Leaving Certificate: Higher Level Maths Discussion

plmko · 05-06-2014 9:41pm

Daithi MacG wrote: »

Im about 95% sure binomial theorem is NOT on the course this year.

I'm gonna look over it incase, there's not too much to it!

And amortisation formula for whoever was asking, you need to be able to prove it

Oh and we have to be able to prove sum of n to infinity and to n

FatRat · 05-06-2014 9:43pm

I'll actually be annoyed if they don't ask for a proof of some sort tomorrow. I made an effort to learn those proofs, it'd be nice to know I'd didn't waste my time!

FatRat · 05-06-2014 9:50pm

Also there are two proofs ye are leaving out:

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

2thousand14 · 05-06-2014 9:51pm

so wait, pascals triangle is not on it?

Daniel2590 · 05-06-2014 9:52pm

2thousand14 wrote: »

so wait, pascals triangle is not on it?

You probably won't be asked it directly but it is on our course so you'll need to know how to do it for binomial expansion (especially if we're asked a identity using De Moivre's theorem)

Aspiring · 05-06-2014 9:53pm

Is there anywhere I can get a definitive list of things I need to learn off for tomorrow such as proofs?

I have some but not sure of everything we need.

2thousand14 · 05-06-2014 9:54pm

Daniel2590 wrote: »

You probably won't be asked it directly but it is on our course so you'll need to know how to do it for binomial expansion (especially if we're asked a identity using De Moivre's theorem)

and is the binomial theorem people have mentioned earlier. is it not on paper 2?

Daniel2590 · 05-06-2014 9:58pm

Aspiring wrote: »

Is there anywhere I can get a definitive list of things I need to learn off for tomorrow such as proofs?

I have some but not sure of everything we need.

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

Daniel2590 · 05-06-2014 9:59pm

2thousand14 wrote: »

and is the binomial theorem people have mentioned earlier. is it not on paper 2?

You might be thinking of Bernoulli Trials in statistics and probability?

Aspiring · 05-06-2014 10:01pm

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

Hardly everything is it? Sounds a bit easy :pac:

Daniel2590 · 05-06-2014 10:03pm

Aspiring wrote: »

Hardly everything is it? Sounds a bit easy :pac:

That's it all

FatRat · 05-06-2014 10:04pm

Do you know what never comes up? Arithmetic! Just thinking about there..Theres a whole chapter dedicated to it but they never test it, imagine getting a question on JC stuff like tax and universal social charge!! Too easy I guess..

Aspiring · 05-06-2014 10:06pm

Do we think it'll be a handy paper to keep boosting the Honours Maths numbers or will they just fúck us over :pac:

Hotale.com · 05-06-2014 10:08pm

Aspiring wrote: »

Do we think it'll be a handy paper to keep boosting the Honours Maths numbers or will they just fúck us over :pac:

It just has to be easy.... Otherwise I'm fecked.

Aspiring · 05-06-2014 10:10pm

Hotale.com wrote: »

It just has to be easy.... Otherwise I'm fecked.

I got a C in the first mock (DEB)
I got a B in the second mock (Examcraft)
My mathematical senses point to an A here

I'm only messing, I'd love a B tho!

You'll do grand lad, look at last year, easy stuff.

XtotheZ · 05-06-2014 10:11pm

Colleges are saying the standard of maths has gone way down recently..

Saskatchewan · 05-06-2014 10:11pm

Aspiring wrote: »

Do we think it'll be a handy paper to keep boosting the Honours Maths numbers or will they just fúck us over :pac:

they'll want to show that all the mistakes in last years paper didn't impact on anyones result so, it'll be pretty much the exact same difficulty of last year.... I hope anyways!

Aspiring · 05-06-2014 10:14pm

Saskatchewan wrote: »

they'll want to show that all the mistakes in last years paper didn't impact on anyones result so, it'll be pretty much the exact same difficulty of last year.... I hope anyways!

Even if not, we'll get the grade we deserve at the end of the day.

Not surprised the standard of maths has gone down. However, the maths you tend to be doing in college is quite different to what we do :pac:

PaleMoonlight · 05-06-2014 10:16pm

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

XtotheZ · 05-06-2014 10:17pm

Aspiring wrote: »

Even if not, we'll get the grade we deserve at the end of the day.

Not surprised the standard of maths has gone down. However, the maths you tend to be doing in college is quite different to what we do :pac:

yeah i heard now they have to run extra modules to cover the stuff thats been left out of the project maths course

Aspiring · 05-06-2014 10:19pm

XtotheZ wrote: »

yeah i heard now they have to run extra modules to cover the stuff thats been left out of the project maths course

They had a choice really: Have a high standard of maths or, have a lot of people doing higher level maths.

Quite clear which was picked

accountname · 05-06-2014 10:20pm

Eh, how does one derive the sum to infinity formula?

