****Leaving Certificate: Higher Level Maths Discussion****

Days 298

2thousand14 wrote: »

Dont think they give USC cut off points?

Ask the supervisor can you view his pay slip? Nah they will have to give it Id say. Its around 40000 i think

2thousand14

Days 298 wrote: »

Ask the supervisor can you view his pay slip? Nah they will have to give it Id say. Its around 40000 i think

On the first €10,036 2%
On the next €5,980 4%
On the balance 7%

Days 298

What is the proof of geometric series by induction??

XtotheZ

does anyone else struggle with Rates of change in diferentiation? I cant get my head around it atall :S

little sis...

Days 298 wrote: »

What is the proof of geometric series by induction??

2012 Q4 (A)

Shane15

Is financial maths going to come up for definite?

XtotheZ

Shane15 wrote: »

Is financial maths going to come up for definite?

guaranteed

aleatorio

XtotheZ wrote: »

does anyone else struggle with Rates of change in diferentiation? I cant get my head around it atall :S

It's a hard thing to grasp but once you get it it's fine

Basically, let's say your given the rate of change of the volume (dV/dt), and you want to find the rate of change of the radius (dr/dt)

First thing to note is that when they say 'rate of change' that means it was differentiated in terms of t, time.

So you have dV/dt, and you want to find dr/dt

So if you view them as fractions, you'd want to multiply dV/dt by dr/dV to get the dV's to cancel and leave you with dr/dt, the thing were trying to find

Want = Need x Given
dr/dt = dr/dV x dV/dt

If we know it's a sphere, say, we know the formula for it's volume in terms of r is 4/3 pi r^3
So dV/dr is 4 pi r^2
So we have what dV/dr is, but what we need is dr/dV - we simply just flip the expression, so we have 1/(4 pi r^2)

Then we just sub in 'r' which should be given, and multiply dr/dV by dV/dt (which we were given)

And that's it, the answer is dr/dt

2thousand14

XtotheZ wrote: »

guaranteed

its not guaranteed , paper 1 is the most unpredictable paper of all

XtotheZ

aleatorio wrote: »

It's a hard thing to grasp but once you get it it's fine

Basically, let's say your given the rate of change of the volume (dV/dt), and you want to find the rate of change of the radius (dr/dt)

First thing to note is that when they say 'rate of change' that means it was differentiated in terms of t, time.

So you have dV/dt, and you want to find dr/dt

So if you view them as fractions, you'd want to multiply dV/dt by dr/dV to get the dV's to cancel and leave you with dr/dt, the thing were trying to find

Want = Need x Given
dr/dt = dr/dV x dV/dt

If we know it's a sphere, say, we know the formula for it's volume in terms of r is 4/3 pi r^3
So dV/dr is 4 pi r^2
So we have what dV/dr is, but what we need is dr/dV - we simply just flip the expression, so we have 1/(4 pi r^2)

Then we just sub in 'r' which should be given, and multiply dr/dV by dV/dt (which we were given)

And that's it, the answer is dr/dt

thats really helpful thanks

XtotheZ

2thousand14 wrote: »

its not guaranteed , paper 1 is the most unpredictable paper of all

Though it was always up, deffo be up in Paper 2 tho?

Saskatchewan

The only thing that is certain for paper 1 is tears

aleatorio

I'm actually kind of looking forward to this... How sad am I :pac:

XtotheZ

aleatorio wrote: »

I'm actually kind of looking forward to this... How sad am I :pac:

Im somewhat the same, i like a challenge.. although that will change as soon as i get in there.

Saskatchewan

May the logs be in your favour

stevemanu

Anoyone have answers for the financial Maths question on the deb mock ? We didn't have it covered before the mock so I didn't do it. Just doing it now to test myself. Please and thank you

aleatorio

XtotheZ wrote: »

Im somewhat the same, i like a challenge.. although that will change as soon as i get in there.

