plumiInduction: matrices, recurrences and inequalities: OCR MEI A‑Level Further Maths questions
OCR MEI A-Level Further Maths past-paper questions on 1.3 Induction: matrices, recurrences and inequalities, 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 7 questions on Induction: matrices, recurrences and inequalities, as a list
- June 2025, Core Pure, Q8 (7 marks): The function ( )x f is defined as ( ) f x ln ( 1 x ) , for x 2- . 1 = + f ( ) n (a) Prove by mathematical induction that the nth derivative of ( ) f x , ( )x ,
- June 2024, Core Pure, Q8 (10 marks): (a) Specify fully the transformation T of the plane associated with the matrix M, where = c 1 m and m is a non-zero constant. m M [2] 0 1 (b) (i) Find det M. [1
- June 2024, AS Core Pure, Q6 (9 marks): J N 4 9 - KK OO. 6 You are given that M = 1 2 - L P J N n n 1 3 9 + - n = KK OO for all positive integers n. (a) Prove that M [6] n 1 3 n - L P (b) A student th
- June 2023, AS Core Pure, Q6 (8 marks): J N 2 1 KK OO. 6 The matrix M is 1 0 - L P (a) Calculate M2, M3 and M4. [2] (b) Hence make a conjecture about the matrix Mn. [1] (c) Prove your conjecture. [5]
- June 2022, Core Pure, Q6 (5 marks): J N J N n 2 0 2 0 KK OO KK OO for all positive integers n. 6 Prove by mathematical induction that [5] = n 1 1 1 2 1 - - L P L P 3 Answer all the questions.
- November 2020, AS Core Pure, Q5 (6 marks): You are given that u 1 = and u 5 u 2 n 4 . 1 = + + n n + 2 Prove by induction that u n 3 n + for all positive integers n. 1 [6] = + n
- June 2018, AS Core Pure, Q8 (6 marks): c m n c n m for all positive integers n. Prove by induction that 1 1 1 2 1 - 8 [6] = n 0 2 0 2
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