Mathematics > As Level Question Papers > > Friday 22 October 2021 – Afternoon A Level Further Mathematics A Y545/01 Additional Pure Mathema (All)

> Friday 22 October 2021 – Afternoon A Level Further Mathematics A Y545/01 Additional Pure Mathematics

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Answer all the questions. 1 In this question you must show detailed reasoning. Express the number 4172310 in hexadecimal (base 16). [3] 2 The following Cayley table is for G, a group of order 6. Th... e identity element is e and the group is generated by the elements a and b. G e a a2 b ab a b 2 e e a a 2 b ab a b 2 a a a 2 e ab a b 2 b a 2 a 2 e a a b 2 b ab b b a b 2 ab e a2 a ab ab b a b 2 a e a2 a b 2 a b 2 ab b a2 a e (a) List all the proper subgroups of G. [4] (b) State another group of order 6 to which G is isomorphic. [1] 3 The points P, Q and R have position vectors p i = + 2 5 j k + , q i = -j k + and r i = + 2 j k +t respectively, relative to the origin O. Determine the value(s) of t in each of the following cases. (a) The line OR is parallel to p q # . [2] (b) The volume of tetrahedron OPQR is 13. [4] 4 Solve the simultaneous linear congruences x / 1 (mod 3), x / 5 (mod 11), 2 5 x / (mod 17). [6] 5 The surface S has equation x y z 2 2 + + 2 = - xyz 1. (a) Show that ( ) z xy x zx y z zy 2 2 1 2 22 22 - + c m = + ^ h. [6] (b) Deduce that S has no stationary point [Show More]

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