AQA PC3 Overview

Key things to know for PC3 AQA Maths

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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 mapped to a single y-value
One-to-many mapping = each x-value mapped to several y-values
Many-to-one mapping = several x-values map onto the same y-value
Many-to-many mapping = each x and y-value mapped to several other values
Modulus
|x| is an absolute value function; y-values always positive
Solve by squaring each side, or by considering each non-modulus value as both positive and
negative
Composite functions
One function followed by another
f(x) followed by g(x) = gf(x)
Inverse functions
To find inverse, swap x and y-values over in the f(x) equation
Domain of inverse = range of original
Range of inverse = domain of original
Can only find inverse for one-to-one or one-to-many mappings
Inverse is a reflection in the line y=x of the original function
Inverse trigonometric functions can be found if you restrict the domain to make the original
function a one-to-one mapping

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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 differentiated equation = 0
Second differentiation shows if a stationary point is a maximum or a minimum; maximum if
less than 0, minimum if more than 0…read more

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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…read more

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Exponentials and logarithms
Differentiating and integrating
+c…read more

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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…read more

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Numerical methods
Iterative method
Staircase diagram/cobweb diagram
Converging/diverging
Mid-ordinate rule
Simpson's rule…read more

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