Wednesday 13 October 2021 – Afternoon AS Level Mathematics A H230/02 Pure Mathematics and Mechanics. 100% proven passing rate.

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Formulae AS Level Mathematics A (H230) Binomial series a b n a a n nC C n n b an n b a C b b r n r r n 1 1 2 2 2 ^ + = h + + - - + + f f - + + ^n ! Nh, where C ! ! n ! r r n r n nC r ... n r = = = c m ^ - h Differentiation from first principles x lim h x h x f f f h 0 = + - " l^ h ^ ^ h h Standard deviation n x x xn x 2 2 - 2 = - /^ h / or f f x x f fx x 2 2 - 2 = - ^ h / / // The binomial distribution If X n + B^ , ph then X x n x P^ = = h c mp p x^1- hn x - , mean of X is np, variance of X is np^1-ph Kinematics v u = +at s ut at 12 2 = + s u v t 12 = + ^ h v u 2 2 = +2as s vt at 12 2 = -3 © OCR 2021 H230/02 Oct21 Turn over Section A: Pure Mathematics Answer all the questions. 1 Given that ( ) x-2 is a factor of 2 4 x k 3 + - x , find the value of the constant k. [2] 2 y R x O 2 –4 4 The diagram shows the line y x = -2 4 + and the curve y x = - 2 4. The region R is the unshaded region together with its boundaries. Write down the inequalities that define R. [3] 3 Sam invested in a shares scheme. The value, £V, of Sam’s shares was reported t months after investment. • Exactly 6 months after investment, the value of Sam’s shares was £2375. • Exactly 1 year after investment, the value of Sam’s shares was £2825. (a) Using a straight-line model, determine an equation for V in terms of t. [3] Sam’s original investment in the scheme was £1900. (b) Explain whether or not this fact supports the use of the straight-line model in part (a). [2]4 © OCR 2021 H230/02 Oct21 4 The quadratic polynomial 2 3 x2 - is denoted by f(x). Use differentiation from first principles to determine the value of f′(2). [5] 5 (a) Show that the equation 2 3 cos t x x an2 = + ( ) 1 cos x can be expressed in the form 5 3 cos c 2x x + - os 2 0 = . [3] (b) In this question you must show detailed reasoning. Hence solve the equation 2 3 cos t i i an23 3 = + ( ) 1 3 cos i , giving all values of i between 0° and 120°, correct to 1 decimal place where appropriate. [6] 6 A curve C has an equation which satisfies y x 3 2 x d d 2 2 2 = + , for all values of x. (a) It is given that C has a single stationary point. Determine the nature of this stationary point. [1] The diagram shows the graph of the gradient function for C. x –1 O dydx 3 (b) Given that C passes through the point ( , -1 4 1), find the equation of C in the form y x = f( ). [5 [Show More]

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