OCR 2023 GCE MATHEMATICS A H240/03: PURE MATHEMATICS AND MECHANICS A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

2 © OCR 2023 H240/03 Jun23 ^ h = n+1 2 n 2 2 2! r! dx dx Formulae A Level Mathematics A (H240) Arithmetic series S = 1 n^a + lh = 1 n"2a +^n - 1hd, Geometric series Sn = a 1-r n 1 -r a 3 1-r for r 1 1 Binomial series ^a+bh n = a n + nC1 a n-1 b+ nC2 a n-2 b 2 +f+ nCr a n-r b r +f+b n ^n e Nh, where nC = C = c n m = n! r n r r r!^n -rh! ^1+xh n = 1+nx+ n^n -1h x 2 +f+ n^n -1hf^n -r+1h x r +f ^x 1 1, n e Rh Differentiation f x fl x tan kx k sec2 kx sec x sec x tan x cot x -cosec 2 x cosec x -cosec x cot x u dy v du -u dv Quotient rule y = v , dx = dx dx v 2 Differentiation from first principles fl^xh = lim f^x+hh-f^xh h " 0 h Integration c f l^xh d f^xh dx = ln f^xh + c ;fl^xhaf^xhk n dx = 1 af^xhk n+1 +c Integration by parts ; u dv dx = uv - ; v du dx Small angle approximations sin i.i, cosi. 1 - 1 i 2 , tan i.i where i is measured in radians e S 3 © OCR 2023 H240/03 Jun23 Turn over /^x - - xh 2 n 2 ^ hP B x 2 2 2 2 2 2 2 n 1 2 n n v n v n Trigonometric identities sin cos A!B A!B = sin A cos B ! cos A sin B = cos A cos B " sin Asin B tan A ! tan B 1 " tan A tan B aA!B ! ^k+ 1hrk Numerical methods Trapezium rule: y b y dx . 1 h"^y +y h +2^y +y +