plumiDifferentiation: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P4.5 Differentiation, 2019–2025, with its mark scheme and examiner’s report.
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All 39 questions on Differentiation, as a list
- June 2025, Pure 4 (P4), Q1 (8 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. The curve C has equation 2 6 7 13 2 2
- June 2025, Pure 4 (P4), Q2 (4 marks): A spherical ball of ice with radius r cm is melting. The volume of the ball of ice, V cm 3, is decreasing at a constant rate, k cm 3 per second, where k is a co
- June 2025, Pure 4 (P4), Q5 (9 marks): The curve C has parametric equations x t t y t t 3 2 1 1 1 2 The point P, where t = 2, lies on C. (a) Use parametric differentiation to find the equation of the
- June 2025 (A), Pure 4 (P4), Q2 (5 marks): x cm Figure 1 Figure 1 shows a cube which is increasing in size. At time t seconds, • the length of each edge of the cube is x cm • the volume of the cube is V
- June 2025 (A), Pure 4 (P4), Q5 (6 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 2x + 4y 2 = 6 +
- June 2025 (A), Pure 4 (P4), Q6 (11 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 parametric equa
- January 2025, Pure 4 (P4), Q2 (8 marks): The curve C has equation 3 5 4 10 2 35 2 2 x y x y x ( ) y > 0 (a) Find an expression for d d y x in terms of x and y Curve C cuts the y‑axis at the point P (b)
- January 2025, Pure 4 (P4), Q4 (10 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) The volume, V, of a spher
- January 2025, Pure 4 (P4), Q9 (12 marks): y P x O l C Figure 2 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Figure 2
- October 2024, Pure 4 (P4), Q3 (9 marks): O x y Figure 1 Figure 1 shows a sketch of the curve C with parametric equations 3 3sin 1 cos2 2 2 π π x θ y θ θ (a) Show that d cosec d y k θ x θ ≠ 0 where k is
- October 2024, Pure 4 (P4), Q4 (9 marks): O P C x y Figure 2 Figure 2 shows a sketch of the curve C with equation 3 2 4 8 11 0 2 2 x y xy x The point P has coordinates (1, 2). (a) Verify that P lies on
- October 2024, Pure 4 (P4), Q5 (6 marks): h cm 30 cm 12 cm r cm Figure 3 Figure 3 shows a container in the shape of a hollow, inverted, right circular cone. The height of the container is 30 cm and the
- June 2024, Pure 4 (P4), Q3 (7 marks): The curve C is defined by the equation 8 3 2 9 3 2 x y xy Find an equation of the normal to C at the point (2, 5), giving your answer in the form ax + by + c =
- June 2024, Pure 4 (P4), Q4 (6 marks): R 5 cm O θ Q P Figure 1 Figure 1 shows a sketch of a segment PQRP of a circle with centre O and radius 5 cm. Given that • angle POR is θ radians • θ is increasi
- January 2024, Pure 4 (P4), Q3 (9 marks): y C P x O Figure 1 The curve C, shown in Figure 1, has equation y 2 x + 3y = 4x 2 + k y > 0 where k is a constant. (a) Find d d y x in terms of x and y The poin
- January 2024, Pure 4 (P4), Q4 (5 marks): 5 cm r cm l cm Figure 2 A cone, shown in Figure 2, has • fixed height 5 cm • base radius r cm • slant height l cm (a) Find an expression for l in terms of r Giv
- January 2024, Pure 4 (P4), Q9 (12 marks): y C O x Figure 4 Figure 4 shows a sketch of the curve C with parametric equations x t y t t sec tan 3 3 6 2 < < (a) Find d d y x in terms of t (b)
- October 2023, Pure 4 (P4), Q2 (7 marks): x cm Figure 1 Figure 1 shows a cube which is increasing in size. At time t seconds, • the length of each edge of the cube is x cm • the surface area of the cube
- October 2023, Pure 4 (P4), Q5 (10 marks): y = x P O C x y Figure 2 Figure 2 shows a sketch of the curve C with equation y x x y k 3 2 2 4 where k is a positive constant greater than 1 (a) Find d d y x i
