> AS Level Further Mathematics B (MEI) (H635) A Level Further Mathematics B (MEI) (H645) Formulae Booklet

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Contents A level Mathematics Core Pure Mechanics Further Pure with Technology Extra Pure Numerical Methods Statistics Statistical tables A level Mathematics Arithmetic series S n n = + 2 1 ... ( ) a l = + 2 1 n a { ( 2 1 n d - ) } Geometric series ( ) S r a r 11 n n = - - S for r a r 3 = 1- 1 1 Binomial series ( ) a b + = n n a a + + n n C C 1 - - 1b a n n 2 2 2 b a + + f f nCr n r - b b r n + + ( ) n ! N , where !( )! ! C C nr r n r n n r n r = = = - JKKL NOOP ( ) , ! ( ) ! ( ) ( ) x nx x n n n x r n n n r 1 1 x 1 2 1 1 1 + = n r + + - 2 + + f - - f + +f ^ 1 ! Rh Differentiation f( ) x f l( ) x tankx k k sec2 x sec x sec t x x an cot x -cosec2x cosec x -cosec c x x ot Quotient Rule , dd dd dd y uv yx v v ux u vx = = 2 - Differentiation from first principles f ( ) x lim f f ( ) ( ) h x h x h 0 = + - " l3 © OCR 2020 Further Mathematics B (MEI) Turn over Integration ( ) ( ) f ( ) y fl xx d l x x = + n f c f f ( ) x x ( ) d f x ( ) n x c 1 n 1 n 1 = y l ^ ^ h h + + + Integration by parts d y y u dvx dx u = - v v ddux dx Small Angle Approximations sin c i i . . , , os i i 1 - 2 1 2 tan i i . where i is measured in radians Trigonometric identities sin s ( ) A B ! ! = inA B cos cosA B sin cos c ( ) A B ! " = osA B cos sinA B sin tan( ) ( ( ) ) tan tan tan tan A B A B A B A B k 1 2 1 ! " ! = + ! ! r Numerical methods Trapezium rule: y x d h y {( y y ) ( 2 y y )} b a 2 n n 1 y . 0 1 + + + + 2 1 f + - , where h = b a -n The Newton-Raphson iteration for solving ( ) : ( ) ( ) f ff x x x x x 0 n n n n = = +1 - l Probability P( ) A B , + = + P P P ( ) A B A ( ) - ( ) B P P ( ) A B + = = ( ) A B P P ( ) A B ( )P( ) A B or ( ) ( ) ( ) P P P A B B A B + = Sample Variance s n S 1 1 xx 2 = - where S x ( ) x x xn x nx xx i i i i 2 2 2 2 = - = - = - ^ h 2 / / / / Standard deviation, s = variance [Show More]

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