Definite integrals and area under a curve: Edexcel A‑Level Maths questions

Edexcel A-Level Maths past-paper questions on 8.2 Definite integrals and area under a curve, 2010–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 14 questions on Definite integrals and area under a curve, as a list

June 2025, Pure 1, Q5 (3 marks): (a) Express 2.89 0 1.44 2 lim δx x δx x as an integral. (1) (b) Hence show that 2.89 0 1.44 2 lim δx x δx k x where k is an integer to be found. (Solutions rely
June 2025, Pure 2, Q15 (13 marks): R y x P Q O –1 1 Figure 5 In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Figure 5 sho
June 2024, Pure 2, Q11 (5 marks): O R C 1 x 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
June 2024, AS Statistics, Q3 (7 marks): Customers in a shop have to queue to pay. The partially completed table below and partially completed histogram opposite, give information about the time, x min
June 2022, Pure 2, Q8 (6 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. y x O R Figure 3 Figure 3 shows a sket
June 2022, AS Statistics, Q3 (8 marks): The histogram summarises the heights of 256 seedlings two weeks after they were planted. Height of seedling (cm) Frequency density 60 50 40 30 20 10 0 0 1 2 3 4
November 2021, AS Pure, Q9 (4 marks): Find the value of the constant k, 0 < k < 9, such that 6 20 9 x x k d = ∫ (4)
November 2020, AS Pure, Q7 (8 marks): Given that k is a positive constant and 5 2 3 4 1 x x k +     = ∫ d (a) show that 3k + 5 k – 12 = 0 (4) (b) Hence, using algebra, find any values of k suc
November 2020, AS Pure, Q10 (10 marks): g(x) = 2x3 + x2 – 41x – 70 (a) Use the factor theorem to show that g(x) is divisible by (x – 5). (2) (b) Hence, showing all your working, write g(x) as a produc
June 2019, Pure 1, Q8 (10 marks): y O x R1 R2 b Figure 2 Figure 2 shows a sketch of part of the curve with equation y = x(x + 2)(x – 4). The region R1 shown shaded in Figure 2 is bounded by the
June 2019, Pure 2, Q5 (3 marks): y O x į[ y P 4 9 y x = Figure 3 Figure 3 shows a sketch of the curve with equation y x = The point P(x, y) lies on the curve. The rectangle, shown shaded on Fig
June 2019, AS Pure, Q3 (6 marks): (a) Given that k is a constant, find 4 3 x kx + ⎛ ⎝⎜ ⎞ ⎠⎟ ∫ dx simplifying your answer. (3) (b) Hence find the value of k such that 4 3 0 5 2 x kx + ⎛ ⎝⎜ ⎞ ⎠⎟ ∫
June 2019, AS Pure, Q13 (7 marks): y x O k R Figure 3 Figure 3 shows a sketch of part of the curve with equation y = 2x3 – 17x2 + 40x The curve has a minimum turning point at x = k. The region R,
June 2018, Pure 1, Q7 (7 marks): Given that k  + (a) show that 2 3 3 ( ) x k x k k − ∫ d is independent of k, (4) (b) show that 2 2 2 2 ( ) x k x k k − ∫ d is inversely proportional to k. (3)

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