Mathematics formula sheet, Cheat Sheet of Mathematics

Download Mathematics formula sheet and more Cheat Sheet Mathematics in PDF only on Docsity! List of formulae and tables of the normal distribution (MF9) 28 Cambridge International AS and A Level Mathematics 9709. Syllabus for examination in 2017 and 2018. 6. List of formulae and tables of the normal distribution (MF9) PURE MATHEMATICS Algebra For the quadratic equation :ax bx c 02 + + = : x a b b ac 2 42!= − −^ h For an arithmetic series: ,u a n d S n a l n a n d1 2 1n n 2 1 2 1= + − = + = + −^ ^ ^h h h" , For a geometric series: , ,u ar S r a r r S r a r1 1 1 1 1<n n n n 1 != = − − = −3 − ^ ^ ^ h h h Binomial expansion: ,a b a n a b n a b n a b b1 2 3 n n n n n n1 2 2 3 3 g+ = + + + + +− − − J L K K K J L K K K J L K K K ^ N P O O O N P O O O N P O O O h where n is a positive integer and ! ! !n r r n r n= − J L K K K ^ N P O O O h ! ! ,x nx n n x n n n x1 1 2 1 3 1 2n 2 3g+ = + + − + − − ^ ^ ^ ^ h h h h where n is rational and x 1< Trigonometry Arc length of circle r in radiansi i= ^ h Area of sector of circle r in radians2 1 2i i= ^ h tan cos sin /i i i . ,cos sin tan sec cot cosec1 1 12 2 2 2 2 2 / / /i i i i i i+ + + sin sin cos cos sinA B A B A B! !/^ h cos cos cos sin sinA B A B A B! "/^ h tan tan tan tan tanA B A B A B 1! " ! /^ h sin sin cosA A A2 2/ cos cos sin cos sinA A A A A2 2 1 1 22 2 2 2 / / /− − − tan tan tanA A A2 1 2 2= − Principal values: sin x2 1 1 2 1 G Gr r− − cos x0 1 G G r− tan x< <2 1 1 2 1r r− − List of formulae and tables of the normal distribution (MF9) 29Cambridge International AS and A Level Mathematics 9709. Syllabus for examination in 2017 and 2018. Differentiation xf^ h xf l^ h xn nxn–1 1n x x 1 ex ex sin x cos x cos x –sin x tan x sec2 x uv u x v v x u d d d d+ u v v v x u u x v d d d d 2 − x y x y t y t xIf f ( ) and g( ) then d d d d d dt t '= = = Integration xf^ h ( )x xf dy xn n x c n1 1 n 1 !+ + − + ^ h x 1 x c1n + ex ex + c sin x – cos x + c cos x sin x + c sec2 x tan x + c u x v x uv v x u x x x x x c1 d d d d d d f f d n f = − = + l ^ ^ ^ h h h yy y Vectors If a = a1i + a2j + a3k and b = b1i + b2j + b3k then a.b = a1b1 + a2b2 + a3b3 = cosa b i Numerical integration Trapezium rule: f ,h hwhere. =dxx y y y y y n b a2 a b n n2 1 0 1 2 1g+ + + + + − −^ ^h h" ,y