OCR 2023 GCE MATHEMATICS A H230/02: PURE MATHEMATICS AND MECHANICS AS LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

2 © OCR 2023 H230/02 Jun23 x 2 2 Formulae 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 Nh, 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 h "0 h Standard deviation / x 2 / fx2 = n -x 2 or = / f -x 2 The binomial distribution If X ~ B^n, ph then P^X = xh = c n mp x^1-ph n-x , mean of X is np, variance of X is np^1 -ph 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 2 3 © OCR 2023 H230/02 Jun23 Turn over 3 3 Section A Pure Mathematics 1 The quadratic equation kx2 + 3x + k = 0 has no real roots. Determine the set of possible values of