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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-NT-0041 markL1 FoundationNon-calculatorFermat
Find 4872 mod 94872\bmod9 using the digit sum.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-NT-G011 markL1 FoundationNon-calculatorCongruences
Find 47 mod 547\bmod5.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-NT-Q011 markL1 FoundationNon-calculatorCongruences
a≡b(modn)a\equiv b\pmod n means
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-NT-X011 markL1 FoundationNon-calculatorEuclid
Find gcd⁡(84,36)\gcd(84,36).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-NT-X021 markL1 FoundationNon-calculatorCongruences
Find 34 mod 53^4\bmod5.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-NT-0012 marksL2 StandardNon-calculatorEuclid
Use the Euclidean algorithm to find gcd⁡(252,198)\gcd(252,198).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-NT-0022 marksL2 StandardNon-calculatorCongruences
Solve 3x≡4(mod7)3x\equiv4\pmod7, giving 0≤x<70\le x<7.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-NT-X032 marksL2 StandardNon-calculatorCongruences
Solve 5x≡3(mod7)5x\equiv3\pmod7, giving 0≤x<70\le x<7.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-NT-X041 markL2 StandardNon-calculatorFermat
Use Fermat's little theorem to find 210 mod 112^{10}\bmod11.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-NT-0033 marksL3 ExamNon-calculatorFermat
Find 2100 mod 72^{100}\bmod7.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-NT-X052 marksL3 ExamNon-calculatorFermat
Find the last digit of 71007^{100}.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-NT-0054 marksL4 ChallengingNon-calculatorEuclid
Find the smallest positive integer xx for which there is an integer yy with 252x+198y=18252x+198y=18.

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Salam Academy Original Practice · Proposed mark scheme