plumiExponentials and logarithms: OCR MEI A‑Level Maths questions
Every OCR MEI A-Level Maths exam question on P.6 Exponentials and logarithms, 2018–2025, with its mark scheme and examiner’s report.
Find questions560
![June 2025 AS Paper 2, question 1: You are given that b, c and d are integers greater than 1. a k . c 0 (a) State the value of d [1] (b) State the value of log b b . [1]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h63002-jun25-01-qp.webp?v=3)
![June 2025 AS Paper 2, question 15: 3x 15 (a) On the axes in the Printed Answer Booklet, sketch the graph of y [2] . = 3x (b) Determine the exact coordinates of the points of intersection of the c](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h63002-jun25-15-qp.webp?v=3)
![June 2024 Paper 1, question 5: (a) Make y the subject of the formula log ( y k ) x log 2 , where k is a positive constant. [2] - = 10 10 (b) Sketch the graph of y against x. [3]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64001-jun24-05-qp.webp?v=3)
![June 2023 Paper 1, question 14: (a) Use the laws of logarithms to show that log 200 log 20 is equal to 1. [2] - 10 10 The first three terms of a sequence are log 20 , log 200 , log 2000 . 10 1](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64001-jun23-14-qp.webp?v=3)
![June 2023 AS Paper 1, question 9: x 9 The graph shows the function y e . = y x O x 2 x (a) Describe the transformation of the graph of y e that gives the graph of y e . [2] = = x A second functi](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h63001-jun23-09-qp.webp?v=3)
![June 2022 Paper 2, question 3: 4x 3 (a) On the axes in the Printed Answer Booklet, sketch the curve with equation y 3 . . [3] = # x (b) Given that 3 0 4 . 0 8 . , determine the value of x cor](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64002-jun22-03-qp.webp?v=3)
![June 2022 AS Paper 2, question 3: Ae . 0 02 t 3 You are given that y . = • Make t the subject of the formula. • Find the value of t when y 108 107 and A 6 62 . . [3] = = #](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h63002-jun22-03-qp.webp?v=3)
![November 2021 Paper 3, question 5: x 5 (a) The diagram shows the curve y e . = y x O On the axes in the Printed Answer Booklet, sketch graphs of y against x, d (i) [1] x d y against y. d (ii) [2]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64003-nov21-05-qp.webp?v=3)
All 33 questions on Exponentials and logarithms, as a list
- June 2025, Paper 1, Q9 (6 marks): The table below shows information about four of the moons of the planet Jupiter. The semi-major axis is the greatest distance that each moon reaches from the ce
- June 2025, Paper 3, Q7 (9 marks): A group of scientists is studying how a population of insects grows in the laboratory. At the start of the study, there are 48 insects. At the end of the first
- June 2025, AS Paper 1, Q12 (13 marks): A student dissolves 0.5 kg of salt in a bucket of water. Water leaks out of a hole in the bucket so the student lets fresh water flow in so that the bucket stay
- June 2025, AS Paper 2, Q1 (2 marks): You are given that b, c and d are integers greater than 1. a k . c 0 (a) State the value of d [1] (b) State the value of log b b . [1]
- June 2025, AS Paper 2, Q15 (7 marks): 3x 15 (a) On the axes in the Printed Answer Booklet, sketch the graph of y [2] . = 3x (b) Determine the exact coordinates of the points of intersection of the c
- June 2024, Paper 1, Q5 (5 marks): (a) Make y the subject of the formula log ( y k ) x log 2 , where k is a positive constant. [2] - = 10 10 (b) Sketch the graph of y against x. [3]
- June 2024, Paper 1, Q10 (10 marks): Zac is measuring the growth of a culture of bacteria in a laboratory. The initial area of the culture is 8 cm2. The area one day later is 8.8 cm2. , where A cm2
- June 2024, Paper 3, Q5 (6 marks): In this question you must show detailed reasoning. Using the substitution u x + , find the value of the positive integer c such that 1 = x 1 c 4 +y d x ln 3 . [
- June 2024, AS Paper 1, Q11 (6 marks): A student records the time a pendulum takes to swing for different lengths of pendulum. The student decides to plot a graph of log T against log 10 where T is t
- June 2023, Paper 1, Q9 (10 marks): d y - . x x 9 The gradient of a curve is given by d e 4 e = - x (a) Show that the x-coordinate of any point on the curve at which the gradient is 3 satisfies th
- June 2023, Paper 1, Q11 (10 marks): The height h cm of a sunflower plant t days after planting the seed is modelled by h a b ln t = + for t 9 , where a and b are constants. The sunflower is 10 cm
