Edexcel A-level Further Mathematics 'Further Pure Mathematics 2 (FP2)' 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 2 (FP2).

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Further Pure Mathematics 2

Formulae
Coordinate Systems = cos cos =
= sin sin =
= 2 + 2 2 = 2 + 2

= arctan tan =

1
= 2
2
1
= 2 2
1
=
2

=0 ( sin ) = 0; parallel



=0
( cos )…

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1

= - = cos - sin ; Euler's relation
1
+ = 2 cos
1
- = 2 sin

= ( ) = = [(cos + sin )] = (cos + sin ); de Moivre's theorem
1
+ = 2 cos
1
- = 2 sin
Differentiation 1

=…

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() ()
() = () + ()( - ) + 2!
( - )2 + + !
( - ) + ; Taylor series
3 5 2+1
sin = - 3!
(-1) (2+1)!,
+ 5! + +
2 4 2
cos = 1 - 2! + 4! + + (-1)…

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Notes Tips
Coordinate Systems = cos cos = To convert a Cartesian coordinate to a polar
= sin sin = coordinate or a polar equation to a Cartesian
(, ) ( cos , sin ) equation:
= 2 + 2 2 = 2 + 2 Find by substituting = 2…

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Find or by substituting the equation into

( cos ) =0


Algebra and Functions < , Remember that , or
- -
( - ) < ( - )2 < 0 To solve an inequality:
( - )[ - ( - )] < 0 Draw a sketch by rearranging the…

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arg (1 ) = arg(1 ) - arg(2 )
2




= = cos + sin ; Euler's relation Know the proof of de Moivre's theorem for +

1
= - = cos - sin ; Euler's relation Basis step by letting = 1:

1 = [(cos + sin )]1 =…

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As de Moivre's theorem is true for = 1, then
it has been shown true for all 1 and
+ by mathematical induction
Know the proof of de Moivre's theorem for -
[(cos + sin )] = [(cos + sin )]-
1
= [(cos + sin )]
1
= (cos…

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Find by differentiating the substitution

Find the new equation by substituting and


into the first order differential equation


2
2 + + = () = . . +. . Remember to re-substitute at the end
To use substitution:
2 + + = 0; auxiliary equation
Find , and by rearranging…

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complementary function 3 If two equal real roots, use complementary
= + + - = ( cos + function 2
sin ); complementary function 4 If two imaginary roots, use complementary
function 3
If two complex roots, use complementary
function 4
= + + 2 ; particular integral 1a Know…

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() or Taylor series
() = () + ()( - ) + 2!
( - )2 +
()
+ !
( - ) + ; Taylor series

sin = -
3
+
5
+ +
2+1
(-1) (2+1)!, Know how to derive the series expansion of sin ,
3! 5!…

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