OCR A Level Further Mathematics B (MEI) Y420-01 Core Pure QUESTION PAPER JUNE 2022

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In this question you must show detailed reasoning. Find the exact value of 3 d x x x 4 5 1 2 3 - + y . [5] 3 In this question you must show detailed reasoning. Solve the equation 3 2 cosh x... x sinh , 2 = giving your solutions in exact logarithmic form. [6] 4 (a) A transformation with associated matrix m 0 2 2 1 0 1 2 3 - J L K K K N P O O O , where m is a constant, maps the vertices of a cube to points that all lie in a plane. Find m. [3] (b) The transformations S and T of the plane have associated matrices M and N respectively, where k M 3 1 4 = - J L K K N P O O and the determinant of N is 3 1 k+ . The transformation U is equivalent to the combined transformation consisting of S followed by T. Given that U preserves orientation and has an area scale factor 2, find the possible values of k. [4] 5 (a) Sketch the polar curve r a = - ( ) 1 0 cos i i , , G 1 2r where a is a positive constant. [2] (b) Determine the exact area of the region enclosed by the curve. [Show More]

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