!

Des23

Not doing Q5 on PI, I might do the 7 then, time permitting. I always have to come back and do a few part (b)s which I know I messed up on. If I dont get it the first time I move on rather than sticking at it.

Not doing the Circle on PII, don't know what it is but I really hate it (I have the exact same mental block for Optics in Physics, I know its easy but I just don't like it) , I'll prob do Q2-8 on PII aswell, provided I don't spend ages trying to figure stuff out. I'll probably have to do some of the Probability parts more than once.

galway.gaa

im leaving out 4 and 5 on p1 and im leavin out trig on p2 but if it came down to it id reckon id still be able to do 1 of the trig qs

aine-maire

Des23 wrote: »

Not doing the Circle on PII, don't know what it is but I really hate it (I have the exact same mental block for Optics in Physics, I know its easy but I just don't like it)

Yep that's how vectors is for me, I get that it's easy but I just don't like it/can't get my head around it!
Thank God it's just one question,if it was probability it'd be pretty bad :pac: