edexcel level 3 gce 8fm0/22 further mathematics advanced subsidiary further ma thematics may 2023

EDEXCEL LEVEL 3 GCE
8FM0/22

FURTHER MATHEMATICS
ADVANCED SUBSIDIARY FURTHER MATHEMATICS
May 2023

,1. The operation * is defined on the set G = {0, 1, 2, 3} by

x * y ≡ x + y – 2xy (mod 4)




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(a) Complete the Cayley table below.
(2)


* 0 1 2 3


0


1


2




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3



(b) Show that G is a group under the operation *
(You may assume the associative law is satisfied.)
(3)
(c) State the order of each element of G.
(2)
(d) State whether G is a cyclic group, giving a reason for your answer.
(1)


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2
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, Question 1 continued
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(Total for Question 1 is 8 marks)

3
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