plumiNumerical methods: AQA A‑Level Maths questions
Every AQA A-Level Maths exam question on I Numerical methods, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 Paper 3, question 9: (a) Describe a sequence of two transformations which maps the graph with equation y = 1 x onto the graph with equation y = 3 x – 4 [2 marks] 9 (b) State the equ](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73573-jun25-09-qp.webp)
![June 2024 Paper 1, question 14: (a) The equation x3 = e6 – 2x has a single solution, x = α By considering a suitable change of sign, show that α lies between 0 and 4 [2 marks] 14 (b) Show that](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73571-jun24-14-qp.webp)
![June 2023 Paper 1, question 13: The function f is defined by f (x) = arccosx for 0 × x × a The curve with equation y = f (x) is shown below. O a x 2 2 y 13 (a) State the value of a [1 mark] 13](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73571-jun23-13-qp.webp)
![November 2021 Paper 1, question 7: The equation x2 = x3 + x − 3 has a single solution, x = a 7 (a) By considering a suitable change of sign, show that a lies between 1.5 and 1.6 [2 marks] 7 (b) S](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73571-nov21-07-qp.webp)
![June 2019 Paper 1, question 7: (a) By sketching the graphs of y = 1 x and y = sec 2x on the axes below, show that the equation 1 x = sec 2x has exactly one solution for x > 0 [3 marks] x ϖ 2ϖ](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73571-jun19-07-qp.webp)
All 21 questions on Numerical methods, as a list
- June 2025, Paper 1, Q15 (12 marks): A curve has equation y = x2 The point Q has coordinates (3, 2.5) The point P on the curve which is closest to the point Q is shown on the diagram below. x Q (3,
- June 2025, Paper 2, Q6 (6 marks): The curve with equation y = e 2 x – 3 is shown in the diagram. x 4 8 y O y = x – 3 x e2 The region shaded is bounded by the curve, the x-axis, and the lines x =
- June 2025, Paper 3, Q9 (5 marks): (a) Describe a sequence of two transformations which maps the graph with equation y = 1 x onto the graph with equation y = 3 x – 4 [2 marks] 9 (b) State the equ
- June 2024, Paper 1, Q14 (10 marks): (a) The equation x3 = e6 – 2x has a single solution, x = α By considering a suitable change of sign, show that α lies between 0 and 4 [2 marks] 14 (b) Show that
- June 2024, Paper 1, Q16 (5 marks): Figure 2 below shows a 1.5 metre length of pipe. Figure 2 1.5 m The symmetrical cross-section of the pipe is shown below, in Figure 3, where x and y are measure
- June 2023, Paper 1, Q5 (4 marks): The graph of y = 5 ex − 1 is shown in the diagram below. x O 4 1 y The trapezium rule with 6 ordinates (5 strips) is to be used to find an approximation for the
- June 2023, Paper 1, Q13 (9 marks): The function f is defined by f (x) = arccosx for 0 × x × a The curve with equation y = f (x) is shown below. O a x 2 2 y 13 (a) State the value of a [1 mark] 13
- June 2023, Paper 3, Q2 (1 mark): The trapezium rule is used to estimate the area of the shaded region in each of the graphs below. Identify the graph for which the trapezium rule produces an ov
- June 2022, Paper 1, Q10 (12 marks): The diagram shows a sector of a circle OAB. O θ C A B The point C lies on OB such that AC is perpendicular to OB. Angle AOB is y radians. 10 (a) Given the area
- June 2022, Paper 1, Q14 (9 marks): The region bounded by the curve y = (2x × 8) ln x and the x-axis is shaded in the diagram below. x 4 1 y 14 (a) Use the trapezium rule with 5 ordinates to find
- November 2021, Paper 1, Q7 (7 marks): The equation x2 = x3 + x − 3 has a single solution, x = a 7 (a) By considering a suitable change of sign, show that a lies between 1.5 and 1.6 [2 marks] 7 (b) S
- November 2021, Paper 2, Q10 (11 marks): The function h is defined by h(x) = x p x − 3 where h has its maximum possible domain. 10 (a) Find the domain of h. Give your answer using set notation. [3 mark
- November 2021, Paper 2, Q14 (4 marks): A motorised scooter is travelling along a straight path with velocity v m s−1 over time t seconds as shown by the following graph. 20 30 40 0 0 2 4 6 8 10 10 t
- November 2020, Paper 1, Q2 (1 mark): A student is searching for a solution to the equation f (x) = 0 He correctly evaluates f (×1) = ×1 and f (1) = 1 and concludes that there must be a root between
- November 2020, Paper 1, Q11 (9 marks): The region R enclosed by the lines x = 1 , x = 6 , y = 0 and the curve y = ln (8 × x) is shown shaded in Figure 3 below. Figure 3 2 R 4 x y 6 0 1 3 5 7 All dist
- November 2020, Paper 1, Q14 (9 marks): The function f is defined by f (x) = 3x x p × 1 where x ≥ 0 14 (a) f (x) = 0 has a single solution at the point x = a By considering a suitable change of sign,
- November 2020, Paper 2, Q15 (5 marks): A particle is moving in a straight line with velocity v m s−1 at time t seconds as shown by the graph below. 40 60 80 0 0 40 80 120 160 200 20 60 100 140 180 20
- June 2019, Paper 1, Q7 (11 marks): (a) By sketching the graphs of y = 1 x and y = sec 2x on the axes below, show that the equation 1 x = sec 2x has exactly one solution for x > 0 [3 marks] x ϖ 2ϖ
- June 2019, Paper 1, Q14 (10 marks): The graph of y = 2x3 x2 + 1 is shown for 0 ≤ x ≤ 4 4 x 0 0 2 4 6 8 y 2 A Caroline is attempting to approximate the shaded area, A, under the curve using the tra
- June 2018, Paper 1, Q8 (8 marks): The diagram shows a sector of a circle OAB. C is the midpoint of OB. Angle AOB is y radians. C O θ B A 8 (a) Given that the area of the triangle OAC is equal to
- June 2018, Paper 1, Q11 (10 marks): The daily world production of oil can be modelled using V = 10 + 100 t 30 3 −50 t 30 4 where V is volume of oil in millions of barrels, and t is time in years s
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