plumiSequences and series: OCR A‑Level Maths questions
Every OCR A-Level Maths exam question on P.4 Sequences and series, 2018–2025, with its mark scheme and examiner’s report.
Find questions494
![June 2025 Paper 1, question 3: 3 (a) A sequence has terms u1, u2, u3, … defined by u 3 and u u 5 for n H . 1 1 = = - n 1 n + (i) Find the values of u2, u3 and u4. [2] (ii) Describe the behavi](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun25-03-qp.webp?v=3)
![June 2025 Paper 1, question 8: 8 (a) Find the first three terms in the expansion of ( 2 )x - in ascending powers of x. [4] + 1 4 x + (b) Hence find the first three terms in the expansion of (](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun25-08-qp.webp?v=3)
![June 2025 AS Paper 1, question 5: (a) Find the coefficient of x7 in the expansion of ( 3 9 5 2 x ) . [2] + 21 (b) The following questions are about the binomial expansion of ( 1 )x in ascending](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h23001-jun25-05-qp.webp?v=3)
![June 2024 Paper 1, question 4: 4 A sequence has terms u1, u2, u3, … defined by u 2 and u 1 for n H . 1 1 = 1 = - u n + n (a) Find the values of u2, u3 and u4. [2] (b) Describe the behaviour o](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun24-04-qp.webp?v=3)
![June 2024 Paper 3, question 3: - in ascending powers of x up to and including the term in x2. 2 3 (a) Expand ( )x [4] 3 2 - (b) State the set of values of x for which this expansion is valid.](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24003-jun24-03-qp.webp?v=3)
![June 2024 AS Paper 1, question 4: (a) Write down the term in b5 in the expansion of ( b 12 4 a ) . [1] + (b) A variable X has a binomial distribution such that P(X = 5) is given by the term in p](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h23001-jun24-04-qp.webp?v=3)
![June 2023 Paper 1, question 8: ^ h in ascending powers of x. 3 8 (a) Find the first three terms in the expansion of 4 3 x [4] + 2 (b) State the range of values of x for which the expansion in](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun23-08-qp.webp?v=3)
![June 2023 AS Paper 2, question 4: a k , 6 1 4 (a) Find and simplify the first three terms in the expansion, in ascending powers of x, of 2 kx + 3 where k is a constant. [3] a k , the constant te](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h23002-jun23-04-qp.webp?v=3)
![June 2022 Paper 1, question 6: 6 (a) Find the first four terms in the expansion of ( 3 2 )x in ascending powers of x. [4] + (b) Hence determine the coefficient of y3 in the expansion of ( 4 2](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun22-06-qp.webp?v=3)
![June 2022 AS Paper 1, question 1: Find the term in x3 in the binomial expansion of ( 5 1 3 2 )x . [2] -](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h23001-jun22-01-qp.webp?v=3)
![November 2021 Paper 1, question 6: ^ h in ascending powers of x. 1 6 (a) Find the first three terms in the expansion of 8 3 x [4] - 3 (b) State the range of values of x for which the expansion in](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-nov21-06-qp.webp?v=3)
![November 2021 Paper 2, question 3: The 15th term of an arithmetic sequence is 88. The sum of the first 10 terms is 310. Determine the first term and the common difference. [6]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24002-nov21-03-qp.webp?v=3)
All 32 questions on Sequences and series, as a list
- June 2025, Paper 1, Q3 (6 marks): 3 (a) A sequence has terms u1, u2, u3, … defined by u 3 and u u 5 for n H . 1 1 = = - n 1 n + (i) Find the values of u2, u3 and u4. [2] (ii) Describe the behavi
- June 2025, Paper 1, Q8 (10 marks): 8 (a) Find the first three terms in the expansion of ( 2 )x - in ascending powers of x. [4] + 1 4 x + (b) Hence find the first three terms in the expansion of (
- June 2025, Paper 2, Q7 (5 marks): An arithmetic progression has first term a and common difference d, where a and d are non-zero. The first, third and fourth terms of the arithmetic progression
- June 2025, AS Paper 1, Q5 (5 marks): (a) Find the coefficient of x7 in the expansion of ( 3 9 5 2 x ) . [2] + 21 (b) The following questions are about the binomial expansion of ( 1 )x in ascending
- June 2024, Paper 1, Q4 (6 marks): 4 A sequence has terms u1, u2, u3, … defined by u 2 and u 1 for n H . 1 1 = 1 = - u n + n (a) Find the values of u2, u3 and u4. [2] (b) Describe the behaviour o
- June 2024, Paper 1, Q10 (8 marks): In this question you must show detailed reasoning. The first three terms of a convergent geometric progression are x 2 + , x 3 + and x 9 2 6 - respectively. Det
- June 2024, Paper 2, Q7 (8 marks): Two arithmetic progressions, A and B, each have 100 terms denoted by ai and bi respectively, where i = 1, 2, 3, . . . 100. The common difference of A is d, wher
- June 2024, Paper 2, Q8 (6 marks): Sweets from a certain manufacturer are sold in packets. Thirty per cent of the sweets are orange, and these are randomly distributed amongst the packets. Each p
- June 2024, Paper 3, Q3 (7 marks): - in ascending powers of x up to and including the term in x2. 2 3 (a) Expand ( )x [4] 3 2 - (b) State the set of values of x for which this expansion is valid.
