plumiSubgroups, cyclic groups and Lagrange: OCR MEI A‑Level Further Maths questions
OCR MEI A-Level Further Maths past-paper questions on 7.2 Subgroups, cyclic groups and Lagrange, 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.
Questions from
Paper
All papers
Exam
All years
Loading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDF
All 4 questions on Subgroups, cyclic groups and Lagrange, as a list
- June 2025, Extra Pure, Q3 (8 marks): M is the group ({0, 1, 2, 3, 4, 5, 6, 7, 8}, + ) where + denotes the binary operation of addition 9 9 modulo 9. (a) Write down the identity element of M. Justif
- 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
- November 2021, Extra Pure, Q2 (7 marks): G is a group of order 8. (a) Explain why there is no subgroup of G of order 6. [1] You are now given that G is a cyclic group with the following features: • e i
- 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
Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? OCR MEI A-Level Further Maths past papers.
The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.