Useful formula sheet

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

This preview shows pages 1–5. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/21/2010 for the course MATH 262 taught by Professor Faber during the Spring '08 term at McGill.

### Page1 / 8

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online