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 parabola, the standard form is , the
, parametric form is , the focus is
( ) and the directrix is
For a rectangular hyperbola, the standard form is
, the parametric form is ,…read more

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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
( )
( ) ( )
( )
( )( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ); no transformation
( ); 90° rotation anticlockwise
( ); reflection in
( ); reflection in
(…read more

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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 been shown true for .…read more

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If the matrix equation is true for , then it has
been shown true for .…read more

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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 .…read more

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