plumiIntegration: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P2.8 Integration, 2019–2025, with its mark scheme and examiner’s report.
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All 36 questions on Integration, as a list
- June 2025, AS Pure 2 (P2), Q3 (5 marks): O R C y x P (1, 11) Q (4, 5) Figure 1 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acc
- June 2025, AS Pure 2 (P2), Q5 (6 marks): x –2 –0.5 1 2.5 4 5.5 7 y 12 4.243 1.5 0.530 0.188 0.066 0.023 The table above shows corresponding values of x and y for y = 3 1 2 x The values of y ar
- June 2025 (A), AS Pure 2 (P2), Q4 (9 marks): O y x 1 5 Figure 1 Figure 1 shows a sketch of part of the curve with equation y = log3 (x + 1) – log3 x The point P(a, 4) lies on the curve. (a) Find the exact
- June 2025 (A), AS Pure 2 (P2), Q8 (9 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 = f
- June 2025 (A), AS Pure 2 (P2), Q10 (9 marks): O Q N M y x P R C Figure 3 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Fi
- January 2025, AS Pure 2 (P2), Q7 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) The table below shows val
- January 2025, AS Pure 2 (P2), Q9 (12 marks): O P M R y 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
- October 2024, AS Pure 2 (P2), Q1 (5 marks): A continuous curve has equation y = f (x). A table of values of x and y for y = f (x) is shown below. x 0.5 1.75 3 4.25 5.5 y 3.479 6.101 7.448 6.823 5.182 Usin
- October 2024, AS Pure 2 (P2), Q8 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. O x y P R Q C1 C2 Figure 1 Fi
- June 2024, AS Pure 2 (P2), Q6 (9 marks): (a) Sketch the curve with equation y = a x + 4 where a is a positive constant greater than 1 On your sketch, show • the coordinates of the point of intersection
- June 2024, AS Pure 2 (P2), Q9 (8 marks): y x k R1 P C O R2 Figure 1 Figure 1 is a sketch of the curve C with equation y = 2x 3 2 (4 – x) x 0 The point P is the stationary point of C. (a) Find, using
- June 2024 (R), AS Pure 2 (P2), Q2 (5 marks): The table shows corresponding values of x and y for a continuous curve with equation y = f (x) between x = –4 and x = 5, where a is a constant. x –4 –2.5 –1 0.5
- June 2024 (R), AS Pure 2 (P2), Q10 (9 marks): y O 1 P R C x Figure 1 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Figure
- January 2024, AS Pure 2 (P2), Q4 (9 marks): (a) Sketch the curve with equation y = a – x + 4 where a is a constant and a > 1 On your sketch show • the coordinates of the point of intersection of the curve
- January 2024, AS Pure 2 (P2), Q10 (9 marks): In this question you must show detailed reasoning. Solutions relying entirely on calculator technology are not acceptable. O P x R l y Figure 2 Figure 2 shows a
- October 2023, AS Pure 2 (P2), Q6 (6 marks): (0, 0) (15, 0) (12, 3.08) (9, 3.12) (6, 2.74) (3, 1.52) y x Figure 1 A river is being studied. At one particular place, the river is 15 m wide. The depth, y met
- October 2023, AS Pure 2 (P2), Q9 (12 marks): P (9, 40) y l C R O x Figure 3 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable
- June 2023, AS Pure 2 (P2), Q1 (3 marks): The continuous curve C has equation y = f(x). A table of values of x and y for y = f(x) is shown below. x 4.0 4.2 4.4 4.6 4.8 5.0 y 9.2 8.4556 3.8512 5.0342 7.8
- June 2023, AS Pure 2 (P2), Q10 (10 marks): The curve C has equation y = ( ) x k x − 2 x > 0 where k is a positive constant. (a) Show that ( ) x k x 2 1 16 dx = ak 2 + bk + 2046 5 where a and b are intege
