OCR Thursday 7 October 2021 – Afternoon A Level Further Mathematics A Y541/01 Pure Core 2

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Answer all the questions. 1 Two matrices, A and B, are given by a A 12 231 111 = - - J - KKKL NOOOP and B 618 368 441 = - - - - - - JKKKL NOOOP where a is a constant. Find the v... alue of a for which AB = BA. [3] 2 In this question you must show detailed reasoning. The complex numbers z1 and z2 are given by z1 = - 3 7i and z2 = + 2 4i. (a) Express each of the following as exact numbers in the form a + bi. (i) 3 4 z z 1 2 + [1] (ii) z z 1 2 [2] (iii) zz 1 2 [2] (b) Write z1 in modulus-argument form giving the modulus in exact form and the argument correct to 3 significant figures. [3]3 © OCR 2021 Y541/01 Oct21 Turn over 3 The line l 1 has equation r 133 322 = - + m - JKKKL JKKKL NOOOP NOOOP . The plane P has equation r. 253 - 4 - = JKKKL NOOOP . (a) Find the position vector of the point of intersection of l1 and P. [3] (b) Find the acute angle between l1 and P. [3] A is the point on l1 where m = 1. l 2 is the line with the following properties. • l 2 passes through A • l 2 is perpendicular to l1 • l 2 is parallel to P (c) Find, in vector form, the equation of l2. [3] 4 In this question you must show detailed reasoning. Determine the value of ( ) 2 3 r r 2 1 100 + /= . [3] 5 In this question you must show detailed reasoning. (a) Using the definition of coshx in terms of exponentials, show that cosh 2 2 x x / cosh2 -1. [2] (b) Solve the equation cosh 2 3 x x = + cosh 1, giving all your answers in exact logarithmic form [Show More]

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