1 - Algebra

2016-09-20 12:20:00 +0000, 1 year and 11 months ago

0 - Factorisation and Quadratic Formulae

Take for example the following:

In order to factorise it you must find which two numbers add up to -28, yet multiply to equal 13?
In this case it would be -2, -26, you then factorise them:

Quadratic and Linear eqn. case

1 - Use and manipulation of surds

Rationalizing the denominator:

A surd is any number that contains a square root sign
We leave in a square root so that:

For example is an irrational number, it goes on for ever:

Simplification:
We simplfy surds by splitting them into 2 factors, where one of the factors is a square number.
(Square number: The product of a number multiplied by itself, e.g. 1, 4, 9, 16.) \

e.g.

is the biggest square factor, we could have used but that would have not given use the most simplified answer.

Simplfying more complex surds:

In order to do this we must find a common factor between each surd, e.g.

Expanding dual bracket surds:
This in done the same way as a normal dual bracket is done, multiply the front, and then the back.
e.g.

Rationalising the denominator \

Take for example: , the denominator is irrational, to simplify this we must remove the surd on the bottom.

e.g.

2 - Quadratic functions and their graphs

3 - The discriminant of a quadratic function

is descriminant

The expression is called the descriminant of the quadratic

If then there are 2 distinct roots.

If then there is a repeating root.

If then there are no roots, and therefore there is no solution.

4 - Factorisation of quadratic polynomials

5 - Completing the square

Give in the form

6 - Solution of quadratic equations

7 - Simultaneous Equations

8 - Solution of linear and quadratic inequalities

9 - Polynominals

10 - Simple algebraic division

11 - Remainder Theorum

12 - Factor Theorum

13 - Graphs of functions

14 - Geometric interpretation of algebraic solutions

15 - Graphical translations

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