Calculus: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 3.4 Calculus, 2019–2025, with its mark scheme and examiner’s report.

All 31 questions on Calculus, as a list

June 2025 (R), Paper 2 Higher, Q22 (5 marks): The diagram shows a solid cuboid. Diagram NOT accurately drawn x cm x cm ( 15 − x cm 4 ) The volume of the cuboid is V cm3 Find the maximum value of V
June 2025, Paper 2 Higher, Q17 (6 marks): y x 3 x 2 x 4 5 2 (a) Find d y d x d y x = d (b) Find the coordinates of the turning points on the graph with equation y x 3 x 2 x 4 5 2 Show clear algebraic wo
November 2024, Paper 1 Higher, Q20 (4 marks): The curve with equation y x x has a minimum point. 2 4 64 Find an equation of the tangent to the curve at the minimum point. Show clear algebraic working.
June 2024 (R), Paper 1 Higher, Q19 (5 marks): A curve C has equation y x 3 x 2 x 8 12 5 Curve C has exactly two stationary points, one at point A and one at point B such that x coordinate of point A > x coo
June 2024, Paper 1 Higher, Q18 (5 marks): A curve C has equation y = x 3 ‒ 40x + 1 Find the coordinates of both the points on C at which the gradient is 8 ( , ) ( , )
November 2023, Paper 1 Higher, Q16 (4 marks): A curve has equation y x 3 x 4 8 5 Find the x coordinates of the two points on the curve where the gradient is 1 3
November 2023, Paper 2 Higher, Q18 (4 marks): A particle is moving along a straight line that passes through the fixed point O The displacement, s metres, of the particle from O at time t seconds is given b
June 2023 (R), Paper 1 Higher, Q21 (6 marks): The curve T has equation y = x3 – 2x2 – 9x + 15 (a) Find d y d x d y x = d (b) Find the range of values of x for which T has a positive gradient. Give your valu
June 2023, Paper 1 Higher, Q11 (6 marks): The curve C has equation y = 4x 3 + x 2 – 20x (a) Find d y d x d y x = d (b) Find the x coordinates of the points on C where the gradient is 4 Show clear algebr
January 2023 (R), Paper 1 Higher, Q23 (5 marks): G is the point on the curve with equation y = 8x2 – 14x – 6 where the gradient is 10 The straight line Q passes through the point G and is perpendicular to the
January 2023 (R), Paper 2 Higher, Q21 (3 marks): The diagram shows the graph of y = f(x) y 6 4 P 2 O x –8 –6 –4 –2 2 4 6 8 –2 –4 The point P has x coordinate –2 Use the graph to find an estimate for the gradie
January 2023, Paper 1 Higher, Q20 (5 marks): The radius of a right circular cylinder is x cm.   The height of the cylinder is 800 − x cm.   πx   The volume of the cylinder is V cm3 Find the maximum v
June 2022 (R), Paper 1 Higher, Q22 (7 marks): The diagram shows a sketch of part of the curve with equation y = x where p is a x positive constant. y Diagram NOT accurately drawn T O x For all values of p,
June 2022, Paper 1 Higher, Q17 (5 marks): A particle P moves along a straight line. The fixed point O lies on this line. The displacement of P from O at time t seconds, t  1, is s metres where s = 4t2
January 2022 (R), Paper 1 Higher, Q23 (6 marks): Two particles, P and Q, move along a straight line. The fixed point O lies on this line. The displacement of P from O at time t seconds is s metres, where s = t
January 2022 (R), Paper 2 Higher, Q17 (3 marks): Part of the curve with equation y = f (x) is shown on the grid. y 6 5 4 3 2 1 x –2 –1 O 1 2 3 4 –1 –2 –3 Find an estimate for the gradient of the curve at the p
January 2022, Paper 1 Higher, Q24 (6 marks): The curve C has equation y = ax3 + bx2 – 12x + 6 where a and b are constants. The point A with coordinates (2, –6) lies on C The gradient of the curve at A is 1
January 2022, Paper 2 Higher, Q24 (5 marks): A particle P moves along a straight line that passes through the fixed point O The displacement, x metres, of P from O at time t seconds, where t  0 , is given
June 2021, Paper 2 Higher, Q21 (5 marks): The point A is the only stationary point on the curve with equation y = kx 2 + x where k is a constant. Given that the coordinates of A are 2   3 , a   fi
January 2021 (R), Paper 1 Higher, Q20 (5 marks): A particle P is moving along a straight line. The fixed point O lies on the line. At time t seconds (t  0), the displacement of P from O is s metres where 3 –
January 2021, Paper 1 Higher, Q17 (5 marks): A solid, S, is made from a hemisphere and a cylinder. The centre of the circular face of the hemisphere and the centre of the top face of the cylinder are at th
January 2021, Paper 2 Higher, Q19 (5 marks): A particle P is moving along a straight line. The fixed point O lies on this line. At time t seconds where t  0, the displacement, s metres, of P from O is giv
November 2020 (R), Paper 1 Higher, Q13 (6 marks): The curve C has equation y = 5x3 – x2 – 6x + 4 (a) Find d y d x d y x = d There are two points on the curve C at which the gradient of the curve is 2 (b) Find t
November 2020, Paper 1 Higher, Q23 (4 marks): Curve C has equation y = px3 − mx where p and m are positive integers. Find the range of values of x, in terms of p and m, for which the gradient of C is negati
January 2020 (R), Paper 1 Higher, Q23 (6 marks): A particle moves along a straight line. The fixed point O lies on this line. The displacement of the particle from O at time t seconds, t  0, is s metres where
January 2020, Paper 1 Higher, Q15 (8 marks): Diagram NOT accurately drawn (x + 1) cm (3 − x) cm (2x + 5) cm The diagram shows a cuboid of volume V cm3 (a) Show that V = 15 + 16x − x2 − 2x3 There is a value
June 2019 (R), Paper 1 Higher, Q16 (5 marks): A particle P is moving along a straight line. The fixed point O lies on this line. At time t seconds, the displacement, s metres, of P from O is given by s = 4t
June 2019, Paper 1 Higher, Q24 (4 marks): A particle P is moving along a straight line that passes through the fixed point O. The displacement, s metres, of P from O at time t seconds is given by s = t3
June 2019, Paper 2 Higher, Q18 (5 marks): The diagram shows a solid cuboid. Diagram NOT accurately drawn (12 – 3x) cm x cm x cm The total surface area of the cuboid is A cm2 Find the maximum value of A.
January 2019 (R), Paper 1 Higher, Q13 (7 marks): A curve C has equation y = x3 – x2 – 8x + 12 (a) Find d y d x d y x = d The curve C has two turning points. (b) Work out the x coordinates of the two turning po
January 2019, Paper 1 Higher, Q12 (5 marks): The curve C has equation y x 3 9 x 1 = − + 3 (a) Find d y d x d y x = d (b) Find the range of values of x for which C has a negative gradient.

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