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 

     - Multiplying: add the powers 

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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