- June 2024, AS Paper 1, Q4 (4 marks): (a) Write down the term in b5 in the expansion of ( b 12 4 a ) . [1] + (b) A variable X has a binomial distribution such that P(X = 5) is given by the term in p
- June 2023, Paper 1, Q8 (9 marks): ^ h in ascending powers of x. 3 8 (a) Find the first three terms in the expansion of 4 3 x [4] + 2 (b) State the range of values of x for which the expansion in
- June 2023, Paper 3, Q6 (6 marks): The first, third and fourth terms of an arithmetic progression are u1, u3 and u4 respectively, where 7 u 2 sin , u 3 cos , u sin , = i =- i = i 1 3 4 2 1 and 2
- June 2023, AS Paper 2, Q4 (6 marks): a k , 6 1 4 (a) Find and simplify the first three terms in the expansion, in ascending powers of x, of 2 kx + 3 where k is a constant. [3] a k , the constant te
- June 2022, Paper 1, Q6 (8 marks): 6 (a) Find the first four terms in the expansion of ( 3 2 )x in ascending powers of x. [4] + (b) Hence determine the coefficient of y3 in the expansion of ( 4 2
- June 2022, Paper 2, Q4 (5 marks): An artist is creating a design for a large painting. The design includes a set of steps of varying heights. In the painting the lowest step has height 20 cm and
- June 2022, Paper 3, Q4 (8 marks): The positive integers x, y and z are the first, second and third terms, respectively, of an arithmetic progression with common difference -4. 15 and z are the f
- June 2022, AS Paper 1, Q1 (2 marks): Find the term in x3 in the binomial expansion of ( 5 1 3 2 )x . [2] -
- June 2022, AS Paper 1, Q9 (10 marks): Last year, market research showed that 8% of adults living in a certain town used a particular local coffee shop. Following an advertising campaign, it was expe
- November 2021, Paper 1, Q6 (9 marks): ^ h in ascending powers of x. 1 6 (a) Find the first three terms in the expansion of 8 3 x [4] - 3 (b) State the range of values of x for which the expansion in
- November 2021, Paper 2, Q3 (6 marks): The 15th term of an arithmetic sequence is 88. The sum of the first 10 terms is 310. Determine the first term and the common difference. [6]
- November 2021, Paper 3, Q2 (6 marks): B A 60° C The diagram shows triangle ABC in which angle A is 60° and the lengths of AB and AC are ( 4 h ) cm and ( 4 h ) cm respectively. + - (a) Show that the
- November 2021, Paper 3, Q3 (5 marks): An arithmetic progression has first term 2 and common difference d, where d 0 . The first, third ! and thirteenth terms of this progression are also the first,
- November 2020, Paper 1, Q7 (11 marks): Two students, Anna and Ben, are starting a revision programme. They will both revise for 30 minutes on Day 1. Anna will increase her revision time by 15 minutes
- November 2020, Paper 2, Q3 (7 marks): In this question you should assume that 1 1 x 1 1 . - 2 (a) For the binomial expansion of ( 1 )x - - (i) find and simplify the first four terms, [2] (ii) write
- November 2020, AS Paper 1, Q4 (5 marks): 4 (a) Expand ( 1 )x . [1] + (b) Use your expansion to determine the exact value of 10024. [4]
- June 2019, Paper 1, Q4 (7 marks): Sam starts a job with an annual salary of £16 000. It is promised that the salary will go up by the same amount every year. In the second year Sam is paid £17 2
- June 2019, Paper 1, Q7 (8 marks): In this question you must show detailed reasoning. n A sequence u , u , u f is defined by u 25 0 6 . . = # 1 2 3 n N 3 / / 4 Use an algebraic method to find the
- June 2019, Paper 2, Q2 (8 marks): (a) Find the coefficient of x5 in the expansion of ( 8 2 3 2 )x . [1] - .0 5 as far as the term in x3. (b) (i) Expand ( 1 3 )x [3] + (ii) State the range of val
- June 2019, AS Paper 2, Q4 (6 marks): ^ h in ascending powers of x. 5 4 (a) Find and simplify the first three terms in the expansion of 2 5 x - [3] ^ h ^ h , the coefficient of x is 48. 2 5 (b) In t
- June 2018, Paper 1, Q7 (9 marks): Chris runs half marathons, and is following a training programme to improve his times. His time for his first half marathon is 150 minutes. His time for his sec
- June 2018, Paper 1, Q8 (7 marks): 8 (i) Find the first three terms in the expansion of ( )x - in ascending powers of x. [4] 4 - 2 a bx + (ii) The expansion of 16- … . Find the values of the cons
- June 2018, Paper 3, Q4 (8 marks): In this question you must show detailed reasoning. The functions f and g are defined for all real values of x by ^ h ^ h x3 2 f x and g x x 2 . = = + (i) Write
Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every OCR A-Level Maths paper.
Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.