OCR 2023 GCE MATHEMATICS B MEI H640/01: PURE MATHEMATICS AND MECHANICS A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

2 © OCR 2023 H640/01 Jun23 = r n r Kr O e n+1 2 Formulae A Level Mathematics B (MEI) (H640) Arithmetic series S = 1 n^a+lh = 1 n"2a+^n-1hd, n 2 2 Geometric series Sn = a^1-r nh 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 = J n N = L P n! 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 2! Differentiation f^xh r! fl^xh tan kx k sec2 kx sec x sec x tan x cot x -cosec2 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 fl^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 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 H640/01 Jun23 Turn over 2 i i P 2 2 2 2 2 2 Trigonometric identities sin^A!Bh = sinAcosB! cosAsinB cos^A!Bh = cosA cos B " sin Asin B tanA!tanB 1 " tan A tan B Numerical methods aA!B ! ^k+ 1hrk Trapezium rule: ; b y dx ≈ 1 h"^y +y h +2^y +y +f+ y h,, where h = b-a a 2 0 n 1 2 n-1 n f^x h The Newton-Raphson iteration for solving f^xh = 0: xn+1 Probability = xn - n f