Chapter 11: Further Pure 2: Groups

A-level Further MathsFurther Pure 1 & 24 topicsHigher

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Releases 1 August 2026

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Further Pure 2: Groups: Edexcel Further Maths Optional Long-Answer Questions

Examiner-style long-answer practice with automatic marking, improvement advice and ProofCoach tracking.

4 questions32 marks64 min

standard / hard / synoptic

8 marksfindstandardEdexcel

FP11-1 Find the required result for Further Pure 2: Groups. Given The set {1, 3, 5, 7} under multiplication modulo 8 is given. Construct the Cayley table and find the order of each element. Use check closure, identity, inverses and associativity for a small modular group. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

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8 marksshow thathardEdexcel

FP11-2 Show that every non-identity element has order 2 for Further Pure 2: Groups. Start from The set {1, 3, 5, 7} under multiplication modulo 8 is given. Construct the Cayley table and find the order of each element. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

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8 marksdeterminehardEdexcel

FP11-3 Determine the requested value in this structured Further Pure 2: Groups problem: decide whether the group is cyclic. Use the same data: The set {1, 3, 5, 7} under multiplication modulo 8 is given. Construct the Cayley table and find the order of each element. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

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8 markshencesynopticEdexcel

FP11-4 Hence use the result every non-identity element has order 2 to complete the extension for Further Pure 2: Groups: decide whether the group is cyclic. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

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10. Further Pure 2: Number Theory

12. Further Pure 2: Complex Numbers

Key learning objectives

Understand the key principles behind Further Pure 2: Groups.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.