Edexcel A-level Mathematics 'Core Mathematics 4 (C4)' 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 Core Mathematics 4 (C4).

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Core Mathematics 4

Formulae
!
Sequences and Series (
) =
!(-)!
(-1)...(--1)
[(1 + ) ] = [1 + ( ) + + ( ) + ] , || < ,
1 1×2×...×
Differentiation
= () = ()

= () = () () ln


Integration = = +1 +…

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= -

=


=


=
2

=
2

-
=



[0 + 2(1 + 2 + + -1 ) + ]
2
1
= ()() = ()
()

Vectors = ||

|| = 2 + 2 + 2
| | = (2 - 1 )2 + (2 - 1 )2…

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Notes Tips
Algebra and Functions
...
= + + To split improper fractions:
(-)(... )
... Use algebraic division
= - + (-)2 +
(-)2 (... ) To split proper fractions:
... +
( 2 ++)(... )
= 2 ++ + Use substitution
Use comparing coefficients
Use substitution = 0…

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Differentiation = ()

= ()

Remember to include the differential


= ()
= () () ln



= ×
...
Know the areas and volumes of the triangle, square,
...
rectangle, parallelogram, trapezium, sphere, cone,

= (... ); directly proportional increase
cylinder, prism, pyramid, cube and cuboid

= -(... ); directly…

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= (+)
1
= ln + +
1
= + +
1
= +
1
= ln | + | +

= sin2 ( + ) To integrate sin2 ( + ) or cos2 ( + ), use the
cos 2 = 1 - 2 sin2 double-angle formulae:
1 1…

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1
= - 4 cos(2 + 2) +
= sin( + ) cos( + ) etc.
1
sin cos = [sin( + ) + sin( - )]
2
1
sin( + ) cos( + ) = 2 sin[( +
1
) + ( + )] + 2 sin[( - )…

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() () ()
= ()
= ln|()| + To integrate ,
() [()]
or ()[()] , use
() 1 integration by inspection:
= [()]
= -+1 [()]-+1 +
1 ( + 1)( 2 + 2 + 3)4
= ()[()] = +1 [()]+1 +
(2 + 1) 2 + + 5…

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= -

To integrate () or ln , use integration by
parts:
= [()] ; = , = ()


= [ln ] ; = ln , = 2 ln
(ln )2
( 2 + 1) ln
2 -
12 2 (3 + 2)5
2 2 sin 2
2 2 sec…

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Vectors = || Remember to draw a diagram
Use substitution to eliminate to solve a two vector
= -
intersection
= +
= + ( - ) Know the area of the triangle, rectangle and
= ; parallel parallelogram

|| = 2 + 2 + 2
| | = (2…

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