Links to all my posts by subject

I decided to make a sort of contents page here with all the links to my previous posts to save you the time having to scroll through everything wondering if i have posted anything about whatever the topic you are looking for is!
I have divided them up by subject for the purpose of this post, not in the order they are on my blog. I will update this as i post more material!

My posts

http://leaving-cert-helpnotes.blogspot.ie/2013/04/im-back-next-few-posts.html

http://leaving-cert-helpnotes.blogspot.ie/2013/04/posting-notes-on-this-blog-helping.html

http://leaving-cert-helpnotes.blogspot.ie/2013/01/hi-everyone.html

http://leaving-cert-helpnotes.blogspot.ie/2012/06/welcome-to-my-leaving-cert-help-notes.html

Useful Links

http://leaving-cert-helpnotes.blogspot.ie/2013/01/studying-tips.html

http://leaving-cert-helpnotes.blogspot.ie/2013/04/helpful-website-links.html

http://leaving-cert-helpnotes.blogspot.ie/2013/01/stop-internet-distractions-when-studying.html

http://leaving-cert-helpnotes.blogspot.ie/2012/06/helpful-links-for-leaving-cert-notes.html

English 

http://leaving-cert-helpnotes.blogspot.ie/2012/06/english-comparitive-essay-relationships.html

http://leaving-cert-helpnotes.blogspot.ie/2012/06/leaving-cert-english-poetry-robert.html

Irish

http://leaving-cert-helpnotes.blogspot.ie/2014/06/an-triail-summary-in-english.html

http://leaving-cert-helpnotes.blogspot.ie/2014/04/aiste-todhchai-na-gaeilge.html

http://leaving-cert-helpnotes.blogspot.ie/2014/04/aiste-timpeallacht.html

http://leaving-cert-helpnotes.blogspot.ie/2014/04/hl-irish-essay-imirce-diospoireacht.html

http://leaving-cert-helpnotes.blogspot.ie/2014/04/irish-essay-phrases.html

http://leaving-cert-helpnotes.blogspot.ie/2014/04/hl-irish-essay-coiriulacht.html

http://leaving-cert-helpnotes.blogspot.ie/2013/04/irish-grammar-aidiocht-sheallbhach.html

http://leaving-cert-helpnotes.blogspot.ie/2013/04/irish-grammar-forainm-reamhfhocalach-eg.html

http://leaving-cert-helpnotes.blogspot.ie/2013/04/irish-grammar-reamhfhocal-shimpli-eg-i.html

http://leaving-cert-helpnotes.blogspot.ie/2013/01/iregular-irish-verbs.html

http://leaving-cert-helpnotes.blogspot.ie/2012/08/irish-regular-verbs.html

http://leaving-cert-helpnotes.blogspot.ie/2012/06/irish-essay-hl-old-and-new-in-ireland.html

http://leaving-cert-helpnotes.blogspot.ie/2012/06/irish-hl-sample-triail-answer.html

http://leaving-cert-helpnotes.blogspot.ie/2012/06/irish-higher-level-sample-essay-poverty.html

Maths

http://leaving-cert-helpnotes.blogspot.ie/2014/02/differentiation-what-is-it.html

Biology

http://leaving-cert-helpnotes.blogspot.ie/2014/06/biology-revision-quesions-with-answers.html

http://leaving-cert-helpnotes.blogspot.ie/2014/06/biology-revision-questions-with-answers_18.html

http://leaving-cert-helpnotes.blogspot.ie/2014/06/biology-revision-questions-with-answers.html

http://leaving-cert-helpnotes.blogspot.ie/2014/06/biology-revision-questions.html

Music

http://leaving-cert-helpnotes.blogspot.ie/2012/06/music-notes-gerald-barry.html

http://leaving-cert-helpnotes.blogspot.ie/2012/06/music-notes-bachs-cantata.html

http://leaving-cert-helpnotes.blogspot.ie/2012/06/leaving-cert-irish-traditional-music.html

History 

http://leaving-cert-helpnotes.blogspot.ie/2013/01/history-1916-rising-essay.html

http://leaving-cert-helpnotes.blogspot.ie/2013/01/history-essay-civil-right-america-1945.html

http://leaving-cert-helpnotes.blogspot.ie/2012/07/history-essay-winston-churchill.html

http://leaving-cert-helpnotes.blogspot.ie/2012/06/history-essay-dictators-power.html

