plumiDifferentiation: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P3.4 Differentiation, 2019–2025, with its mark scheme and examiner’s report.
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All 53 questions on Differentiation, as a list
- June 2025, Pure 3 (P3), Q4 (5 marks): The function f is defined by f ( ) x x x x x x 49 12 7 4 2 x > 3 (a) Show that f ( ) x x x 7 3 x > 3 (b) Hence find fʹ(x) giving your answer in simplest form.
- 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, Pure 3 (P3), Q7 (9 marks): A continuous curve has equation y = e –x2 sin3x 0 x 3 π The curve has a stationary point at the point P. (a) Show, using calculus, that the x coordinate of
- June 2025, Pure 3 (P3), Q9 (11 marks): x y B A O C Figure 2 Figure 2 shows a sketch of the curve C with equation 2 sin 3 3 4 π x y 12 π < y < 3 4 π The curve intersects the y-axis at the poin
- June 2025 (A), Pure 3 (P3), Q3 (8 marks): The curve C has equation x y y 4 3 2 1 2 y 1 2 (a) Find d d y x in terms of y, giving the answer in simplest form. A point P lies on C. Given that • the gradien
- June 2025 (A), Pure 3 (P3), Q5 (10 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A curve C has equation y = 5
- June 2025 (A), Pure 3 (P3), Q6 (8 marks): y x O Figure 2 Figure 2 shows a sketch of the curve with equation y = f (x) where f (x) = (2x – 3) 3e 4x – 2 (a) Show that f′(x) = 2(Px + Q)(2x – 3) ne 4x – 2 w
- January 2025, Pure 3 (P3), Q3 (6 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. A curve has equation y = 4 1 3 2 x x x
- 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
- January 2025, Pure 3 (P3), Q9 (8 marks): y P x Q O Figure 1 Figure 1 shows a sketch of part of the curve C with equation y = f (x) where f (x) = 6 x ln (4x) x > 0 The curve cuts the x-axis at point P (
- January 2025, Pure 3 (P3), Q10 (9 marks): y P (a, b) O x Figure 2 Figure 2 shows a sketch of the curve with equation x = 3 cos 2y –3 x 3 0 y 2 π (a) Find d d x y in terms of y. (b) Hence show th
- October 2024, Pure 3 (P3), Q2 (5 marks): y x O P Figure 1 Figure 1 shows a sketch of the curve with equation x = 2y 2 + 5y – 6 (a) Find d d y x in terms of y. The point P lies on the curve and is shown
- 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
- October 2024, Pure 3 (P3), Q7 (10 marks): y x O P C Figure 3 The curve C has equation y = f (x) , where f (x) = x 3 4 7 x + x – 7 4 (a) Show that f′ (x) = kx x x 2 2 3 4 7 where k is a constant to be
- October 2024, Pure 3 (P3), Q8 (12 marks): H t O Figure 4 The heart rate of a horse is being monitored. The heart rate H, measured in beats per minute (bpm), is modelled by the equation H = 32 + 40e –0.2
- October 2024, Pure 3 (P3), Q9 (14 marks): y x O P l C R Figure 5 Figure 5 shows a sketch of part of the curve C with equation y = f (x) where f (x) = 6 4 2 2 1 2x x x x > – 1 2 (a) Find f′ (x) , giving
- June 2024, Pure 3 (P3), Q6 (9 marks): y R P l O x Figure 3 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Figure 3
- June 2024, Pure 3 (P3), Q8 (10 marks): h x d O Figure 4 Figure 4 is a graph showing the path of a golf ball after the ball has been hit until it first hits the ground. The vertical height, h metres,
- June 2024, Pure 3 (P3), Q9 (10 marks): y O x , 3 π P k Figure 5 The curve shown in Figure 5 has equation x = 4sin 2 y – 1 0 y 2 π The point , 3 π P k lies on the curve. (a) Verify that k
- January 2024, Pure 3 (P3), Q6 (7 marks): O y = f(x) R P Q x y Figure 1 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
- January 2024, Pure 3 (P3), Q7 (12 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The curve C has equation y x
- 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), Q5 (7 marks): The curve C has equation y = ln x k x k 2 2 x ∈ where k is a positive constant. (a) Show that d d y x Ax B x k x k ln 2 2 2 where A and B are constants
- October 2023, Pure 3 (P3), Q7 (10 marks): y O x Figure 1 Figure 1 shows a sketch of the curve C with equation y = f (x) where f e ( ) x x x 2 2 2 2 3 (a) Find the range of f (b) Show that f e ( ) x
- October 2023, Pure 3 (P3), Q10 (9 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. A curve C has equation 2 sin 4 0 0 1 8
- June 2023, Pure 3 (P3), Q3 (7 marks): (i) Find d dx x ln sin 2 3 writing your answer in simplest form. (ii) (a) Find d dx x 3 4 2 6 (b) Hence show that x x x R 3 4 2 0 2 5 d where R is an integer
- June 2023, Pure 3 (P3), Q8 (9 marks): y O x C Figure 3 Figure 3 shows a sketch of the curve C with equation y = f(x) , where f(x) = (2x + 1) 3e –4x (a) Show that f′(x) = A(2x + 1) 2 (1 – 4x) e –4x w
- June 2023, Pure 3 (P3), Q10 (8 marks): y O x Q P Figure 4 Figure 4 shows a sketch of the curve with equation x = 2 6 3 3 2y y (a) Find d d x y giving your answer as a fully simplified fraction. The t
- January 2023, Pure 3 (P3), Q7 (9 marks): The curve C has equation (a) Show that d d y x a x b 2 where a and b are integers to be found. The point P with y coordinate lies on C. Given that the tangent t
- January 2023, Pure 3 (P3), Q9 (11 marks): O y P C x Figure 3 Figure 3 shows a sketch of part of the curve C with equation y x x 3 4 0 2 e (a) Find d d y x , giving your answer in simplest form. The po
- October 2022, Pure 3 (P3), Q3 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. y (2, 0) A O x Figure 1 Figur
- October 2022, Pure 3 (P3), Q4 (5 marks): y = log10 (2x + 1) (a) Express x in terms of y. (b) Hence, giving your answer in terms of x, find d d y x
- October 2022, Pure 3 (P3), Q6 (6 marks): y = 2 3 + + sin cos sin x x x Show that d d y x = a x b x c x x tan sec sec sin + + + 2 where a, b and c are integers to be found.
