Maths

Square numbers - 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

Cube numbers - 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Powers -  For example 2 to the power of 3 would be 2 x 2 x 2 which is 8

Prime numbers - A prime number is a number that divides only by 1 and itself. 

The prime numbers are - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 etc

LCM - Lowest common multiple

E.g. 6 and 7 

6 - 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, etc

7 - 7, 14, 21, 28, 35, 42, 49, 56, 63, 77, etc

So the LCM of 6 and 7 is 42

HCF - Highest common factor

E.g. 36 and 54

36 - 1, 2, 3, 4, 6, 9, 12, 18, 36

54 - 1, 2, 3, 6, 9,18,27,54

So the HCF of 36 and 54 is 18

Multiplying - Multiply the top and bottom seperatley.

E.g 3/5 x 4/7 = 3 x 4 = 12    5 x 7 = 45 

So... it equals ... 12/45

Dividing - Turn the 2nd fraction upside down then multiply

E.g. 3/4  /  1/3 = 3/4  /  3/1  =  3x3/4x1 = 9/4

Adding and subtracting - Only add/subtract the top line but only if the bottom numbers are the same

E.g. 2/6 + 1/ 6 = 3/6

      5/7 - 3/7 = 2/7

Cancelling down - Divide the top and the bottom by the same

E.g. 18/ 24 cancels down to 6/8 by dividing by 3, then that cancels down to 3/4 by dividing by 2.

Simplifying - Also known as 'collecting like terms'

E.g. 2x-4+5x+6 

       2x+5x = 7x

       -4 +6 = 2

       7x + 2

Multiplying out brackets - Taking the brackets away by multiplying

E.g. 3(2x + 5) 

       3 x 2x = 6x

       3 x 5 = 15

       6x + 15

Factorising - Putting the brackets in

E.g. X2 + 5X + 6

Find two numbers that add together to get 5X and times together to get 6 

So in this case 2 and 3

(x + 2) (x + 3) is the answer 

Another one .... X2 + 7x + 6

So two number that add together to get 7x and times togetehr to get 6 are ...

1 and 6

(x + 1) (x + 6) is the answer

 Y = MX + C

Y = Value of Y   M = Gradient    X = Value of X    C = Intercept

E.g. 2Y = 4X + 2

Its easier if you get Y by itself so divide it by two

 Y = 2X + 1

Then with this in formation make a table

X  0  1  2  3  4 

Y  1  3  5  7  9

With this data you can make a graph

Surds

E.g. 45 = 5 x 9

                  = 3  5 

E.g. 108 = 9 x 12 

                    = 3  12

When using surds you always need to use the surd sign ( ).

Also, when x's two numbers, remember one of them needs to be a square number!

Finally! When cancelling down the square number remember to put it  BEFORE the symbol!

The Nth Term

E.g.  5, 14, 23, 32

        9   9   9     9

So the difference is 9 so the beggining of the equation will be 9X

Next... you do 9x1 to get 9 so to get 5 you need to -4

To make sure of this try with the next one.... 9x2= 18 to get 14 - 4

So the answer is 9X - 4

Remember to repeat the number by 1, 2, 3, etc to make sure it is the right answer!