OCR 2023 GCE MATHEMATICS A H230/01: PURE MATHEMATICS AND STATISTICS AS LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

2 Formulae © OCR 2023 H230/01 Jun23 x 2 2 2 h"0 h AS Level Mathematics A (H230) 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 , where nC = C = c n m = n! r n r r r!^n -rh! Differentiation from first principles fl^xh = lim f^x + hh-f^xh Standard deviation /x 2 / fx2 = n -x 2 or = / f -x 2 The binomial distribution If X + B n, p then P^X = xh = c n mp x^1 -ph n-x , mean of X is np, variance of X is np 1 -p Kinematics v = u+at s = ut + 1 at2 s = 1^u + vht v 2 = u 2 + 2as s = vt1 at2 /^x - xh 2 n / f ^x - xh 2 / f 3 Section A © OCR 2023 H230/01 Jun23 Turn over OP OP 3 6 12 2 Pure Mathematics 1 (a) Prove that cos x +sin x tan x / 1 (where x ! 1 nr for any odd integer n). [3] cos x 2 (b) Solve the equation 2 sin2 x = cos2 x for 0c G x G 180c. [2] 2 (a) The points A, B and C have position vectors c -4 m, c -3 m and c -1 m respectively. (i) Show that B lies on AC. [2] (ii) Find the ratio AB| BC