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

PaleMoonlight

c0unterpart wrote: »

is codomain the output values ?

Codomain is the set all possible outputs and range is the set all the actual outputs. So to be surjective all possible outputs must be used.

peekachoo

Daniel2590 wrote: »

Check near the end of the last page

Thank you

c0unterpart

2014lchelp wrote: »

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)

thanks man this makes sense now

2014lchelp

Forgot a few things:
Know the diff between injective surjective and bijective (horiZontal line test) ( and the vertical line test for the function)
How to complete the square
Nature of quadratic roots (I.e. bsquared + 4ac greater than, less than equal to 0)

aleatorio

2014lchelp wrote: »

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)

To get the inverse you let the function equal y and rearrange it to have x in terms of y and them sub in x for y, correct?

2014lchelp

FatRat wrote: »

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

What's amortisation I feckin hate financial maths

aleatorio wrote: »

To get the inverse you let the function equal y and rearrange it to have x in terms of y and them sub in x for y, correct?

You got it

XtotheZ

Thanks so much Daniel.

chatterboxxx95

Holy mother of god...thank you people who confirmed that proof is on the course.
Having heart attacks here because realising there's a growing list of stuff my teacher never taught us. It's times like these I utterly fúcking dispair.

c0unterpart

PaleMoonlight wrote: »

Codomain is the set all possible outputs and range is the set all the actual outputs. So to be surjective all possible outputs must be used.

so the codomain could be 1,2,3,4,5 etc but for y = x^2 when x =1,2,3,4,5 the range is 1,2,9,16,25 so the range isnt the codomain so its not surjective,i am right thinking this aha ?

Whistlingmilk

chatterboxxx95 wrote: »

Holy mother of god...thank you people who confirmed that proof is on the course.
Having heart attacks here because realising there's a growing list of stuff my teacher never taught us. It's times like these I utterly fúcking dispair.

A lot of that list are important because they need to be understood beforehand as opposed to done from scratch on the day. But in the bigger picture of the whole exam they aren't worth too much marks compared to the more intuitive questions, so don't fret the 'small' stuff!

Janeh9

I have absolutely no idea what any of you are talking about what am I doing jesus XD

eefah

My God, this whole thread is a lifesaver.
I have such a list of things to cram into my brain by tomorrow afternoon.
I'm not sure if I have the most incompetent teacher in the country, if Project Maths is just not for me , or if I just ... don't care about maths enough; but I just have my fingers crossed for a pass at this stage (I got an A in maths for the JC! I have no idea what went wrong), and several people here are reeeeeally helping me make that happen.
I literally just made an account specifically for this message, take that as an example of how grateful I am and maybe also how much I am procrastinating.

EoghanIRL

c0unterpart wrote: »

so the codomain could be 1,2,3,4,5 etc but for y = x^2 when x =1,2,3,4,5 the range is 1,2,9,16,25 so the range isnt the codomain so its not surjective,i am right thinking this aha ?

Surjective means that each output has at least one input . Many to one mapping . So that each y value can have more than one corresponding x value . You can tell Surjective functions by the horizontal line test .

Days 298

2014lchelp wrote: »

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!

If someone has these handy could they post it up please

Im hoping de moivres proof and proof by contradiction come up.

c0unterpart

EoghanIRL wrote: »

Surjective means that each output has at least one input . Many to one mapping . So that each y value can have more than one corresponding x value . You can tell Surjective functions by the horizontal line test .

I've never been so lost in my life

marno21

In the same boat as chatterbox95

Only heard about most of this stuff today.. Hoping there'll be little of it on the paper as I need a c3

EoghanIRL

c0unterpart wrote: »

I've never been so lost in my life

That is the easiest way to think about it!
Do you know what the horizontal line test is?

eefah

c0unterpart wrote: »

I've never been so lost in my life

I find the easiest way to remember is just that a SURjective function can be cut at OVER one point by a horizontal line... a horizontal line can hit it more than once.
so any horizontal line has to hit it AT LEAST once.
As opposed to injective which is where a horizontal line will hit it AT MOST once.

this isnt much help if any like, theoretical questions come up, but its how I remember.

