Chapter 1

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Indices + Surds
closetkido
Mind Map by closetkido, updated more than 1 year ago
closetkido
Created by closetkido over 8 years ago
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Resource summary

Chapter 1
  1. Surds
    1. Simplifying
      1. Find something that can be simplified
        1. sqrt(16)=4
          1. sqrt(25)=5
        2. Rationalising
          1. Simple
            1. Multiply by the root on top and bottom
              1. sqrt(7) x sqrt(7) = 7
            2. Complex
              1. Multiply by the same numbers with opposite add/subtract sign
                1. 3+sqrt(7) x 3-sqrt(7) = 9+7 = 16
          2. Indices
            1. Rules of Indices
              1. Addition/Subtraction
                1. Factors with different indices do not combine by addition or subtraction they stay separate.
                2. Division
                  1. Subtract the indices
                    1. e.g. 2^5 / 2^3 = 2^2 as 5-3 = 2.
                  2. Multipication
                    1. Add the indices
                      1. e.g. 2^5 x 2^3 = 2^8 as 5+3 = 8
                    2. Brackets
                      1. Multiply the brackets
                        1. e.g. (2^5)^3 = 2^15 as 5 x 3 = 15
                    3. More Indices
                      1. Negative Powers
                        1. If power is negative, then flip and make power positive
                          1. e.g. 2x^-2 = 2/x^2
                        2. Fractional Powers
                          1. x^a/b = (brt(x))^a
                            1. e.g. x^4/3 = (4rt(x))^3
                          2. Equations
                            1. When moving fractional powers, flip but keep +- the same
                              1. e.g. x^2/3 = 100 ==> x = 100^3/2
                              2. Moving integer powers
                                1. If positive, then make a root.
                                  1. e.g. x^3 = 100 => x = 3rt(100)
                                  2. If negative, then make into fraction and cross-multiply.
                                  3. Moving fractional powers
                                    1. If positive, then make power.
                                      1. e.g. x^1/2 = 100 => x = 100^2
                                      2. If negative, the move over the other side, and flip top and bottom then simplify.
                                        1. e.g. x^-3/2 = 100 => x = 100^-2/3
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