plumiGroups and Cayley tables: OCR MEI A‑Level Further Maths questions
OCR MEI 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 7 questions on Groups and Cayley tables, as a list
- June 2025, Extra Pure, Q1 (7 marks): A binary operation, ○, is defined on real numbers a and b by a ○ b 3 ab . = (a) Prove that ○ is associative over the real numbers R. [2] (b) Determine the value
- June 2024, Extra Pure, Q3 (12 marks): Fig. 3.1 shows an equilateral triangle, with vertices A, B and C, and the three axes of symmetry of the triangle, S S , b and Sc. The axes of symmetry are fixed
- June 2023, Extra Pure, Q4 (15 marks): The set G is given by G = {M: M is a real 2 # matrix and det M 2 = }. 1 (a) Show that G forms a group under matrix multiplication, #. You may assume that matrix
- June 2022, Extra Pure, Q4 (16 marks): A binary operation, , is defined on a set of numbers, A, in the following way. a b = k a k b k , for a, b ! A, - + 1 2 3 where k , k and k 3 are constants (whic
- November 2020, Extra Pure, Q4 (13 marks): (a) In each of the following cases, a set G and a binary operation are given. The operation may be assumed to be associative on G. Determine which, if any, of t
- June 2019, Extra Pure, Q4 (8 marks): T is the set {1, 2, 3, 4}. A binary operation • is defined on T such that a • a = 2 for all a ! T. It is given that (T, •) is a group. (a) Deduce the identity e
- June 2019, Extra Pure, Q6 (13 marks): ! 2 6 (a) Given that 7 is an irrational number, prove that a 7 b 0 for all ,a b where a and b - ! Q are not both 0. [2] (b) A set G is defined by G { a b 7 : ,a
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