First order recurrence relations: OCR A‑Level Further Maths questions

OCR A-Level Further Maths past-paper questions on 9.1 First order recurrence relations, 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.

All 15 questions on First order recurrence relations, as a list

June 2025, Additional Pure Mathematics, Q8 (16 marks): (a) The members of the family of the sequences { Gn satisfy the first-order recurrence relation } G 1 25 . qG , for n 0 , 1 = - H n n + where q is a positive co
June 2025, AS Additional Pure Mathematics, Q6 (10 marks): An investment company offers customers a three-year investment scheme. The scheme is modelled by the recurrence system 2 I I I I n and 0 000625 . 0 625 . for 0
June 2024, Additional Pure Mathematics, Q5 (10 marks): In a conservation project in a nature reserve, scientists are modelling the population of one species of animal. The initial population of the species, P0, is 1
June 2024, AS Additional Pure Mathematics, Q7 (12 marks): In a long-running biochemical experiment, an initial amount of 1200 mg of an enzyme is placed into a mixture. The model for the amount of enzyme present in the
June 2023, AS Additional Pure Mathematics, Q2 (4 marks): " , are given by the formula 2 For all positive integers n, the terms of the sequence un 2 u 3 n 3 n 7 ( mod 10 ). = + + n (a) Show that u u for all positive in
June 2023, AS Additional Pure Mathematics, Q6 (9 marks): When 106 of a certain type of bacteria are detected in a blood sample of an infected animal, 6 a course of treatment is started. The long-term aim of the treatm
June 2022, Additional Pure Mathematics, Q6 (12 marks): In a national park, the number of adults of a given species is carefully monitored and controlled. The number of adults, n months after the start of this projec
June 2022, AS Additional Pure Mathematics, Q6 (14 marks): The sequence { un is such that u } 7 , u 37 , u 337 , u 3337 , … . 1 = 2 = 3 = 4 = (a) Write down a first‑order recurrence system for { un . } [2] 1 n (b) By so
November 2021, Additional Pure Mathematics, Q9 (10 marks): " , is given by u k 9 For each value of k the sequence of real numbers un 2 and u . 1 = 1 = 6 u n + + n For each of the following cases, either determine a valu
November 2021, AS Additional Pure Mathematics, Q8 (7 marks): A sequence { un is defined by the recurrence system } 2 a u 1 = and u 1 a for n H 1, where a is a positive constant. = - 2 u n 1 + n Determine with justificatio
November 2020, Additional Pure Mathematics, Q8 (12 marks): u 3 " , of positive real numbers is defined by u + n 8 The sequence un 1 = and u for n H . 1 1 1 = u 2 n + + n 2 (a) Prove by induction that u 3 1 0 for all pos
November 2020, AS Additional Pure Mathematics, Q5 (8 marks): (a) Determine the general solution of the first-order recurrence relation V 2 V n . [6] 1 = + n n + (b) Given that V 8 , find the exact value of V20 . [2] 1 =
November 2020, AS Additional Pure Mathematics, Q7 (10 marks): In a conservation project, a batch of 100 000 tadpoles which have just hatched from eggs is introduced into an environment which has no frog population. Previou
June 2019, AS Additional Pure Mathematics, Q2 (4 marks): " , is defined by a 4 2 (a) The convergent sequence an 0 = and a 1 a for n 0 . 1 = + H n n a + n Calculate the limit of the sequence. [1] " , is defined by b k
June 2019, AS Additional Pure Mathematics, Q4 (8 marks): " , is defined by u 2 4 The sequence un 1 = and u 1 2 u n for n 1 . = + H n 1 n + Determine un as a function of n. [8]

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