OCR A Level Further Mathematics A Paper 1 Y541-01 Pure Core 2 June 2022 QUESTION PAPER

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Answer all the questions. 1 (a) Find a vector which is perpendicular to both 3i - 5j - k and i + 3j - 4k. [1] The equations of two lines are r = 2i + 3j + 3k+ m(i - 2j + k) and r = i + 11j - 4k + n... (-i + 3j - 2k). (b) Show that the lines intersect, stating the point of intersection. [5] 2 Two polar curves, C1 and C2 , are defined by C r: 2 1 = i and C r: 1 2 = +i where 0 2 G Gi r. C1 intersects the initial line at two points, the pole and the point A. (a) Write down the polar coordinates of A. [2] (b) Determine the polar coordinates of the point of intersection of C1 and C2 . [2] The diagram below shows a sketch of C1 . O Initial line A (c) On the copy of this sketch in the Printed Answer Booklet, sketch C2 . [1] 3 In this question you must show detailed reasoning. The roots of the equation 463 xxx 9 0 3 2 + - + = are a, b and c. Find a cubic equation with integer coefficients whose roots are a + b, b + c and c + a. [6] 3 © OCR 2022 Y541/01 Jun22 Turn over 4 In this question you must show detailed reasoning. Determine the smallest value of n for which ... ... n n 1 2 1 2 341 2 2 2 2 + + + + + + . [4] 5 (a) By using the exponential definitions of sinhx and coshx, prove the identity cosh 2x x cosh sinh x 2 2 / + . [2] (b) Hence find an expression for cosh2x in terms of coshx. [1] (c) Determine the solutions of the equation 5cosh 2x = 16cosh x + 21, giving your answers in exact logarithmic form. [Show More]

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