OCR 2023 GCE MATHEMATICS B MEI H630/01: PURE MATHEMATICS AND MECHANICS AS LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

2 © OCR 2023 H630/01 Jun23 -1 2 2 2 L P 2! r! Formulae AS Level Mathematics B (MEI) (H630) Binomial series (a + b) n = a n + nC1 a n–1 b + nC2 a n–2 b 2 + ... + nCr a n–r b r + ... +bn n e N , n Jn N n! where Cr = n Cr = K r O = r!^n -rh! ^1+xh n = 1+nx+ n^n -1h x 2 +...+ n^n - 1h...^n -r+1h x r +... x 1 1, n e R Differentiation from first principles f l(x) = lim f^x + hh -f(x) h"0 h Sample variance 2 1 2 2 ^/x ih 2 2 2 s = n Sxx where Sxx = /(xi - - x) = /xi - n = /xi -n - x Standard deviation, s = The binomial distribution If X + B n, p then P(X = r) = nCr p r q n-r where q = 1 -p Mean of X is np Kinematics Motion in a straight line v = u+at s = ut+ 1 at2 s = 1 (u + v) t v 2 = u 2 + 2as s = vt1 at2 variance 3 © OCR 2023 H630/01 Jun23 Turn over 1 A particle moves along a straight line. Its velocity vms -1 at time ts is given by v = 2t+0.6t 2 . Find an expression for the acceleration of the particle at time t. [2] 2 The height of the first part of a rollercoaster track i