Useful formula sheet

Useful formula sheet - List MF15 THE MINISTRY OF EDUCATION,...

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List MF15 THE MINISTRY OF EDUCATION, SINGAPORE in collaboration with UNIVERSITY OF CAMBRIDGE LOCAL EXAMINATIONS SYNDICATE General Certificate of Education Advanced Level MATHEMATICS (8864) MATHEMATICS (9740) MATHEMATICS (9810) LIST OF FORMULAE AND STATISTICAL TABLES
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PURE MATHEMATICS Algebraic series Binomial expansion: n n n n n n b b a n b a n b a n a b a + + + + + = + - - - K 3 3 2 2 1 3 2 1 ) ( , where n is a positive integer and )! ( ! ! r n r n r n = Maclaurin’s expansion: K K + + + + + = ) 0 ( f ! ) 0 ( f ! 2 ) 0 ( f ) 0 f( ) f( ) ( 2 n n n x x x x K K K + + - - + + - + + = + r n x r r n n n x n n nx x ! ) 1 ( ) 1 ( ! 2 ) 1 ( 1 ) 1 ( 2 ( ) 1 < x K K + + + + + + = ! ! 3 ! 2 1 e 3 2 r x x x x r x (all x ) K K + + - + - + - = + )! 1 2 ( ) 1 ( ! 5 ! 3 sin 1 2 5 3 r x x x x x r r (all x ) K K + - + - + - = )! 2 ( ) 1 ( ! 4 ! 2 1 cos 2 4 2 r x x x x r r (all x ) K K + - + - + - = + + r x x x x x r r 1 3 2 ) 1 ( 3 2 ) 1 ln( ( x < - 1 Y 1) Partial fractions decomposition Non-repeated linear factors: ) ( ) ( ) )( ( d cx B b ax A d cx b ax q px + + + = + + + Repeated linear factors: 2 2 2 ) ( ) ( ) ( ) )( ( d cx C d cx B b ax A d cx b ax r qx px + + + + + = + + + + Non-repeated quadratic factor: ) ( ) ( ) )( ( 2 2 2 2 2 c x C Bx b ax A c x b ax r qx px + + + + = + + + + 2
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Trigonometry B A B A B A sin cos cos sin ) sin( ± ± B A B A B A sin sin cos cos ) cos( m ± B A B A B A tan tan 1 tan tan ) tan( m ± ± A A A cos sin 2 2 sin A A A A A 2 2 2 2 sin 2 1 1 cos 2 sin cos 2 cos A A A 2 tan 1 tan 2 2 tan ) ( cos ) ( sin 2 sin sin 2 1 2 1 Q P Q P Q P + + ) ( sin ) ( cos 2 sin sin 2 1 2 1 Q P Q P Q P + ) ( cos ) ( cos 2 cos cos 2 1 2 1 Q P Q P Q P + + ) ( sin ) ( sin 2 cos cos 2 1 2 1 Q P Q P Q P + Principal values: π 2 1 - Y= sin - 1 x Y= π 2 1 ( x Y 1) 0 Y cos - 1 x Y π ( x Y 1) π π 2 1 1 2 1 tan < < - - x Derivatives ) f( x ) ( f x x 1 sin - 2 1 1 x - x 1 cos - 2 1 1 x - - x 1 tan - 2 1 1 x + x sec x x tan sec 3
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Integrals (Arbitrary constants are omitted; a denotes a positive constant.) ) f( x x x d ) f( 2 2 1 a x + - a x a 1 tan 1 2 2
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This note was uploaded on 12/21/2010 for the course MATH 262 taught by Professor Faber during the Spring '08 term at McGill.

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Useful formula sheet - List MF15 THE MINISTRY OF EDUCATION,...

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