I admit its a lot less helpful to anyone who doesnt do french

Ompala

Days 298 wrote: »

If someone has these handy could they post it up please

Im hoping de moivres proof and proof by contradiction come up.

Just a guess at sum of 2 odd numbers...
2m + 1 and 2n +1 with m and n integers, are both odd as they aren't divisible by 2
their sum is
2m + 1 + 2n + 1 = 2m + 2n + 2 = 2(m+n+2) which is even since it is divisible by 2
Hence the sum of two odd numbers is even

Mario95

Yeah, you have to derive the Amortization formula.
Its pretty much just 'simplifying' a geometric series.
Here's a nice explanation if you forgot how to do it: en.wikipedia.org/wiki/Amortization_calculator#Derivation_of_the_formula

Paper 1 tomorrow I am so excited!

Good Luck everyone!

Ciaran8

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

How do you know this?

c0unterpart

EoghanIRL wrote: »

That is the easiest way to think about it!
Do you know what the horizontal line test is?

yes but im sure you cant use that in reasoning out why its not injective/surjective you get me ?

Ompala

Days 298 wrote: »

If someone has these handy could they post it up please

Im hoping de moivres proof and proof by contradiction come up.

Actually page 24 of this might be what you are looking for for geometric series with induction https://betterexaminations.ie/show?paper_id=4897&mksurl=http://www.examinations.ie/archive/markingschemes/2002/LC003ALP1EV.pdf

EoghanIRL

c0unterpart wrote: »

yes but im sure you cant use that in reasoning out why its not injective/surjective you get me ?

But the the horizontal line test holds the answer.
If it intersects the graph in one place then the y value has only one x value ok?
Therefore injective - one to one mapping (not perfect )
If it intersects it in more than one place then y value has more than one corresponding x value . Thus it's Surjective .

sarahkiely125

What do you use for proof of contradicton?

c0unterpart

EoghanIRL wrote: »

But the the horizontal line test holds the answer.
If it intersects the graph in one place then the y value has only one x value ok?
Therefore injective - one to one mapping (not perfect )
If it intersects it in more than one place then y value has more than one corresponding x value . Thus it's Surjective .

right thank you,I get it

Daniel2590

Ciaran8 wrote: »

How do you know this?

Was given the list from my teacher

FatRat

That definition of surjective function is only half correct really. You have to account for the domain and range also. Like a post said a while back the domain must equal the range for it to be surjective. That means when you see the question you have to take the information people don't usually look at. For example when is say the values of of the graph are R -> R. Well if its a quadratic graph (with one turning point) then it cannot be surjective... Even though a horizontal line cuts it more than once. The reason for this is that the range of a quadratic graph doesn't equal the codomain. The codomain is "R" I.e. any real number. But the range of the graph can't be any real number since it has one turning point, and the range is therefore restricted.

However if the Range of the graph is x > -4 (for example) than if you restrict the codomain to x > -4 (i.e the values for the graph are now R -> [x>-4] instead of R-> R), the function is then surjective. The only time that a graph of R --> R is surjective is when it its range is [infinity, infinity] .. Sorry I cant do the symbol for infinity! Linear (sometimes, i think?) and cubic graphs are generally surjective! Exponential and log graphs cant be surjective however.


Its hard to explain without diagrams. And PLEASE correct me if I'm wrong. I could be wrong. Maybe. And if I am, I need to learn it.

little sis...

So.Screwed.

Never thought I'd be learning maths proofs the morning of my leaving cert maths exam...And I'm actually a very organized person!

Saskatchewan

little sis... wrote: »

So.Screwed.

Never thought I'd be learning maths proofs the morning of my leaving cert maths exam...And I'm actually a very organized person!