- June 2022, Pure 3 (P3), Q1 (6 marks): The curve C has equation y = (3x – 2) 6 (a) Find d d y x Given that the point P 1 3 1 , lies on C, (b) find the equation of the normal to C at P. Writ
- June 2022, Pure 3 (P3), Q6 (10 marks): P x O y C Figure 3 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The functi
- June 2022, Pure 3 (P3), Q8 (12 marks): T t O v Figure 4 Figure 4 is a graph showing the velocity of a sprinter during a 100 m race. The sprinter’s velocity during the race, v m s –1, is modelled by t
- June 2022, Pure 3 (P3), Q9 (9 marks): M x O y Figure 5 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Figure 5 sho
- January 2022, Pure 3 (P3), Q1 (4 marks): Find, using calculus, the x coordinate of the stationary point on the curve with equation y = (2x + 5)e 3x
- January 2022, Pure 3 (P3), Q5 (9 marks): y x O M Q P Figure 1 Figure 1 shows a sketch of part of the curve with equation y = 6 ln(2x + 3) – 1 2 x 2 + 4 x > – 3 2 The curve cuts the negative x‑axis at t
- January 2022, Pure 3 (P3), Q10 (7 marks): y x O C Figure 3 Figure 3 shows a sketch of the curve C with equation x = ye 2y y ∈ (a) Show that d d y x y x y = + ( ) 1 2 Given that the straight line with
- October 2021, Pure 3 (P3), Q6 (8 marks): (i) The curve C1 has equation y = 3 ln(x2 – 5) – 4x2 + 15 x > 5 Show that C1 has a stationary point at x = p 2 where p is a constant to be found. (ii) A differe
- October 2021, Pure 3 (P3), Q8 (7 marks): A curve C has equation y = f(x), where f(x) = arcsin 1 2 x –2 x 2 – 2 π y 2 π (a) Sketch C. (b) Given x = 2 sin y, show that d d y x A x = - 1 2 wher
- October 2021, Pure 3 (P3), Q9 (9 marks): O y = f(x) x P y l Figure 3 Figure 3 shows a sketch of part of the curve with equation y = f(x), where f(x) = x(x2 – 4)e - 1 2 x (a) Find f′(x). The line l is t
- June 2021, Pure 3 (P3), Q1 (7 marks): The curve C has equation y = x 2 cos 1 2 x 0 < x π The curve has a stationary point at the point P. (a) Show, using calculus, that the x coordinate
- 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), Q7 (5 marks): Given that x = 6 sin2 2 y 0 < y < 4 π show that d d y x = 1 2 A Bx x ( ) − where A and B are integers to be found.
- 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), Q10 (10 marks): The curve C has equation 2 3sec 2 3 0 4 = π x y x y > < < (a) Find d d x y in terms of y. (b) Hence show that d d y x p qx x = −3 where p is irrational and q is
- October 2020, Pure 3 (P3), Q3 (7 marks): . y x O Figure 1 Figure 1 shows a sketch of a curve with equation y = f (x) where f (x) = 2 3 4 1 x x + − x > 1 4 (a) Find, in simplest form, f ʹ(x). (b) Hence
- October 2020, Pure 3 (P3), Q8 (9 marks): (i) The curve C has equation y = g(x) where g(x) = e3x sec 2x −4 π < x < 4 π (a) Find gʹ(x) (b) Hence find the x coordinate of the stationary point of C. (ii) A
- October 2020, Pure 3 (P3), Q9 (14 marks): (a) Given that x x x x x x x P Q x x 4 3 2 2 2 10 3 9 12 4 3 − − + − − − ≡ + + − − > find the value of the constant P and show that Q = 5 The curve C has equati
- January 2020, Pure 3 (P3), Q4 (11 marks): (i) f(x) = ( ) 2 5 3 2 x x + − x ≠ 3 (a) Find f′(x) in the form P x Q x ( ) ( ) where P(x) and Q(x) are fully factorised quadratic expressions. (b) Hence find t
- January 2020, Pure 3 (P3), Q7 (11 marks): y O P Q R x Figure 3 Figure 3 shows a sketch of part of the curve with equation y = 2 cos 3x – 3x + 4 x > 0 where x is measured in radians. The curve crosses th
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