OCR 2023 GCE MATHEMATICS B MEI H640/02: PURE MATHEMATICS AND STATISTICS A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

2 © OCR 2023 H640/02 Jun23 ^ h = e n+1 2 n 2 2 L P Formulae A Level Mathematics B (MEI) (H640) 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 N , n J n N n! where Cr = n Cr = K r O = 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 R 2! Differentiation f x r! 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 ; f l^xhaf^xhk n dx = 1 af^xhk n +1 + c Integration by parts ; u dv dx = uv -; v du dx dx dx Small angle approximations sin i.i, cosi. 1 - 1 i 2 , tan i.i where i is measured in radians S 3 © OCR 2023 H640/02 Jun23 Turn over 2 i i 2 2 2 2 2 2 2 n 1 2 n Trigonometric identities sin cos A!B A!B = sinAcosB! cosAsinB = cosAcosB" sinAsinB tanA!tanB 1" tanAtanB Numerical methods aA!B ! ^k+ 1hr