Edexcel AS Further Mathematics 'Further Pure Mathematics 1 (FP1)' Revision

Contains a list of all the formulae you need for the exam, as well as further notes and tips on the Edexcel specification of Further Pure Mathematics 1 (FP1).

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Further Pure Mathematics 1

Formulae
Numerical Methods ( )
( )
Coordinate Systems ,
( )

,
Complex Numbers
,
( ( ) ( )),
,
( ) ( ) ,

Series
( )
( )( )

( )

Matrices ( )
( )

( )
( )

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Notes Tips
Numerical Methods ( ) Know how to use interval bisection

( )
Know how to use linear interpolation
( )
Know how to use the Newton-Raphson process

The Newton-Raphson process may diverge from the
( )
root and not converge to the root
Coordinate Systems , For a…

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Series
( )
( )( )

( )

Matrices ( ) ; singular An matrix has rows and columns
( ) ; non-singular An transformation matrix represents the
( ) transformation followed by the transformation and
( ) followed by the transformation

( )

( ) ( )
( )…

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Proof by Induction Let Know to use proof by induction:
( ) Use the basis step
Assume true Use the assumption step
( ) Use the inductive step
Let Use the conclusion step
( )
( )

( )
If the summation formula is true for , then it
has…

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If the matrix equation is true for , then it has
been shown true for . As the matrix
equation is true for , it has now also been
shown true for all by
mathematical induction

Let ( ) and let
( )
( )
Assume true
( )
Let…

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Let , , for general formula


( ) ( )
Assume , true for general formula

( ) ( )

Let for recurrence formula

[ ( ) ( )
]

( ) ( )

If is true for and , then it has
been shown true for . As is…

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