# MATHS YEAR 9 UNIT 1: Numbers

## Mean & Mode

• Mean: the sum of the sequence divied by the number of numbers in the sequence

E.G:  1,2,2,3

1+2+2+3

=8/4

=2

• Mode: the most common number found in the sequence

E.G:  1,2,2,3

=2 (is shown twice)

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## Median & Range

• Median: the middle number is the sequence is put in order of smallest to largest

E.G:  1,3,2,2

= 1,2,2,3

= 1  2  2  3

= 2

• Range:the difference between the biggest number and smallest

E.G:  1,2,2,3          = 3-1         =2

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## HCF & LCM

• HCF: highest common factor
• LCM: lowest common multiple
• To find the HCF draw out a number tree for both numbers

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• Then put all the prime numbers in a venn diagram

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## Powers

• Powers have rules to follow when multiplying, dividing and bracketing

E.G:  2^2 x 2^2

= 2+2          =2^4

- Dividing: subtract the powers

E.G:  2^3 / 2^2

= 3-2           = 2^1

- Bracketing: multipy the powers

E.G:  (2^2)^2          = 2 x 2          =2^4

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## Indicies

•  x^-n = 1/x^n

E.G:  6^-2 = 1/6^2

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• ax^-n = a/x^n

E.G:  6*2^-4 = 6/2^4

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• (a/b)^-n = (b/a)^n

E.G:  (2/4)^-6 = (4/2)^6

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## Standard Form

• There are certain rules to standard form:

a x 10^n

- 'a' is allways between 1 and 10

- 'n' is allways a whole number

E.G:  6.3 x 10^4          = 6 . 3 0 0 0 0         =63000

E.G:  6.3 x 10^-4          = 0 0 0 0 6 . 3        = 0.00063

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## Surds

• Surds look like this, 2V5

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• Simplifying surds:

E.G:  V40                                 =V4 x 10                         = V4 x V10

= 2 x V10                         = 2V10

- If it is not obvious that the number can be split into a square number them use a number tree

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