plumiEuclid's algorithm and Bezout: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 7.5 Euclid's algorithm and Bezout, 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 11 questions on Euclid's algorithm and Bezout, as a list
- June 2025, Additional Pure Mathematics, Q5 (6 marks): (a) Determine the solution of the linear congruence x 3 7 (mod 13). Give your answer in the / form x a (mod 13), where 0 a 13 . [2] 1 / G (b) Hence or otherwise
- June 2025, AS Additional Pure Mathematics, Q7 (9 marks): A n n B n n Consider the two arithmetic sequences { 2 7 : } and { 3 1 : } . = + = + ! N ! N n n h A B for each chosen value of n. Let hcf ( , ) = n n (a) (i) Fi
- June 2024, Additional Pure Mathematics, Q3 (6 marks): Determine all integers x for which x / (mod 7) and x 1 22 (mod 37) and x 7 (mod 67). / / Give your answer in the form x qn + for integers n, q, r with q r 0 and
- June 2023, Additional Pure Mathematics, Q8 (9 marks): Let ( ) f n denote the base-n number 2121n where n H . 3 (a) (i) For each n H , show that ( ) 3 f n can be written as the product of two positive integers great
- June 2023, AS Additional Pure Mathematics, Q5 (11 marks): (a) Express as a decimal (base-10) number the base-23 number 711923. [2] (b) Solve the linear congruence 7 n 11 9 ( mod 23 ) . [3] + / (c) Let N 10 a + and M b
- June 2022, Additional Pure Mathematics, Q2 (5 marks): Consider the integers a and b, where, for each integer n, a 7 n + and b 4 8 n + . 5 = = Let h hcf ( , ) a b . = (a) Determine all possible values of h. [3] (b)
- November 2021, Additional Pure Mathematics, Q4 (6 marks): Solve the simultaneous linear congruences x / (mod 3), x 1 / (mod 11), x 5 2 / (mod 17). [6] 5
- November 2021, AS Additional Pure Mathematics, Q4 (6 marks): (a) Let a = 1071 and b = 67. (i) Find the unique integers q and r such that a bq + , where q 2 0 and 0 G r 1 b. r [1] = (ii) Hence express the answer to (a)(i)
- November 2020, AS Additional Pure Mathematics, Q1 (4 marks): (a) Evaluate 13 19 modulo 31. [1] # (b) Solve the linear congruence 13 x 9 (mod 31). [3] /
- June 2019, Additional Pure Mathematics, Q3 (4 marks): (a) Solve x 7 6 (mod 19). [2] / (b) Show that the following simultaneous linear congruences have no solution. x / (mod 4), x 3 4 (mod 6). [2] /
- June 2019, AS Additional Pure Mathematics, Q6 (8 marks): (a) Determine all values of x for which 16 x / (mod 101). 5 [4] (b) Solve (i) 95 x 6 (mod 101), [2] / (ii) 95 x / (mod 101). 5 [2]
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