Yeah same for me probably :pac:

Just hoping for proof of de Moivres by induction or a geometric series by induction, the amortization proof and a nice complex numbers q XD

For the proof of de Moivres, if they don't specify, do you have to do it for positive, negative and 0, or?

Saskatchewan

stevemanu wrote: »

Anoyone have answers for the financial Maths question on the deb mock ? We didn't have it covered before the mock so I didn't do it. Just doing it now to test myself. Please and thank you

for part i 0.367%
Part II €2344 to nearest euro

aleatorio

Saskatchewan wrote: »

for part i 0.367%
Part II €2344 to nearest euro

Could you be amazing and post the question...? I did the examcraft mock

aleatorio

Need some clarification:

When doing the geometric series financial maths qs,

If you're given the amount borrowed and need to find the repayments, you use the P=F/(1+i)^t formula

And when you're given the total amount of savings and want to find the amount paid monthly/yearly you use F=P(1+i)^t
Yeah?

Mario95

What do we need to have for the exam? pencil, pen, ruler, calculator... is there anything else?

Peregrine

aleatorio wrote: »

For the proof of de Moivres, if they don't specify, do you have to do it for positive, negative and 0, or?

They should specify.

Mario95 wrote: »

What do we need to have for the exam? pencil, pen, ruler, calculator... is there anything else?

Compass.

aleatorio

Nimrod 7 wrote: »

They should specify.

Ok grand
Hopefully not negative... Don't like that one :pac: I get all confused with letting n= -p and subbing it back in at the end

Peregrine

aleatorio wrote: »

Ok grand
Hopefully not negative... Don't like that one :pac: I get all confused with letting n= -p and subbing it back in at the end

Pray for n = 0

2 lines. ****ing win.

:pac:


Won't happen though

XtotheZ

Mario95 wrote: »

What do we need to have for the exam? pencil, pen, ruler, calculator... is there anything else?

Idk do you need it but i bring everything in compass, set squares etc

Saskatchewan

aleatorio wrote: »

Could you be amazing and post the question...? I did the examcraft mock

im not sure how to upload pictures from my phone. But it basically asks:

Find the value of 4.5% aer if compunded monthly for part I

Part 2 asks: if a member of the club can make 12 equal monthly installments of 200 euro at 4.5% find how much a member would pay in advance.

Hope this helps, sorry again

XtotheZ

Saskatchewan wrote: »

im not sure how to upload pictures from my phone. But it basically asks:

Find the value of 4.5% aer if compunded monthly for part I

Part 2 asks: if a member of the club can make 12 equal monthly installments of 200 euro at 4.5% find how much a member would pay in advance.

Hope this helps, sorry again

I couldnt understand that part atall, it was phrased so badly

Saskatchewan

XtotheZ wrote: »

I couldnt understand that part atall, it was phrased so badly

I think you mean in the actual mock? Well if you do, it was. Makes no sense because they left out the fact they they pay the same amount, present values etc. Also why would someone who is paying in advance need to pay the 4.5% aer. Was ridiculous! I just did a quick amortisation formula in 6\7 lines and git it right.... Even though its wrong...

Emilyjaneoh

Does anyone have the proof for the amortisation formula? Just heard about it there, and would it take long to learn?

Shane15

Emilyjaneoh wrote: »

Does anyone have the proof for the amortisation formula? Just heard about it there, and would it take long to learn?

I learnt it this morning, it's not too bad.

Edit: Oh nevermind, I misread this. I'm unsure.

Emilyjaneoh

Emilyjaneoh wrote: »

Does anyone have the proof for the amortisation formula? Just heard about it there, and would it take long to learn?

Sorry I seen it, thanks daniel!

plmko

FatRat wrote: »

Also there are two proofs ye are leaving out:

Tn=Sn-Sn-1
Sn= a(1-r^t) / 1-r

@FatRat how do you prove Tn = Sn - Sn-1??

plmko

Daniel2590 wrote: »

Prove √2 is irrational
Construct √2 and √3
Proof by induction:
1+2+...+n
1²+2²+...+n²
1³+2³+...+n³
a+ar+ar²+...+ar^(n-1) = a(1-r^n) / 1-r
De Moivre's theorem for n E N, n=0 & n E Z.
Derive sum to infinity
Amortisation formula

Don't think we need N E Z for De Moivres anymore!