- June 2023, Paper 1, Q14 (6 marks): (a) Use the laws of logarithms to show that log 200 log 20 is equal to 1. [2] - 10 10 The first three terms of a sequence are log 20 , log 200 , log 2000 . 10 1
- June 2023, Paper 3, Q9 (9 marks): A small country started using solar panels to produce electrical energy in the year 2000. Electricity production is measured in megawatt hours (MWh). For the pe
- June 2023, AS Paper 1, Q9 (9 marks): x 9 The graph shows the function y e . = y x O x 2 x (a) Describe the transformation of the graph of y e that gives the graph of y e . [2] = = x A second functi
- June 2023, AS Paper 1, Q10 (7 marks): Layla invests money in the bank and receives compound interest. The amount £L that she has after 1 023t t years is given by the equation L 2800 . . = # (a) (i)
- June 2022, Paper 1, Q14 (13 marks): Alex places a hot object into iced water and records the temperature i °C of the object every minute. e kt The temperature of an object t minutes after being pl
- June 2022, Paper 2, Q3 (6 marks): 4x 3 (a) On the axes in the Printed Answer Booklet, sketch the curve with equation y 3 . . [3] = # x (b) Given that 3 0 4 . 0 8 . , determine the value of x cor
- June 2022, AS Paper 2, Q3 (3 marks): Ae . 0 02 t 3 You are given that y . = • Make t the subject of the formula. • Find the value of t when y 108 107 and A 6 62 . . [3] = = #
- November 2021, Paper 3, Q5 (8 marks): x 5 (a) The diagram shows the curve y e . = y x O On the axes in the Printed Answer Booklet, sketch graphs of y against x, d (i) [1] x d y against y. d (ii) [2]
- November 2021, AS Paper 1, Q11 (10 marks): On the day that a new consumer product went on sale (day zero), a call centre received 1 call about it. On the 2nd day after day zero the call centre received 3
- November 2021, AS Paper 2, Q5 (7 marks): In 2019 scientists developed a model for comparing the ages of humans and dogs. According to the model, Y = AlnX + B where X = dog age in years and Y = human ag
- November 2020, Paper 3, Q6 (12 marks): (a) (i) Write down the derivative of ekx, where k is a constant. 6 [1] (ii) A business has been running since 2009. They sell maths revision resources online. G
- November 2020, Paper 3, Q12 (8 marks): ln x 12 (a) Show that the only stationary point on the curve y occurs where x = e, as given in = x line 45. [3] (b) Show that the stationary point is a maximum.
- November 2020, AS Paper 1, Q11 (9 marks): In this question you must show detailed reasoning. 1 1 (a) A student is asked to solve the inequality x 4 . 2 1 + The student argues that x 1 4 x 1 16 , so that
- November 2020, AS Paper 2, Q11 (10 marks): - . 11 A car is travelling along a stretch of road at a steady speed of 11ms 1 The driver accelerates, and t seconds after starting to accelerate the speed of t
- June 2019, Paper 3, Q7 (4 marks): In this question you must show detailed reasoning. (a) Express ln 3 ln 9 ln 27 in terms of ln3. [2] # # (b) Hence show that ln 3 ln 9 ln 27 2 6 . [2] # #
- June 2019, AS Paper 2, Q9 (10 marks): In 2012 Adam bought a second hand car for £8500. Each year Adam has his car valued. He believes that there is a non‑linear relationship between t, the time in y
- June 2018, Paper 2, Q5 (3 marks): (i) (A) Sketch the graph of y = 3x. 5 [1] (B) Give the coordinates of any intercepts. [1] The curve y = f(x) is the reflection of the curve y = 3x in the line y
- June 2018, Paper 3, Q5 (11 marks): A social media website launched on 1 January 2017. The owners of the website report the number of users the site has at the start of each month. They believe th
- June 2018, Paper 3, Q9 (4 marks): x e 9 The function ( )x is defined on the domain x x f , 0 . R ! = d x 1 e - f 1 (i) Find ( )x [3] - . f 1 (ii) Write down the range of ( )x [1] - . a 4
- June 2018, AS Paper 1, Q11 (13 marks): The intensity of the sun’s radiation, y watts per square metre, and the average distance from the sun, x astronomical units, are shown in Fig. 11 for the planet
- June 2018, AS Paper 2, Q1 (2 marks): Write down the value of (A) loga (a4), [1] b l. 1 (B) loga a [1]
- June 2018, AS Paper 2, Q12 (10 marks): In an experiment 500 fruit flies were released into a controlled environment. After 10 days there were 650 fruit flies present. Munirah believes that N, the num
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 MEI A-Level Maths paper.
Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.