**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**

- Natural numbers: Positive integers (1, 2, 3 …)
- Integers: (-1, 0, 1 …)
- Rational numbers: “Any number that can be expressed in the form where p and q are integers and q is !=0 “
- Irrational numbers: Cannot be expressed as eg,

Rationalizing the denominator:

A surd is any number that contains a square root sign

We leave in a square root so that:

- We do not need to use a calculator when dealing with them.
- They are more accurate since we do not round them into a decimal.

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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