A-Level MathematicsYear 2022Q1
2 1. The group S4 is the set of all possible permutations that can be performed on the four numbers 1, 2, 3 and 4, under the operation of composition. For the group S4 (a) write down the identity element, (1) (b) write down the inverse of the element a, where a = 1 3 2 4 3 2 4 1 (1) (c) demonstrate that the operation of composition is associative using the following elements a = 1 3 2 4 3 2 4 1 b = 1 2 2 4 3 3 4 1 and c = 1 4 2 1 3 2 4 3 (2) (d) Explain why it is possible for the group S4 to have a subgroup of order 4 You do not need to find such a subgroup. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
Paper Source:9fm0-4a-que-20220628.pdf
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Exam Specification Info
This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.
Syllabus levelAdvanced Level (A-Level)
SubjectMathematics
Official MarksVariable (2–6 marks)