Also, was looking through a few Alison.com videos and they said the proof of amortirisation isn't on the course! As for binomal expansion, it says it is on the syllabus at the start of educate exam papers anyways.

daaniellerc · 05-06-2014 10:21pm

Can I be right in saying that co-ordinate geometry of the line/circle can come up in paper 1? Such as asking you to find the equation of a tangent to a curve at a given point?

XtotheZ · 05-06-2014 10:27pm

accountname wrote: »

Eh, how does one derive the sum to infinity formula?

Also, was looking through a few Alison.com videos and they said the proof of amortirisation isn't on the course! As for binomal expansion, it says it is on the syllabus at the start of educate exam papers anyways.

derive Amortisation is on the course, our teacher put a good bit of emphasis on it. Binomial expansion is also on the course and our teacher also put a good bit of emphasis on it.

Binomial expansion is handy enough

I also need the sum to infinity, greatly appreciated

if anyone has a link for it

Daniel2590 · 05-06-2014 10:28pm

Sum to infinity & amortisation proofs here

daaniellerc wrote: »

Can I be right in saying that co-ordinate geometry of the line/circle can come up in paper 1? Such as asking you to find the equation of a tangent to a curve at a given point?

No that's only paper two

Aspiring · 05-06-2014 10:31pm

Daniel2590 wrote: »

Sum to infinity & amortisation proofs here

Is that your writing?

Daniel2590 · 05-06-2014 10:32pm

Aspiring wrote: »

Is that your writing?

Yep

Aspiring · 05-06-2014 10:33pm

Daniel2590 wrote: »

Yep

So damn neat, thanks btw

XtotheZ · 05-06-2014 10:36pm

Thanks for the sum to infinity.

Does anyone have anything on the trigonometric formulas you have to derive?

Daniel2590 · 05-06-2014 10:43pm

XtotheZ wrote: »

Thanks for the sum to infinity.

Does anyone have anything on the trigonometric formulas you have to derive?

Those are all paper two but here's all the trig proofs too

JDOC1996 · 05-06-2014 10:43pm

XtotheZ wrote: »

Thanks for the sum to infinity.

Does anyone have anything on the trigonometric formulas you have to derive?

They're all in the book.

Daniel2590 · 05-06-2014 10:44pm

End of it here since I can't attach another pic to that post

c0unterpart · 05-06-2014 10:44pm

could anyone please explain the difference between injective surjective and bijective ? only bit of paper one thats dogey

aleatorio · 05-06-2014 10:45pm

Daniel2590 wrote: »

Sum to infinity & amortisation proofs here

For the sum to infinity is it necessary to separate it into the two fractions? In my book it just let's r^n = 0 and that's it

Daniel2590 · 05-06-2014 10:48pm

aleatorio wrote: »

For the sum to infinity is it necessary to separate it into the two fractions? In my book it just let's r^n = 0 and that's it

Haven't a clue but if your book has it that way you should be fine :P

Whistlingmilk · 05-06-2014 10:48pm

daaniellerc wrote: »

Can I be right in saying that co-ordinate geometry of the line/circle can come up in paper 1? Such as asking you to find the equation of a tangent to a curve at a given point?

Daniel2590 wrote: »

No that's only paper two

Equation of a line: y-y1= m(x-x1)
Slop of a line: y= mx+c

Knowledge of those formula can be needed in the Calculus question, if they ask a question regarding a tangent to the curve, m being the slope of the tangent aka dy/dx.

2012 6(b), for example: http:// examinations.ie/archive/exampapers/2012/LC003ALP130EV .pdf

robman60 · 05-06-2014 10:50pm

c0unterpart wrote: »

could anyone please explain the difference between injective surjective and bijective ? only bit of paper one thats dogey

You should probably look it up in your book, as it explains it in more detail, but I'll give it in simple terms.

Injective: Each input gives a unique output. This means no two inputs give an identical output

Surjective: codomain=range

Bijective: Both injective and surjective.

chatterboxxx95 · 05-06-2014 10:50pm

XtotheZ wrote: »

derive Amortisation is on the course, our teacher put a good bit of emphasis on it. Binomial expansion is also on the course and our teacher also put a good bit of emphasis on it.

Binomial expansion is handy enough

I also need the sum to infinity, greatly appreciated if anyone has a link for it

Oh holy sh!te is amortisation proof 100% definitely on the course! ! Our teaher never even mentioned it to us

aleatorio · 05-06-2014 10:53pm

c0unterpart wrote: »

could anyone please explain the difference between injective surjective and bijective ? only bit of paper one thats dogey

(This is me testing myself to see if I can remember :pac:)

I believe surjective means that a horizontal line can intersect it more than once, all y values have to have at least one corresponding x value (so, it can't have asymptotes or whatnot), think something along the lines of a cubic equation

Then injective means that it has to have only one, or no, corresponding y values, so a horizontal line will either intersect it once or not at all, not all y values need to have an x value

Then bijective is essentially a combination of the two, it means every y value has one, and only one, x value, and every y value is corresponding to an x value, something along the lines of say, a straight line graph, a horizontal line will cut it only once :P

Can someone confirm if all this is correct...?