XtotheZ

Saskatchewan wrote: »

I think you mean in the actual mock? Well if you do, it was. Makes no sense because they left out the fact they they pay the same amount, present values etc. Also why would someone who is paying in advance need to pay the 4.5% aer. Was ridiculous! I just did a quick amortisation formula in 6\7 lines and git it right.... Even though its wrong...

oh yeah i did mean the actual mock :P

2thousand14

Emilyjaneoh wrote: »

Does anyone have the proof for the amortisation formula? Just heard about it there, and would it take long to learn?

http://www.projectmaths.ie/documents/teachers/geometric_Seq_ser.pdf

page 14

plmko

PaleMoonlight wrote: »

How do you prove the Amortisation formula? I don't remember learning how and can't find it in my book

You use Sum of Natural Numbers to do it

ms.tinx

Ok so what is like 95% guaranteed to be on paper 1?

eefah

It seems like that for the proofs, even if you don't know them all word for word, you can get through a lot of them just through logic and the steps of induction ....?
Am I right in saying that, or is desperation clouding my judgement?

2thousand14

eefah wrote: »

It seems like that for the proofs, even if you don't know them all word for word, you can get through a lot of them just through logic and the steps of induction ....?
Am I right in saying that, or is desperation clouding my judgement?

once you know how to start it off its grand

ms.tinx

eefah wrote: »

It seems like that for the proofs, even if you don't know them all word for word, you can get through a lot of them just through logic and the steps of induction ....?
Am I right in saying that, or is desperation clouding my judgement?

Well if you know induction really nd ur basics for proofs then ur fine

Mario95

Emilyjaneoh wrote: »

Does anyone have the proof for the amortisation formula? Just heard about it there, and would it take long to learn?

Try this: en.wikipedia.org/wiki/Amortization_calculator#Derivation_of_the_formula
I like the way they did it, its really easy to understand.

ms.tinx

Its so funny we're all here discussing the "tipped topics" rather than actually studying them... :-D ... lol

FatRat

plmko wrote: »

@FatRat how do you prove Tn = Sn - Sn-1??

Sn = T1 +T2 +T3 ... + Tn-1 +Tn
Sn-1 = T1 +T2 +T3 ... + Tn-1

You minuse Sn-1 from Sn and the difference between them is Tn

Sn-Sn-1 = Tn

eefah

Fúck it, I might just take this paper for loss and spend a full day over the weekend revising for paper 2 .....

Days 298

I think this thread has to much emphasis on derivations! :L

Trapozoidal rule with integration may come up and be worth multiplies of them!

XtotheZ

pen or pencil? apparently on the pink paper pencil can be hard to read

Daithi MacG

FatRat wrote: »

Also there are two proofs ye are leaving out:

Tn=Sn-Sn-1
Sn= a(1-r^t) / 1-r

@FatRat How do you prove the Sn=a(1-r^t) / 1-r?

aleatorio

Finding asymptotes of an equation, would the vertical asymptote just be whatever it isn't defined for? And the horizontal would be lim(x-infinity) of the eqn?

little sis...

aleatorio wrote: »

Finding asymptotes of an equation, would the vertical asymptote just be whatever it isn't defined for? And the horizontal would be lim(x-infinity) of the eqn?

Vertical asymptote is letting denominator = 0 so yes
and yes for horizontal also.

eefah

aleatorio wrote: »

Finding asymptotes of an equation, would the vertical asymptote just be whatever it isn't defined for? And the horizontal would be lim(x-infinity) of the eqn?

I think you're right for the vertical asymptote, but I've no idea about the horizontal ones.