Geography

http://leaving-cert-helpnotes.blogspot.ie/2014/09/the-dublin-region-physical-geography.html

http://leaving-cert-helpnotes.blogspot.ie/2014/09/regional-geography-irish-core-region.html

http://leaving-cert-helpnotes.blogspot.ie/2014/09/regional-geography-human-geography-of.html

http://leaving-cert-helpnotes.blogspot.ie/2014/09/regional-gepgraphy-tertiary-economic.html

http://leaving-cert-helpnotes.blogspot.ie/2014/09/regional-geography-secondary-economic.html

http://leaving-cert-helpnotes.blogspot.ie/2014/09/regional-geography-primary-economic.html

http://leaving-cert-helpnotes.blogspot.ie/2014/09/regional-geography-western-region.html

http://leaving-cert-helpnotes.blogspot.ie/2014/09/leaving-cert-regional-geography.html

Home Economics

http://leaving-cert-helpnotes.blogspot.ie/2014/09/home-ec-vitamins-and-minerals-vitamin-c.html

http://leaving-cert-helpnotes.blogspot.ie/2014/09/home-economics-minerals.html

http://leaving-cert-helpnotes.blogspot.ie/2014/09/home-economics-b-group-vitamins.html

http://leaving-cert-helpnotes.blogspot.ie/2014/09/home-economic-fat-soluable-vitamins.html

http://leaving-cert-helpnotes.blogspot.ie/2014/02/home-ec-notes-carbohydrates.html

http://leaving-cert-helpnotes.blogspot.ie/2014/02/home-ec-protein-notes.html

http://leaving-cert-helpnotes.blogspot.ie/2013/08/home-ec-protein.html

http://leaving-cert-helpnotes.blogspot.ie/2013/08/home-economics-factors-that-affect-food.html

Differentiation - what is it?

Okay so in Maths we learn about differentiation and what to do, the formulas etc, but what is differentiation???

Differentiation is finding the slope of a curve at a particular point on the curve.

Eg:

But how do we find slopes?

First consider a straight line:

We get the slope of a straight line by taking two points on the line and using their co-ordinates (x1, y1) and (x2, y2) in a slope formula:

From functions, we know that a point x has a height of f(x), (i.e. y = f(x) ) :

 

 Something else to consider is that the slope at a point on a curve is the same slope as the tangent at that point

 

So if we know two points on the tangent we can work out the tangent slope and thus the curve slope.


Next we require some limits and some imagination.


Picture our curve and tangent:

 

 

Now zoom in on our point:

And again:

And again... It's getting hard to distinguish between the two lines.

We can soom in infintely until they appear as practically the same line! so we can now say that two points on the curve are now alone on the tangent, a distance of  'h' apart.

The second point becomes (x+h, f(x+h) )

If we make the distance 'h' between the two points as small as possible t will appear as if they are the same point.

Beacause we have two points we can use our slope formula

  

Using our co-ordinates (x, f(x) ) and (x+h, f(x+h) ) this formula becomes:

f(x+h) - f(x) 

(x+h) - x

Subtracting the 'x' on the bottom lines makes this:

f(x+h) - f(x) 

h

Now we wat to make the 'h' as small as possible so we limit h - 0

  Slope = lim  f(x+h) - f(x) 

       h-0           h

This is our differentiation formula!

We can apply this to any curve:

Example:

Welcome to my leaving cert help notes blog :)

Hey Everyone :) So I have finished my leaving cert, finally!! wooo :)

During the leaving cert I spent ages looking for notes on different topics on the internet, some were good but most made you pay for them or else had very little information.

Because of that I have decided to make this blog and post notes that I have from my leaving cert that will hopefully help others with theres :)

The subjects I did were:

• Maths (HL)
• Irish (HL)
• English (OL but did higher until a few weeks before it so I will have some higher level notes too)
• Geography (HL)
• Home Ec (HL)
• Music (HL)
• Biology (HL)
• History (HL)
• French (OL but I won't be much help with that)

So over the next few weeks and months I will be posting notes on different topics for the various subject :)

If anyone is looking for notes on a particular topic just comment and I shall try my best to post it :)

I shall also post some links that I found helpful.

Hope this helps at least one person so it's not a waste of my time.

Bye for now!