plumiExponentials and logarithms: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P3.3 Exponentials and logarithms, 2019–2025, with its mark scheme and examiner’s report.
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All 29 questions on Exponentials and logarithms, as a list
- June 2025, Pure 3 (P3), Q3 (5 marks): log10 y log10 x O (–3.5, 0) (0, –2) Figure 1 Figure 1 shows a linear relationship between log10 y and log10 x The line passes through the points (–3.5, 0) and (
- June 2025, Pure 3 (P3), Q6 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The temperature, θ°C, of a co
- June 2025 (A), Pure 3 (P3), Q9 (7 marks): The amount of an antibiotic, x milligrams, in the bloodstream of a horse, t hours after the antibiotic had been administered, is given by the formula x = D e –0
- January 2025, Pure 3 (P3), Q2 (3 marks): The weed on the surface of a pond is being monitored. The surface area of the pond covered by the weed, A m 2, is modelled by the equation log10 A = 1 + 0.03t w
- January 2025, Pure 3 (P3), Q5 (9 marks): A hot piece of metal is cooled by dropping it into water. The temperature, H °C, of the metal, t minutes after it is dropped into the water, is modelled by the
- October 2024, Pure 3 (P3), Q4 (6 marks): The number of bacteria on a surface is being monitored. The number of bacteria, N, on the surface, t hours after monitoring began is modelled by the equation lo
- June 2024, Pure 3 (P3), Q3 (6 marks): (i) The variables x and y are connected by the equation y x x = 10 0 6 3 > Sketch the graph of log10 y against log10 x Show on your sketch the coordinates of th
- January 2024, Pure 3 (P3), Q3 (7 marks): The amount of money raised for a charity is being monitored. The total amount raised in the t months after monitoring began, £D, is modelled by the equation log
- January 2024, Pure 3 (P3), Q5 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The temperature, T °C, of the
- October 2023, Pure 3 (P3), Q4 (7 marks): A new mobile phone is released for sale. The total sales N of this phone, in thousands, is modelled by the equation N = 125 – Ae –0.109t t 0 where A is a cons
- October 2023, Pure 3 (P3), Q6 (6 marks): An area of sea floor is being monitored. The area of the sea floor, S km 2, covered by coral reefs is modelled by the equation S = pq t where p and q are consta
- October 2023, Pure 3 (P3), Q9 (9 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. y y = f (x) x = k B A O x Figure 2 Fig
- June 2023, Pure 3 (P3), Q2 (6 marks): log6 T log6 x (2, 0) (0, 4) O Figure 1 Figure 1 shows the linear relationship between log6 T and log6 x The line passes through the points (0, 4) and (2, 0) as
- June 2023, Pure 3 (P3), Q7 (8 marks): A scientist is studying two different populations of bacteria. The number of bacteria N in the first population is modelled by the equation N = Ae kt t 0 wher
- January 2023, Pure 3 (P3), Q3 (5 marks): O (−4.8, 0) (0, 1.5) y x l log10 Figure 1 The line l in Figure 1 shows a linear relationship between log10 y and x. The line passes through the points (0, 1.5)
- January 2023, Pure 3 (P3), Q10 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A population of fruit flies i
- June 2022, Pure 3 (P3), Q4 (7 marks): O (0, 3.08) (5, 3.85) log10 N t Figure 1 The number of subscribers to an online video streaming service, N, is modelled by the equation N = ab t where a and b a
- January 2022, Pure 3 (P3), Q4 (7 marks): The growth of a weed on the surface of a pond is being studied. The surface area of the pond covered by the weed, A m 2, is modelled by the equation A p p t t =
- January 2022, Pure 3 (P3), Q8 (8 marks): A dose of antibiotics is given to a patient. The amount of the antibiotic, x milligrams, in the patient's bloodstream t hours after the dose was given, is found
- October 2021, Pure 3 (P3), Q3 (6 marks): O t G k Figure 2 The total mass of gold, G tonnes, extracted from a mine is modelled by the equation G = 40 – 30e1–0.05t t k G 0 where t is the number of ye
- October 2021, Pure 3 (P3), Q7 (6 marks): 7 The mass, M kg, of a species of tree can be modelled by the equation log10M = 1.93 log10r + 0.684 where r cm is the base radius of the tree. The base radius o
- June 2021, Pure 3 (P3), Q5 (7 marks): log10 A O (8, 0.56) (0, 0.32) t Figure 1 The growth of duckweed on a pond is being studied. The surface area of the pond covered by duckweed, Am2, at a time t d
- June 2021, Pure 3 (P3), Q8 (13 marks): A scientist is studying a population of fish in a lake. The number of fish, N, in the population, t years after the start of the study, is modelled by the equat
- January 2021, Pure 3 (P3), Q5 (11 marks): The temperature, θ °C, inside an oven, t minutes after the oven is switched on, is given by θ = A – 180e–kt where A and k are positive constants. Given that the
- January 2021, Pure 3 (P3), Q8 (7 marks): The percentage, P, of the population of a small country who have access to the internet, is modelled by the equation P = abt where a and b are constants and t i
- October 2020, Pure 3 (P3), Q2 (6 marks): A scientist monitored the growth of bacteria on a dish over a 30‑day period. The area, N mm2, of the dish covered by bacteria, t days after monitoring began, is
- October 2020, Pure 3 (P3), Q6 (9 marks): . C1 α O β P x y C2 Figure 3 Figure 3 shows a sketch of curve C1 with equation y = 5e x−1 + 3 and curve C2 with equation y = 10 − x2 The point P lies on C1 and
- January 2020, Pure 3 (P3), Q1 (6 marks): A population of a rare species of toad is being studied. The number of toads, N, in the population, t years after the start of the study, is modelled by the equ
- January 2020, Pure 3 (P3), Q3 (5 marks): log10 y O (0, 4) (6, 0) log10 x Figure 1 Figure 1 shows a linear relationship between log10 y and log10 x The line passes through the points (0, 4) and (6, 0) a
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