plumiGroups and Cayley tables: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 7.1 Groups and Cayley tables, 2018–2025, 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 13 questions on Groups and Cayley tables, as a list
- June 2025, Further Pure 2, Q1 (7 marks): The set S = {1, 3, 5, 9, 11, 13} forms the group G, under the operation multiplication modulo 14 (a) Complete the Cayley table below for the group G ×14 1 3 5 9
- June 2025, AS Further Pure 2, Q2 (8 marks): (i) Using a suitable algorithm and without performing any division, determine whether 13 306 617 is divisible by 9 (2) (ii) The group G = {1, 3, 7, 9, 11, 13, 1
- June 2024, Further Pure 2, Q7 (10 marks): The set of matrices G = {I, A, B, C, D, E} where I A B C D 1 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 E 0 1 1 1 with the operation Ä2
- June 2023, Further Pure 2, Q7 (6 marks): The set G 3 2 with the operation of x y x y xy 3 1 2 forms a group. (a) Determine the identity element of this group. (2) (b) Determine the inverse of a gener
- June 2023, AS Further Pure 2, Q1 (8 marks): The operation * is defined on the set G = {0, 1, 2, 3} by x * y ≡ x + y – 2xy (mod 4) (a) Complete the Cayley table below. (2) * 0 1 2 3 0 1 2 3 (b) Show that G
- June 2022, Further Pure 2, Q1 (6 marks): 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
- June 2022, AS Further Pure 2, Q3 (9 marks): (i) Let G be a group of order 5 291 848 Without performing any division, use proof by contradiction to show that G cannot have a subgroup of order 11 (3) (ii) (
- November 2021, Further Pure 2, Q2 (8 marks): A binary operation on the set of non‑negative integers, + 0, is defined by m n = ½m – n½ m, n ∈ + 0 (a) Explain why + 0 is closed under the operation
- November 2020, Further Pure 2, Q6 (10 marks): 1 2 3 4 5 6 Figure 3 Figure 3 shows a plane shape made up of a regular hexagon with an equilateral triangle joined to each edge and with alternate equilateral t
- November 2020, AS Further Pure 2, Q1 (8 marks): The set G = {1, 3, 7, 9, 11, 13, 17, 19} under the binary operation of multiplication modulo 20 forms a group. (a) Find the inverse of each element of G. (3) (b
- June 2019, Further Pure 2, Q6 (12 marks): (i) A binary operation * is defined on positive real numbers by a * b = a + b + ab Prove that the operation * is associative. (4) (ii) The set G ^
- June 2019, AS Further Pure 2, Q4 (7 marks): The set e p q r s , , , , { } forms a group, A, under the operation * Given that e is the identity element and that p*p = s s*s = r p*p*p = q (a) show that (i)
- June 2018, AS Further Pure 2, Q2 (10 marks): A B C O y z x Figure 1 Figure 1 shows an equilateral triangle ABC. The lines x, y and z and their point of intersection, O, are fixed in the plane. The triangle
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