I'm the same....

jellytots95

Can the graphs of sinx and cosx come up on paper 1?

XtotheZ

jellytots95 wrote: »

Can the graphs of sinx and cosx come up on paper 1?

I believe so

Mario95

Do we have to know how to use chain rule backwards to solve things like: "Integrate cos(2x)"?

zinny

is patterns a definite maybe for this exam??

chatterboxxx95

Whistlingmilk wrote: »

A lot of that list are important because they need to be understood beforehand as opposed to done from scratch on the day. But in the bigger picture of the whole exam they aren't worth too much marks compared to the more intuitive questions, so don't fret the 'small' stuff!

Thanks! Praying not too many of them come up, because I actually know everything else inside and out-_- I like maths but I hate not being taught stuff...
B3 on first mock (DEB) and B1 on second (partly made up and last year's DEB) so was really hoping to push to the A2. If too much of this stuff comes up I haven't a hope in hell

chatterboxxx95

Mario95 wrote: »

Do we have to know how to use chain rule backwards to solve things like: "Integrate cos(2x)"?

Integrating something like that general formula is
-(1/a)sinax so ans is -(1/2) sin2x
The tables leave out the (1/a) bit for trig functions but its there for e^x if that helps

Mario95

chatterboxxx95 wrote: »

Integrating something like that general formula is
-(1/a)sinax so ans is -(1/2) sin2x
The tables leave out the (1/a) bit for trig functions but its there for e^x if that helps

I truly hate rules. Especially if they are not in the tables.
Also I believe the answer would be +sin(2x)/2.

Thanks anyway, I will use the e^ax in the tables if I am stuck

little sis...

Quick question, is an exponential graph injective?

sarahkiely125

What the hell is the Admoritasion formula?

XtotheZ

little sis... wrote: »

Quick question, is an exponential graph injective?

horizontal line test cuts it once so yes

Days 298

sarahkiely125 wrote: »

What the hell is the Admoritasion formula?

Formula to discover the monthly/yearly repayments for a loan. Its in the log tables. Much quicker than geometeric series but only works if the loan is being repaid at the end of each time period

little sis...

XtotheZ wrote: »

horizontal line test cuts it once so yes

Thanks just making sure

Days 298

sarahkiely125 wrote: »

What do you use for proof of contradicton?

Square root two being rational.

zinny wrote: »

is patterns a definite maybe for this exam??

A maybe but came up last year. New examiner this year Id say hell want to be different.

chatterboxxx95

[quote="Mario95;90711 truly hate rules. Especially if they are not in the tables.
Also I believe the answer would be +sin(2x)/2.

Thanks anyway, I will use the e^ax in the tables if I am stuck [/quote]
You're right there, that's what I get for integrating whilst lying in bed without bothering to get up to check the maths
tables :pac:


Little sis - yes, an exponential graph is injective, because the y value for a given x value will be different to any other y, ie one to one mapping

Days 298

i really hope surjective bijective and injective dont show.
The whole point of project maths was to make it more accessible yet now we have zero choice and still must rote learn :mad:

Mario95

What do we need to know for the Income Tax section (that isn't already in the Tables)?
Do we need to know all the cut-off points and other stuff or they will give it to us in the paper?

XtotheZ

Days 298 wrote: »

i really hope surjective bijective and injective dont show.
The whole point of project maths was to make it more accessible yet now we have zero choice and still must rote learn :mad:

I hope they dont but i think they will. Functions will be a big part I reckon

Irish_gal

Anyone know what terms we need to know for paper one? and what proofs you think will come up??

chatterboxxx95

Mario95 wrote: »

What do we need to know for the Income Tax section (that isn't already in the Tables)?
Do we need to know all the cut-off points and other stuff or they will give it to us in the paper?

They give cut off points, percentage rates etc on the paper

2thousand14

chatterboxxx95 wrote: »

They give cut off points, percentage rates etc on the paper

Dont think they give USC cut off points?