## Friday, 2 December 2011

### C1- Algebra and Functions - Solving Quadratic and Linear Inequalities

Now we move on to Solving Inequalities. An Inequality is basically a statement comparing to variables, usually about their size. e.g. a < b (a is less than b - the value of a is less than b)

let  x = john's weight and y = rahul's weight
x < y (john's weight is less than rahul's weight)

Let's recap the different signs used in inequalities :

> is more than

< is less than
These are known as STRICT Inequalities. e.g. 7 < 13 is a strict inequality ( 7 is strictly less than 13) [This is not in the spec. - but it may be useful later on]
≥ is more than or equal to
≤ is less than or equal to.

Rules of Inequalities

1) We are allowed to add or subtract the same number on both sides.
2) We are allowed to switch sides, and change the sign.

e.g.   4 < 5-x is the same as 5-x > 4.

3) We are allowed to multiply by the same number on both sides, But if this number is positive, the sign remains the same, if it is negative the sign has to be reversed.

e.g   [6 > 3x + 4 ] * 3 =   [18 > 9x + 12]
[6 > 3x - 4 ] *-2 =   [-12<-6x + 8]

We we looked at so far, are examples of LINEAR Inequalities.

 Solving Linear Inequalities Notes

1) Simplify this Quadratic Inequality, to get one quadratic expression. Rearrange the inequality to get it equal to 0. ( > 0, < 0 or less than equal to or more than equal to).
2) Find the roots of the equation (Solve the quadratic). The roots are called CRITICAL VALUES.
3) Draw the graph of the equation, seeing which x values satisfy the inequality,using the Critical Values.

1. c3 functions hiral-shah@hotmail.co.uk
thanks

2. c1 model solutions
January and June sessions 2005-2011 please
boateng.natalie@hotmail.co.uk

I was wondering when the solomon paper model solutions will be ready as I would like those aswell. Thankyou in advance :)

3. I shall send you the normal edexcel papers c1 model solutions by thursday. I'm really busy at the moment, with uni work. And il get started on the solomon by friday. I haven't done every single edexcel paper, got june 2006, january 2007, june 2008 left. As i soon as i am done with them, i shall email you them as .jpg files.

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