plumiExponentials and logarithms: Edexcel A‑Level Maths questions
Every Edexcel A-Level Maths exam question on P.6 Exponentials and logarithms, 2019–2025, with its mark scheme and examiner’s report.
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All 37 questions on Exponentials and logarithms, as a list
- June 2025, Pure 1, Q11 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The value of a car, £V, is mo
- June 2025, Pure 2, Q3 (2 marks): Given that 3 x = 7 y find the exact value of x y (2)
- June 2025, Pure 2, Q8 (9 marks): O C y x Figure 2 f x x x x ax 4 3 2 1 3 8 17 3 where a is a constant. Figure 2 shows a sketch of the curve C with equation y = f (x) Given that C has a local
- June 2025, AS Pure, Q10 (5 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Solve the equation 2 log3 (x
- June 2025, AS Pure, Q13 (12 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The growth of a particular tr
- June 2024, Pure 2, Q13 (9 marks): The world human population, P billions, is modelled by the equation P = ab t where a and b are constants and t is the number of years after 2004 Using the estim
- June 2024, AS Pure, Q7 (5 marks): O x log10 P (0, 3.3) (6, 2.1) Figure 2 A chimney emits smoke particles. On a particular day, the concentration of smoke particles in the air emitted by this chi
- June 2024, AS Pure, Q9 (5 marks): p = loga 16 q = loga 25 where a is a constant. Find in terms of p and/or q, (a) loga 256 (1) (b) loga 100 (2) (c) loga 80 × loga 3.2 (2)
- June 2024, AS Pure, Q11 (6 marks): The prices of two precious metals are being monitored. The price per gram of metal A, £ VA , is modelled by the equation VA = 100 + 20e 0.04t where t is the num
- June 2023, Pure 1, Q6 (6 marks): a = log2 x b = log2(x + 8) Express in terms of a and/or b (a) log2 x (1) (b) log2(x 2 + 8x) (2) (c) log2 8 64 x Give your answer in simplest form. (3)
- June 2023, Pure 1, Q11 (7 marks): O log10 V (0, 3) (10, 2.79) t Figure 2 The value, V pounds, of a mobile phone, t months after it was bought, is modelled by V = ab t where a and b are constants
- June 2023, Pure 2, Q3 (5 marks): Given that log2(x + 3) + log2(x + 10) = 2 + 2 log2 x (a) show that 3x 2 – 13x – 30 = 0 (3) (b) (i) Write down the roots of the equation 3x 2 – 13x – 30 = 0 (ii)
- June 2023, Pure 2, Q4 (4 marks): Coffee is poured into a cup. The temperature of the coffee, H °C, t minutes after being poured into the cup is modelled by the equation H = Ae – Bt + 30 where A
- June 2023, AS Pure, Q9 (5 marks): Using the laws of logarithms, solve the equation 2 3 2 2 5 5 log log x x (5)
- June 2023, AS Pure, Q11 (6 marks): The height, h metres, of a plant, t years after it was first measured, is modelled by the equation Using the model, (a) find the height of the plant when it was
- June 2022, Pure 1, Q10 (8 marks): A scientist is studying the number of bees and the number of wasps on an island. The number of bees, measured in thousands, Nb , is modelled by the equation Nb
- June 2022, Pure 2, Q2 (4 marks): (a) Sketch the curve with equation y = 4 x stating any points of intersection with the coordinate axes. (2) (b) Solve 4 x = 100 giving your answer to 2 decimal
- June 2022, AS Pure, Q5 (10 marks): The mass, A kg, of algae in a small pond, is modelled by the equation A = pqt where p and q are constants and t is the number of weeks after the mass of algae w
- June 2022, AS Pure, Q8 (6 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The air pressure, P kg/cm2, i
- June 2022, AS Pure, Q9 (6 marks): (a) Given that p = log3 x, where x > 0, find in simplest form in terms of p, (i) log3 x 9 (ii) log3 x ( ) (2) (b) Hence, or otherwise, solve 2 log3 x
- November 2021, Pure 1, Q8 (9 marks): A scientist is studying the growth of two different populations of bacteria. The number of bacteria, N, in the first population is modelled by the equation N =
- November 2021, Pure 2, Q3 (3 marks): Using the laws of logarithms, solve the equation log3 (12y + 5) – log3 (1 – 3y) = 2 (3)
- November 2021, Pure 2, Q10 (6 marks): The time, T seconds, that a pendulum takes to complete one swing is modelled by the formula T = al b where l metres is the length of the pendulum and a and b ar
- November 2021, AS Pure, Q11 (6 marks): The owners of a nature reserve decided to increase the area of the reserve covered by trees. Tree planting started on 1st January 2005. The area of the nature r
- November 2021, AS Pure, Q13 (7 marks): 2.25 log10 h O log10 m Figure 2 The resting heart rate, h, of a mammal, measured in beats per minute, is modelled by the equation h = pm q where p and q are con
- November 2020, Pure 1, Q2 (3 marks): By taking logarithms of both sides, solve the equation 43 p −1 = 5210 giving the value of p to one decimal place. (3)
- November 2020, Pure 1, Q8 (2 marks): A new smartphone was released by a company. The company monitored the total number of phones sold, n, at time t days after the phone was released. The company o
- November 2020, Pure 2, Q1 (5 marks): 1 The table below shows corresponding values of x and y for y = x x 1 + The values of y are given to 4 significant figures. x 0.5 1 1.5 2 2.5 y 0.5774 0.7071 0.
- November 2020, Pure 2, Q9 (6 marks): A quantity of ethanol was heated until it reached boiling point. The temperature of the ethanol, θ °C, at time t seconds after heating began, is modelled by the
- November 2020, Pure 2, Q13 (6 marks): The function g is defined by g (x) = 3 7 2 ln( ) ln( ) x x − − x > 0 x ≠ k where k is a constant. (a) Deduce the value of k. (1) (b) Prove that gʹ (x) > 0 for a
- November 2020, AS Pure, Q8 (9 marks): The temperature, θ °C, of a cup of tea t minutes after it was placed on a table in a room, is modelled by the equation θ = 18 + 65e −t 8 t 0 Find, according t
- November 2020, AS Pure, Q12 (7 marks): An advertising agency is monitoring the number of views of an online advert. The equation log10 V = 0.072t + 2.379 1 t 30, t ∈ is used to model the total
- June 2019, Pure 1, Q7 (7 marks): In a simple model, the value, £V, of a car depends on its age, t, in years. The following information is available for car A Ɣ its value when new is £20 000 Ɣ i
- June 2019, Pure 1, Q9 (5 marks): Given that a b 0 and that a and b satisfy the equation log a – log b = log(a – b) (a) show that a b b = − 2 1 (3) (b) Write down the full restriction on the val
- June 2019, Pure 2, Q8 (6 marks): (i) Find the value of 20 1 2 4 × ⎛ ⎝⎜ ⎞ ⎠⎟ = ∞ ∑ r r (3) (ii) Show that log5 1 48 2 1 2 n n n + + ⎛ ⎝⎜ ⎞ ⎠⎟= =∑ (3)
- June 2019, Pure 2, Q9 (9 marks): A research engineer is testing the effectiveness of the braking system of a car when it is driven in wet conditions. The engineer measures and records the braki
- June 2019, AS Pure, Q14 (9 marks): The value of a car, £V, can be modelled by the equation V = 15 700e– 0.25t + 2300 t \, t . 0 where the age of the car is t years. Using the model, (a) find th
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