Chapter 1

Chapter 1

1. Surds

   • Simplifying
     • Find something that can be simplified
       • sqrt(16)=4
       • sqrt(25)=5
   • Rationalising
     • Simple
       • Multiply by the root on top and bottom
         • sqrt(7) x sqrt(7) = 7
     • Complex
       • Multiply by the same numbers with opposite add/subtract sign
         • 3+sqrt(7) x 3-sqrt(7) = 9+7 = 16

2. Indices

   • Rules of Indices
     • Addition/Subtraction
       • Factors with different indices do not combine by addition or subtraction they stay separate.
     • Division
       • Subtract the indices
         • e.g. 2^5 / 2^3 = 2^2 as 5-3 = 2.
     • Multipication
       • Add the indices
         • e.g. 2^5 x 2^3 = 2^8 as 5+3 = 8
     • Brackets
       • Multiply the brackets
         • e.g. (2^5)^3 = 2^15 as 5 x 3 = 15
   • More Indices
     • Negative Powers
       • If power is negative, then flip and make power positive
         • e.g. 2x^-2 = 2/x^2
     • Fractional Powers
       • x^a/b = (brt(x))^a
         • e.g. x^4/3 = (4rt(x))^3
     • Equations
       • When moving fractional powers, flip but keep +- the same
         • e.g. x^2/3 = 100 ==> x = 100^3/2
       • Moving integer powers
         • If positive, then make a root.
           • e.g. x^3 = 100 => x = 3rt(100)
         • If negative, then make into fraction and cross-multiply.
       • Moving fractional powers
         • If positive, then make power.
           • e.g. x^1/2 = 100 => x = 100^2
         • If negative, the move over the other side, and flip top and bottom then simplify.
           • e.g. x^-3/2 = 100 => x = 100^-2/3