plumiSubgroups, cyclic groups and Lagrange: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on DG.2 Subgroups, cyclic groups and Lagrange, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 6 questions on Subgroups, cyclic groups and Lagrange, as a list
- June 2025, Paper 3 Discrete, Q1 (1 mark): The group A is of order 9 The group B is a proper, non-trivial subgroup of A Find the order of B Circle your answer. [1 mark] 1 3 9 18
- June 2024, Paper 3 Discrete, Q7 (12 marks): (a) By considering associativity, show that the set of integers does not form a group under the binary operation of subtraction. Fully justify your answer. [2 m
- June 2023, Paper 3 Discrete, Q9 (9 marks): The group (C, +4) contains the elements 0, 1, 2 and 3 9 (a) (i) Show that C is a cyclic group. [2 marks] 9 (a) (ii) State the group of symmetries of a regular p
- June 2022, Paper 3 Discrete, Q7 (8 marks): The group G has binary operation * and order p, where p is a prime number. 7 (a) Determine the number of distinct subgroups of G Fully justify your answer. [2 m
- November 2021, Paper 3 Discrete, Q5 (11 marks): (a) Describe the conditions necessary for a set of elements, S, under a binary operation * to form a group. [3 marks] 5 (b) In the multiplicative group of integ
- June 2019, Paper 3 Discrete, Q5 (12 marks): The set S is defined as S = fA, B, C, Dg where A = 1 0 0 1 B = 0 −1 1 0 C = −1 0 0 −1 D = 0 1 −1 0 The group G is formed by S under matrix multiplication. The g
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