- January 2023, AS Pure 2 (P2), Q1 (6 marks): O –1 1 x y Figure 1 Figure 1 shows a sketch of part of the curve with equation y = f (x) The table below shows some corresponding values of x and y for this cur
- January 2023, AS Pure 2 (P2), Q9 (8 marks): In this question you must show all stages of your working. Solutions based entirely on calculator technology are not acceptable. R1 D O E F R2 C l x y Figure 3
- October 2022, AS Pure 2 (P2), Q6 (7 marks): The curve C1 has equation y = f(x). A table of values of x and y for y = f(x) is shown below, with the y values rounded to 4 decimal places where appropriate. x
- October 2022, AS Pure 2 (P2), Q9 (12 marks): In this question you must show detailed reasoning. Solutions relying entirely on calculator technology are not acceptable. R O A T C1 C2 x y l Figure 3 Figure 3
- June 2022, AS Pure 2 (P2), Q2 (8 marks): y O x Figure 1 Figure 1 shows the graph of y = 1 − log10 (sin x) 0 < x < π where x is in radians. The table below shows some values of x and y for this graph, w
- June 2022, AS Pure 2 (P2), Q7 (7 marks): f(x) = Ax3 + 6x2 − 4x + B where A and B are constants. Given that • (x + 2) is a factor of f(x) • f d ( ) x x = ∫ 176 3 5 find the value of A and the value of B
- January 2022, AS Pure 2 (P2), Q1 (7 marks): The table below shows corresponding values of x and y for y x = − 25 The values of y are given to 3 decimal places. x 5 5.5 6 6.5 7 y 6.792 6.298 5.858 5.466 5.
- January 2022, AS Pure 2 (P2), Q9 (10 marks): y x O P C R1 R2 l Figure 2 Figure 2 shows • the curve C with equation y = x – x 2 • the line l with equation y = mx, where m is a constant and 0 < m < 1 The lin
- October 2021, AS Pure 2 (P2), Q3 (8 marks): O 14 2 R x y Figure 1 Figure 1 shows a sketch of part of the curve with equation y = log10 x The region R, shown shaded in Figure 1, is bounded by the curve, th
- October 2021, AS Pure 2 (P2), Q8 (10 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. M l C x O R y Figure 2 Figure
- June 2021, AS Pure 2 (P2), Q5 (10 marks): O x y R C2 C1 2.5 4 Figure 2 Figure 2 shows a sketch of part of the graph of the curves C1 and C2 The curves intersect when x = 2.5 and when x = 4 A table of va
- January 2021, AS Pure 2 (P2), Q7 (6 marks): P (kW) R t (hours) 17 16 15 14 13 12 11 10 9 8 7 O 1 2 3 Figure 1 Solar panels are installed on the roof of a building. The power, P, produced on a particular d
- October 2020, AS Pure 2 (P2), Q2 (4 marks): y = 2 5 3 2 x x ( ) + (a) Complete the table below, giving the values of y to 3 decimal places. x –0.25 0 0.25 0.5 0.75 y 0.462 0.653 0.698 (b) Use the trapeziu
- October 2020, AS Pure 2 (P2), Q6 (9 marks): B A R C1 C2 O x y Figure 1 Figure 1 shows a sketch of part of the curves C1 and C2 with equations C1 : y = x3 – 6x + 9 x 0 C2 : y = –2x2 + 7x – 1 x 0 The cu
- January 2020, AS Pure 2 (P2), Q1 (7 marks): The table below shows corresponding values of x and y for y = log2 (2x) The values of y are given to 2 decimal places as appropriate. x 2 5 8 11 14 y 2 3.32 4 4
- January 2020, AS Pure 2 (P2), Q4 (6 marks): x O R 17 y Figure 1 Figure 1 shows a sketch of the curve with equation . y = 2x2 + 7 x 0 The finite region R, shown shaded in Figure 1, is bounded by the curv
- June 2019, AS Pure 2 (P2), Q10 (11 marks): y O P Q x C Figure 1 Figure 1 shows a sketch of part of the curve C with equation y = f(x) where f(x) = 36 2 x + 2x – 13 x 0 Using calculus, (a) find the range
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