4202515
Beschreibung
Mindmap von closetkido, aktualisiert more than 1 year ago
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Erstellt von closetkido
vor etwa 9 Jahre
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Chapter 1
- Surds
- Simplifying
- Find something that can
be simplified
- sqrt(16)=4
- sqrt(25)=5
- sqrt(16)=4
- Find something that can
be simplified
- Rationalising
- Simple
- Multiply by the root on
top and bottom
- sqrt(7) x sqrt(7) = 7
- sqrt(7) x sqrt(7) = 7
- Multiply by the root on
top and bottom
- Complex
- Multiply by the same
numbers with opposite
add/subtract sign
- 3+sqrt(7) x 3-sqrt(7) = 9+7 = 16
- 3+sqrt(7) x 3-sqrt(7) = 9+7 = 16
- Multiply by the same
numbers with opposite
add/subtract sign
- Simple
- Simplifying
- Indices
- Rules of Indices
- Addition/Subtraction
- Factors with different indices do not combine by
addition or subtraction they stay separate.
- 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.
- e.g. 2^5 / 2^3 = 2^2 as 5-3 = 2.
- Subtract the indices
- Multipication
- Add the indices
- e.g. 2^5 x 2^3 = 2^8 as 5+3 = 8
- e.g. 2^5 x 2^3 = 2^8 as 5+3 = 8
- Add the indices
- Brackets
- Multiply the brackets
- e.g. (2^5)^3 = 2^15 as 5 x 3 = 15
- e.g. (2^5)^3 = 2^15 as 5 x 3 = 15
- Multiply the brackets
- Addition/Subtraction
- More Indices
- Negative Powers
- If power is negative, then flip
and make power positive
- e.g. 2x^-2 = 2/x^2
- e.g. 2x^-2 = 2/x^2
- If power is negative, then flip
and make power positive
- Fractional Powers
- x^a/b = (brt(x))^a
- e.g. x^4/3 = (4rt(x))^3
- e.g. x^4/3 = (4rt(x))^3
- x^a/b = (brt(x))^a
- Equations
- When moving fractional powers,
flip but keep +- the same
- e.g. x^2/3 = 100 ==> x = 100^3/2
- 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)
- e.g. x^3 = 100 => x = 3rt(100)
- If negative, then make into
fraction and cross-multiply.
- If positive, then make a root.
- Moving fractional powers
- If positive, then make power.
- e.g. x^1/2 = 100 => x = 100^2
- 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
- e.g. x^-3/2 = 100 => x = 100^-2/3
- If positive, then make power.
- When moving fractional powers,
flip but keep +- the same
- Negative Powers
- Rules of Indices
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