Pearson Edexcel GCE Advanced Subsidiary Level Further Mathematics (8FM0) Paper 22 Further Pure Mathematics 2 QP &MS JUNE 2024

Pearson Edexcel GCE Advanced Subsidiary Level Further Mathematics
(8FM0) Paper 22 Further Pure Mathematics 2 QP &MS JUNE 2024

, Afternoon


Further Mathematics
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Advanced Subsidiary
Further Mathematics options
22: Further Pure Mathematics 2
(Part of option A only)




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P75672A
©2024 Pearson Education Ltd.
F:1/1/1/

, 1. (i) The table below is a Cayley table for the group G with operation °




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° a b c d e f

a d c b a f e

b e f a b c d

c f e d c b a

d a b c d e f

e b a f e d c

f c d e f a b


(a) State which element is the identity of the group.
(1)




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(b) Determine the inverse of the element (b°c)
(2)
(c) Give a reason why the set {a, b, e, f } cannot be a subgroup of G. You must
justify your answer.
(1)
(d) Show that the set {b, d, f } is a subgroup of G.
(2)
(ii) Given that H is a group with an element x of order 3 and an element y of
order 6 satisfying

yx = xy5

show that y3xy3x2 is the identity element.
(3) DO NOT WRITE IN THIS AREA




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