> Thursday 21 October 2021 – Afternoon A Level Further Mathematics B (MEI) Y435/01 Extra Pure. RATED A+

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Answer all the questions. 1 In this question you must show detailed reasoning. A surface S is defined by z x = f( , y) where f( , x y) = + x x 3 2y y -2 2. (a) On the coordinate axes in the Printed... Answer Booklet, sketch the section z y = f( , 2 ) giving the coordinates of any turning points and any points of intersection with the axes. [4] (b) Find the stationary points on S. [7] 2 G is a group of order 8. (a) Explain why there is no subgroup of G of order 6. [1] You are now given that G is a cyclic group with the following features: • e is the identity element of G, • g is a generator of G, • H is the subgroup of G of order 4. (b) Write down the possible generators of H. [2] M is the group ({0, 1, 2, 3, 4, 5, 6, 7}, +8) where +8 denotes the binary operation of addition modulo 8. You are given that M is isomorphic to G. (c) Specify all possible isomorphisms between M and G. [4] 3 The matrix A is given by A 301 323 024 = JKKKL NOOOP . (a) Determine the characteristic equation of A. [3] (b) Hence verify that the eigenvalues of A are 1, 2 and 6 [Show More]

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