# 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 + , ( -1)
+1
1
= ( + ) = (+1) ( + )+1 +
1
= (+) = + +
1 1
= + = ln | + | +
1
= sin( + ) = - cos( + ) +
1
= cos( + ) = sin( + ) +
1
= sec 2 ( + ) = tan( + ) +
1
= sec( + ) tan( + ) = sec( + ) +
1
= cosec 2 ( + ) = - cot( + ) +
1
= cosec( + ) cot( + ) = - cosec( + ) +
1
= tan( + ) = ln | sec( + )| +
1
= sec( + ) = ln | sec( + ) + tan( + ) | +
1
= cot( + ) = ln | sin( + ) | +
1
= cosec( + ) = - ln|cosec( + ) + cot( + )| +

## Other pages in this set

### Page 2

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

### Page 3

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

### Page 4

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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 proportional decrease Remember that rate is
= ; inversely proportional increase
...
= - ; inversely proportional decrease

### Page 5

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To integrate sin2 ( + ) or cos2 ( + ), use the
cos 2 = 1 - 2 sin2 double-angle formulae:
1 1
sin2( + ) = 2 - 2 cos(2 + 2) (cos - sin )2
1-sin
1 1
= - sin(2 + 2) + cos2
2 4
(1+sin )2
= cos 2( + ) cos2
cos 2 = 2 cos2 - 1 To integrate tan ( + ) or cot 2 ( + ), use the
2
1 1

### Page 6

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To integrate = tan( + ), cosec( + ),
1
=
ln | sec( + )| + sec( + ) or cot( + ), use standard results
= cosec( + )
1
= - ln|cosec( + ) +
cot( + )| +
= sec( + )
1
= ln | sec( + ) + tan( +
) | +
= cot( + )
1
= ln | sin( + ) | +
... ...
= +
1
To integrate (-)(... ) or (-)2 (...…read more

### Page 7

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To integrate ,
() [()]
or ()[()] , use
() 1 integration by inspection:
= [()]
= -+1 [()]-+1 +
1 ( + 1)( 2 + 2 + 3)4
= ()[()] = +1 [()]+1 +
(2 + 1) 2 + + 5
sin5 3 cos 3
cosec 2 2 cot 2
2
cos sin
2
2 +3
2+1
2 ++5
sin cos
cos 2+3
sin cos
cos 2+3
[()] 1
= [()] ; = () To integrate [()] [()] or [()] [()]2 , use

### Page 8

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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 2 tan
ln
3
ln
3
sin2
=
Remember to draw a graph
Remember to change limits from to
=
2
Know the calculation for percentage error
=
2
=
=
(1 - 2 )
=

### Page 9

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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 - 1 )2 + (2 - 1 )2 + (2 - 1 )2
= 1 2 + 1 2 + 1 2