1. Algebra and Functions

2. Introduction This chapter focuses on basic manipulation of Algebra
It also goes over rules of Surds and Indices
It is essential that you understand this whole chapter as it links into most of the others!

3. Teachings for Exercise A

4. Algebra and Functions 1F Extending the rules of Indices
The rules of indices can also be applied to rational numbers (numbers that can be written as a fraction)
Examples a) b) c) d) 1F

5. Algebra and Functions 1F Extending the rules of Indices
The rules of indices can also be applied to rational numbers (numbers that can be written as a fraction)
Examples a) b) c) d) 1F

6. Algebra and Functions 1F Extending the rules of Indices
The rules of indices can also be applied to rational numbers (numbers that can be written as a fraction)
Examples a) b) 1F

7. Differentiation

8. Introduction You will learn what Differentiation is
You will see how to apply it to solve graph based problems
It is one of the single most important topics there is in Maths!

9. Teachings for Exercise B

10. You need to be able to find the gradient function of a formula
Differentiation
You need to be able to find the gradient function of a formula
On a straight line graph, the gradient is constant, the same everywhere along the line.
On any curved graph, the gradient is always changing. Its value depends on where you are along the x-axis.
The different gradients can be shown by tangents. These are lines that touch the curve in only one place.
Differentiation is the process whereby we can find a formula to give the gradient on a curve, at any point on it.
Straight Line = Constant Gradient
tangent
Curved line = Gradient Changes
tangent 7B

11. You need to be able to find the gradient function of a formula
Differentiation
You need to be able to find the gradient function of a formula
As a general rule, if;
then…
Examples
Find the derived function of each of the following… a)
f(x) = x3
f’(x) = 3x2
This is the formula for the curve, ie) the function b)
f(x) = 2x2
f’(x) = 4x1 (4x) c)
f(x) = x-2
This is the gradient function for f(x). The formula that gives the gradient at any point.
Its is also know as the derivative, or ‘derived function’
f’(x) = -2x-3 d)
f(x) = -3x-3
f’(x) = 9x-4 7B

12. You need to be able to find the gradient function of a formula
Differentiation
You need to be able to find the gradient function of a formula
As a general rule, if;
then…
Examples
Find the derived function of each of the following… e)
Must be written in the form axn first!
This is the formula for the curve, ie) the function
This is the gradient function for f(x). The formula that gives the gradient at any point.
Its is also know as the derivative, or ‘derived function’ f)
Must be written in the form axn first! 7B