## Monday, 4 February 2013

### Lesson Summary ~(•O•)~ 4/2/13

RECALL:
~(•o•)~ Partial Fractions! Read through the summaries posted by yourself/others
~(•o•)~ Level Tests are on Week 7 & 8, starting mugging.

HOMEWORK:
~(•o•)~ Check what you haven't done on the homework spreadsheet.
~(•o•)~ AceLearning for those who did badly on the various quizzes and tests.
~(•o•)~ Assignment 01 and 02 are now due on Friday~!

REVISE:
~(•o•)~ The 9 laws of indices: (here's a helpful table)

Please remember to fully revise all laws as they will be used in Indices and Surds.

LESSON:
~(•o•)~ Indices and Surds: Forms

Index Form: When there is an index for the base. (Eg. 2^6)
Surd Form: When the base has a squareroot with it (√5)
Radical Form: When the base has an fractional index (2^(2/123))

~(•o•)~ Indices and Surds: Rationalization
Rationalization is the act of eliminating the squareroot (√x) from the denominator.

BACK TO BASICS– "  1/2 VS 1/3"
How do we determine which is bigger?
We change make them have an equal denominator. Thus, the LCM between 2 and 3 is 6. Therefore, we multiply 1/2 with 3/3 (Note how this is 1 whole), and 1/3 with 2/2. Eventually, we get "3/6 > 2/6"

ON TO SURDS! – "1/2 VS 1/√2"

How do we determine which is bigger?
Once again, we change them to make them have an equal denominator. In this case, we change the denominator to 2. As the first fraction already has a denominator of 2, we will work with 1/√2.
2 divided by √2 is √2. Thus, we multiply 1/√2 by √2/√2 (1 whole), and get √2/2.
Therefore, we would get "1/2 < √2/2"

Rationalizing with a^2 - b^2 – "1/(3 - 2) VS 1/(√3 - √2)"
To rid of the surd denominator, we use the 'a^2  b^2 = (a + b)(a - b)' concept.
In this scenario, our denominator is (√3 - √2) which is our (a - b). Thus, to rid of it, we multiply it by (√3 + √2) which represents our (a + b).
Thus, we multiply 1/(√3 - √2) by (√3 + √2)/(√3 - √2) <-- which is one whole!
This gives us (√3 + √2)/(3 - 2) = (√3 + √2)/1
Therefore, "1 < (√3 + √2)"