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Functions
Domain and range
Domain is the set of permitted x-values
Range is the set of permitted y-values f(x) values
x=R means x can be any of the reals
f(x)=R means f(x) can be any of the reals


Mappings
Show relationship between x and y-values
Ono-to-one mapping = each x-value…

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Differentiation
Chain rule


u=bracketed function
y=u to a power of something


Product rule

u=one bracket
v=other bracket


Quotient rule


u=top of fraction
v=bottom of fraction


x as a function of y




Applications
To find gradient of a curve at a point, substitute x-value into differentiated equation
Stationary point is when…

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Trigonometric functions
Cosec, sec and cot (reciprocal trigonometric functions)







Trigonometric identities









Differentiation of sin, cos and tan







Integration of sin, cos



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Exponentials and logarithms
Differentiating and integrating


+c








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Integration
By substitution
Opposite of chain rule
Take bracketed function as u

Find
Substitute into original
Replace u's with bracketed function


By parts



Volumes of revolution
revolution in y-axis

revolution in x-axis

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Numerical methods
Iterative method
Staircase diagram/cobweb diagram
Converging/diverging



Mid-ordinate rule




Simpson's rule

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