- October 2023, Pure 4 (P4), Q8 (14 marks): k O C x y 2 Figure 3 Figure 3 shows a sketch of the curve C with parametric equations 6 3sin 2 2cos 0 2 π x t t y t t The curve meets the y-axis at 2 and the x-
- June 2023, Pure 4 (P4), Q2 (10 marks): O P y C x Figure 1 Figure 1 shows a sketch of part of the curve C with equation 2 x – 4xy + y 2 = 13 y 0 The point P lies on C and has x coordinate 2 (a) Find
- January 2023, Pure 4 (P4), Q5 (7 marks): O x = p x = q x y Figure 2 Figure 2 shows a sketch of the curve with equation y2 = 2x2 + 15x + 10y (a) Find d d y x in terms of x and y. The curve is not define
- January 2023, Pure 4 (P4), Q7 (12 marks): The volume V cm3 of a spherical balloon with radius r cm is given by the formula V = 4 3 πr3 (a) Find d d V r giving your answer in simplest form. At time t sec
- January 2023, Pure 4 (P4), Q8 (11 marks): O S l P C x y Figure 3 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A curv
- October 2022, Pure 4 (P4), Q6 (8 marks): y x C P O Figure 3 Figure 3 shows a sketch of the curve C with parametric equations x = 1 + 3 tan t y = 2 cos 2t – 6 π t 3 π The curve crosses the x-axis at
- October 2022, Pure 4 (P4), Q11 (9 marks): y x O P Q North East Figure 4 Figure 4 shows a sketch of the closed curve with equation (x + y) 3 + 10y 2 = 108x (a) Show that d d y x x y y x y = − + ( ) + + (
- June 2022, Pure 4 (P4), Q3 (8 marks): 3x x Figure 1 A tablet is dissolving in water. The tablet is modelled as a cylinder, shown in Figure 1. At t seconds after the tablet is dropped into the water,
- June 2022, Pure 4 (P4), Q4 (8 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. A curve has equation 16x 3 – 9kx 2y +
- June 2022, Pure 4 (P4), 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 parametric eq
- January 2022, Pure 4 (P4), Q1 (6 marks): The curve C has equation xy2 = x2 y + 6 x ≠ 0 y ≠ 0 Find an equation for the tangent to C at the point P (2, 3), giving your answer in the form ax + by + c = 0
- January 2022, Pure 4 (P4), Q4 (8 marks): Figure 1 A regular icosahedron of side length x cm, shown in Figure 1, is expanding uniformly. The icosahedron consists of 20 congruent equilateral triangular f
- October 2021, Pure 4 (P4), Q1 (7 marks): The curve C has equation 2x − 4y 2 + 3x 2 y = 4x 2 + 8 The point P (3, 2) lies on C. Find the equation of the normal to C at the point P, writing your answer in
- October 2021, Pure 4 (P4), Q5 (9 marks): C x O y Figure 1 Figure 1 shows a sketch of the curve C with parametric equations x = 5 + 2 tan t y = 8 sec2 t −3 π t 4 π (a) Use parametric differentiation
- October 2021, Pure 4 (P4), Q9 (10 marks): 4.2 metres T h metres 8 metres Figure 4 Figure 4 shows a cylindrical tank that contains some water. The tank has an internal diameter of 8 m and an internal hei
- June 2021, Pure 4 (P4), Q3 (7 marks): 20 cm h cm Figure 2 A bowl with circular cross section and height 20 cm is shown in Figure 2. The bowl is initially empty and water starts flowing into the bowl
- June 2021, Pure 4 (P4), Q5 (9 marks): A curve has equation y2 = y e−2x − 3x (a) Show that d d y x = 2 3 2 2 2 y y x x e e − − + − The curve crosses the y‑axis at the origin and at the point P. The t
- January 2021, Pure 4 (P4), Q6 (9 marks): A curve has equation 4y 2 + 3x = 6ye–2x (a) Find d d y x in terms of x and y. The curve crosses the y-axis at the origin and at the point P. (b) Find the equati
- October 2020, Pure 4 (P4), Q4 (12 marks): A y B O x Figure 2 Figure 2 shows a sketch of part of the curve with parametric equations x = 2t2 − 6t, y = t 3 − 4t, t ∈ The curve cuts the x-axis at the ori
- October 2020, Pure 4 (P4), Q6 (7 marks): A curve C has equation y = xsin x x > 0 y > 0 (a) Find, by firstly taking natural logarithms, an expression for d d y x in terms of x and y. (b) Hence show that
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