1. Index, exponential, power
Principle of Indices
Index, exponential, power
Base

2. Indices Rule 1

3. Indices Rule 2

4. Indices Rule 3
From Rule 1

5. Indices Rule 4

6. Indices Rule 5

7. Indices Rule 6, 7 1

8. Indices Rule 8

9. Irrational Number
Number that cannot be expressed as a fraction of two integers

10. Surd Rules We can use the above rules to:
simplify two or more surds or
combining them into one single surd

11. Simplify the following surds :
Example 1:
Simplify the following surds :
Solution:

12. Rationalization of the Denominator
Process of removing a surd from the denominator
Example 2:
Solution:
Multiple together!

13. Change to common power Change to common base Simplifying Indices
Think of how to make
it common power
Break each term into
its prime factor
Simplify the indices
within each term
Ensure that
common power
Combine the base
and simplify
Simplify the indices
across other terms

14. Quadratic Equation - Definitions (Expression & Equation)
Representation of relationship between two (or more) variables
Y= ax2+bx+c,
Equation : Statement of equality between two expression
ax2 + bx + c = 0 
Root:-value(s) for which a equation satisfies
Example:
x2-4x+3 = 0  (x-3)(x-1) = 0
Roots of x2-4x+3 = 0
satisfies x2-4x+3 = 0
 x = 3 or 1

15. Quadratic Equation Definitions (Quadratic & Roots)
Quadratic: A polynomial of degree=2
y= ax2+bx+c
ax2+bx+c = 0 is a quadratic equation. (a  0 )
A quadratic equation always has two roots

16. Quadratic Equation -Factorization Method
Solve for x2+x-12=0
Step2:
Sum of
factors
factors
-4,3 -1
product
Step1: 4
-2,6
-12
4,-3 1
factors with opposite sign
Step3:
x2+(4-3)x -12=0
 x2+4x-3x-12=0
Roots are -4, 3
(x+4)(x-3)=0

17. Quadratic Equation -Factorization Method
x2+x-12=0
 x2+(4-3)x -12=0
(where roots are –4,3)
Similarly if ax2+bx+c=0 has roots ,
ax2+bx+c
 a(x2-(+)x + )
Comparing co-efficient of like terms:

18. Properties of Roots Quadratic equation ax2+bx+c=0 , a,b,c R  and 
The equation becomes: a { x2+ (b/a)x + (c/a) }= 0
ax2-(+ )x+  =0
a(x-)(x-)=0
 x2-(sum) x+(product) =0

19. This is called the general solution of a quadratic equation
(b2 - 4ac)  discriminant of the quadratic equation, and is denoted by D .
Roots are
This is called the general solution of a quadratic equation

20. Nature of Roots Discriminant, D=b2-4ac  D > 0 is real 
Roots are real
(D is not a perfect square)
a, b, c are rational
(D is perfect square)
Rational
Irrational
 D = 0
Roots are real and equal
 D < 0 is not real 
Roots are imaginary

21. Logarithms Definition
Base: Any postive real number
other than one
Log of N to the base a is x
Note: log of negatives and zero are not Defined in Reals

22. Fundamental laws of logarithms

23. Other laws of logarithms
Change of base
Where ‘a’ is any other base

24. System of logarithms Common logarithm: Base = 10
Log10x, also known as Brigg’s system
Note: if base is not given base is taken as 10
Natural logarithm: Base = e
Logex, also denoted as lnx
Where e is an irrational number given by