plumiDivisibility and modular arithmetic: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 7.4 Divisibility and modular arithmetic, 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 12 questions on Divisibility and modular arithmetic, as a list
- June 2025, Further Pure 2, Q7 (6 marks): (i) Explain why the congruence equation 21x ≡ 11(mod 36) has no solutions. (2) (ii) Use modular arithmetic to solve the congruence equation 36y ≡ 192(mod 40) (4
- June 2025, AS Further Pure 2, Q1 (8 marks): In this question you must show all stages of your working. Solutions based entirely on calculator technology are not acceptable. (i) (a) Use the Euclidean algor
- June 2025, AS Further Pure 2, Q2 (8 marks): (i) Using a suitable algorithm and without performing any division, determine whether 13 306 617 is divisible by 9 (2) (ii) The group G = {1, 3, 7, 9, 11, 13, 1
- June 2024, Further Pure 2, Q3 (11 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Use the Euclidean Algorithm to det
- June 2023, Further Pure 2, Q4 (9 marks): (a) Use the Euclidean algorithm to show that the highest common factor of 168 and 66 is 6 (2) (b) Use back substitution to determine integers a and b such that
- June 2023, AS Further Pure 2, Q5 (8 marks): (i) Making your reasoning clear and using modulo arithmetic, show that 214 6 is divisible by 8 (3) (ii) The following 7‑digit number has four unknown digits a 5
- June 2022, Further Pure 2, Q7 (8 marks): (i) The polynomial F(x) is a quartic such that F(x) = px 4 + qx 3 + 2x 2 + rx + s where p, q, r and s are distinct constants. Determine the number of possible q
- June 2022, AS Further Pure 2, Q4 (11 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (i) (a) Use the Euclidean algorithm to
- November 2021, Further Pure 2, Q1 (4 marks): In this question you must show detailed reasoning. Without performing any division, explain why n = 20 210 520 is divisible by 66 (4)
- November 2020, Further Pure 2, Q8 (12 marks): The four digit number n = abcd satisfies the following properties: (1) n ≡ 3 (mod 7) (2) n is divisible by 9 (3) the first two digits have the same sum as the l
- June 2019, AS Further Pure 2, Q2 (7 marks): (i) Determine all the possible integers a, where a ! 3, such that 15 3 { mod a (2) (ii) Show that if p is prime, x is an integer and x p 2 1 { mod then either x
- June 2018, AS Further Pure 2, Q1 (5 marks): (i) Using a suitable algorithm and without performing any division, determine whether 23 738 is divisible by 11 (2) (ii) Use the Euclidean algorithm to find the
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