2014lchelp · 05-06-2014 10:54pm

Our teachers gave us a list of learning stuff and I'd recommend to learn before tomorrow;
How to construct root 2 and 3
Proof of de moivres theorem by induction
Proof by contradiction (there's about 8 examples) incl.
Prove the sum of 2 odd numbers is always even
Prove of geometric series by induction
Differentiation by first principles formula
I think that's it

if you have these down at least if one of these comes up you'll feel more at ease with it . Hope this helps!

robman60 · 05-06-2014 10:55pm

I have Active Maths and I'm pretty sure there's no derivation of either the amortisation proof or sum to infinity proof. I'm not even going to bother covering it at this point, it'd only frustrate me!

Ompala · 05-06-2014 10:56pm

XtotheZ wrote: »

Colleges are saying the standard of maths has gone way down recently..

It has, a lot! My year was the first to get bonus points, and the drop out rate for science and engineering courses went up a lot from previous years, with many saying they couldn't handle the jump in maths.

Aspiring wrote: »

Even if not, we'll get the grade we deserve at the end of the day.

Not surprised the standard of maths has gone down. However, the maths you tend to be doing in college is quite different to what we do :pac:

True, but a lot of stuff would be built on the basics you are learning atm.

peekachoo · 05-06-2014 10:57pm

robman60 wrote: »

I have Active Maths and I'm pretty sure there's no derivation of either the amortisation proof or sum to infinity proof. I'm not even going to bother covering it at this point, it'd only frustrate me!

I was just about to say the same. Ive never heard of proving amortisation before

FatRat · 05-06-2014 10:57pm

Deriving the Amortisation formula is 100% on the course. I've a feeling there will be a lot of financial maths tomorrow too.

Whistlingmilk · 05-06-2014 10:58pm

chatterboxxx95 wrote: »

Oh holy sh!te is amortisation proof 100% definitely on the course! ! Our teaher never even mentioned it to us

It's on the syllabus, says so on the bottom right of page 25:

http: //www .ncca.ie/en/Curriculum_and_Assessment/Post-Primary_Education/Project_Maths/Syllabuses_and_Assessment/LC_Maths_for_examination_in_2014 .pdf

robman60 · 05-06-2014 10:58pm

peekachoo wrote: »

I was just about to say the same. Ive never heard of proving amortisation before

The book 1 is pretty horrific though, so I'm not surprised. All the examples skip steps with no explanation and it leaves you to try to figure out what they did in their half-arsed examples.

peekachoo · 05-06-2014 11:00pm

robman60 wrote: »

The book 1 is pretty horrific though, so I'm not surprised. All the examples skip steps with no explanation and it leaves you to try to figure out what they did in their half-arsed examples.

True. Did anyone post the proof around this thread? I didn't check :P

Daniel2590 · 05-06-2014 11:00pm

peekachoo wrote: »

True. Did anyone post the proof around this thread? I didn't check :P

Check near the end of the last page

c0unterpart · 05-06-2014 11:00pm

robman60 wrote: »

You should probably look it up in your book, as it explains it in more detail, but I'll give it in simple terms.

Injective: Each input gives a unique output. This means no two inputs give an identical output

Surjective: codomain=range

Bijective: Both injective and surjective.

is codomain the output values ?

2014lchelp · 05-06-2014 11:01pm

aleatorio wrote: »

(This is me testing myself to see if I can remember :pac:)

I believe surjective means that a horizontal line can intersect it more than once, all y values have to have at least one corresponding x value (so, it can't have asymptotes or whatnot), think something along the lines of a cubic equation

Then injective means that it has to have only one, or no, corresponding y values, so a horizontal line will either intersect it once or not at all, not all y values need to have an x value

Then bijective is essentially a combination of the two, it means every y value has one, and only one, x value, and every y value is corresponding to an x value, something along the lines of say, a straight line graph, a horizontal line will cut it only once :P

Can someone confirm if all this is correct...?

Yes this is right but don't forget this ; in order for it to be surjective the range must equal the codomain I.e. every y value has one x value. But in injective the range does not have to equal the codomain. I.e some y values may not have an x value. Then in order for it to be bijective it must be both in ejective and surjective! Therefore the range must equal the codomain (as in surjective) And remember. A function can only have an inverse if and only if it is bijective

(makesure you know how to get the inverse)

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

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Leaving Certificate: Higher Level Maths Discussion