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Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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12 questions

SA-FP-GR-0011 markL1 FoundationNon-calculatorAxioms
In {1,3,5,7}\{1,3,5,7\} under multiplication mod 88, find the inverse of 55.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-GR-Q011 markL1 FoundationNon-calculatorAxioms
Which is NOT one of the group axioms?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-GR-X011 markL1 FoundationNon-calculatorOrders
Find the order of the group of symmetries (rotations and reflections) of an equilateral triangle.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-GR-X021 markL1 FoundationNon-calculatorOrders
Find the order of 44 in (Z6,+6)(\mathbb Z_6,+_6).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-GR-X031 markL1 FoundationNon-calculatorAxioms
In {1,2,3,4}\{1,2,3,4\} under multiplication mod 55, find the inverse of 33.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-GR-0021 markL2 StandardNon-calculatorOrders
Find the order of 22 in (Z10,+10)(\mathbb Z_{10},+_{10}).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-GR-0032 marksL2 StandardNon-calculatorSubgroups
A group has order 1212. How many different orders are possible for its subgroups (including trivial and whole group)?

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-GR-0042 marksL2 StandardNon-calculatorOrders
How many generators does the cyclic group (Z8,+8)(\mathbb Z_8,+_8) have?

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-GR-G012 marksL2 StandardNon-calculatorOrders
Find the order of 33 in the group {1,2,3,4,5,6}\{1,2,3,4,5,6\} under multiplication mod 77.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-GR-X042 marksL2 StandardNon-calculatorSubgroups
A group has order 1010. How many different values are possible for the order of an element?

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-GR-X051 markL2 StandardNon-calculatorSubgroups
A group of prime order pp must be
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-GR-0053 marksL3 ExamNon-calculatorAxioms
On Z\mathbb Z, define a∗b=a+b−2a*b=a+b-2. Find the inverse of 55.

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Salam Academy Original Practice · Proposed mark scheme