Edexcel A-level Mathematics 'Core Mathematics 3 (C3)' 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 3 (C3).

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Preview of Edexcel A-level Mathematics 'Core Mathematics 3 (C3)' Revision

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Core Mathematics 3
Formulae
Exponentials and Logarithms ln = ln
Trigonometry sin - = - sin
cos - = cos
tan - = - tan
sin = cos ( - )
2
cos = sin ( 2 - )
sin
tan = cos
1
cosec = sin
1
sec = cos
cos 1
cot = sin = tan
sin + cos = 1 sin2 = 1 - cos 2 cos 2 = 1 - sin2
2 2
sec 2 - tan2 = 1 sec 2 = 1 + tan2 tan2 = sec 2 - 1
cosec 2 - cot 2 = 1 cosec 2 = 1 + cot 2 cot 2 = cosec 2 - 1
sin( + ) = sin cos + cos sin
sin( - ) = sin cos - cos sin
cos( + ) = cos cos - sin sin
cos( - ) = cos cos + sin sin
tan +tan 1
tan( + ) = 1-tan tan , ± ( + 2)
tan -tan 1
tan( - ) = , ± ( + )
1+tan tan 2
sin 2 = 2 sin cos
cos 2 = cos2 - sin2 = 2 cos2 - 1 = 1 - 2 sin2
2 tan
tan 2 =
1-tan2

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Differentiation
= ×
= +
-
=
2
= = -1
= () = ()-1 ()
= () = () ()
()
= ln () = ()
= sin () = () cos ()
= cos () = -() sin ()
= tan () = () sec 2 ()
= cosec () = -() cosec () cot ()
= sec () = () sec () tan ()
= cot () = -() cosec 2 ()…read more

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Notes Tips
Numerical Know that a solution is within a range by a change of sign
Methods Know that a stationary point is within a range by a change of
sign of the gradient
Remember to justify the number of decimal places
Algebra and () = ()() + () To simplify improper fractions:
Functions
()
= () +
() Use factorisation
() ()
Use algebraic long division
() = [()]
Use the remainder theorem
(||); reflection of positive () in -axis
Know that the domain…read more

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Trigonometry
1
sin 30° = 2 cos 30° =
3 1
tan 30° = 3 Know the graph of arcsin :
2
1 1 -intercept: (0,0)
sin 45° = cos 45° = tan 45° = 1
2 2 -intercept: (0,0)
3 1
sin 60° = cos 60° = 2 tan 60° = 3 Domain: -1 1
2
sin = 0 + , 180 - , ... Range: - 2 () 2
cos = 0 + , 360 - , ...…read more

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± ( + 2)
tan -tan 1
tan( - ) = 1+tan tan , ± ( + 2)
sin 2 = 2 sin cos
cos 2 = cos2 - sin2 = 2 cos2 - 1 = 1 -
2 sin2
2 tan
tan 2 = 1-tan2…read more

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Differentiation
= × =
1
Remember to change the right-hand side from to
( )
= +
-
=
2
= = -1
= () = ()-1 ()
= sin () = () cos ()
= cos () = -() sin ()
= tan () = () sec 2 ()
= sec () = () sec () tan ()
= cot () = -() cosec 2 ()
= cosec () = -() cosec () cot ()
= () = () ()
()
= ln ()…read more

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