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4202515
Chapter 1
Descripción
Indices + Surds
Sin etiquetas
maths
maths
as - level
Mapa Mental por
closetkido
, actualizado hace más de 1 año
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Resumen del Recurso
Chapter 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
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
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