plumiNumerical integration: OCR MEI A‑Level Further Maths questions
OCR MEI A-Level Further Maths past-paper questions on 6.3 Numerical integration, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 20 questions on Numerical integration, as a list
- June 2025, Numerical Methods, Q3 (5 marks): 3 . y 3 3 Approximations to 1 x d x using the midpoint rule, the trapezium rule and Simpson’s rule + 0 5 . with n = and n 1 2 are shown in the table. The table
- June 2025, Numerical Methods, Q6 (7 marks): 1y 6 The midpoint rule is used to find a sequence of approximations to sin x x d . 0 The associated spreadsheet output, together with some further analysis, is
- June 2025, AS Numerical Methods, Q5 (7 marks): 5 . y 5 The spreadsheet output shows a sequence of approximations to f ( )x d x using the trapezium 0 5 . rule and Simpson’s rule, together with some further an
- June 2024, Numerical Methods, Q7 (14 marks): 0y 7 ( )x x A student is using a spreadsheet to find approximations to f d using the midpoint rule, the trapezium rule and Simpson’s rule. Some of the associate
- June 2024, AS Numerical Methods, Q7 (12 marks): A student uses the midpoint rule, the trapezium rule and Simpson’s Rule to find a series of 1y approximations to f ( )x d x . The associated spreadsheet output,
- June 2023, Numerical Methods, Q4 (4 marks): by 4 A spreadsheet is used to approximate f ( )x d x using the midpoint rule with 1 strip. a The output is shown in the table below. B C D 3 x f ( )x M1 4 1.5
- June 2023, Numerical Methods, Q9 (9 marks): 1y 3 9 The trapezium rule is used to calculate 3 approximations to sinh x ( ) d x with 1, 2 and 4 strips 0 respectively. The results are shown in Table 9.1. Tab
- June 2023, AS Numerical Methods, Q5 (9 marks): y 5 2 5 The table shows some approximations to x 3 x 2 d x , correct to 8 decimal places, which + + 0 have been found using the midpoint rule and the trapezium
- June 2022, Numerical Methods, Q5 (9 marks): Kai uses the midpoint rule, trapezium rule and Simpson’s rule to find approximations to by f ( ) x d x , where a and b are constants. The associated spreadsheet
- June 2022, AS Numerical Methods, Q3 (5 marks): Ali uses the trapezium rule with h = 1, h = 0.5 and h = 0.25 to calculate three approximations to 2y f ( )x d x . Ali’s results are shown in the table. 1 h n Tn
- June 2022, AS Numerical Methods, Q6 (10 marks): Fig. 6.1 shows some values of x and the associated values of f (x). x 1 1.25 1.5 1.75 2 f (x) 0 0.1609640 0.2924813 0.4036775 0.5 Fig. 6.1 2y Sam is using the m
- November 2021, Numerical Methods, Q7 (15 marks): y 7 tanh x x Sarah uses the trapezium rule to find a sequence of approximations to ( ) d . 0 Her spreadsheet output is shown in Fig. 7.1. n Tn difference ratio
- November 2021, AS Numerical Methods, Q5 (10 marks): y 5 f x x A student is trying to find an accurate approximation to ( ) d using the trapezium rule, the 1 midpoint rule and Simpson’s rule. Some of the spreadshe
- November 2020, Numerical Methods, Q4 (10 marks): y 3 4 (a) Use the trapezium rule with 1 strip to calculate an estimate of x x 1 d , giving your + [2] answer correct to six decimal places. 1 Fig. 4 shows some
- November 2020, AS Numerical Methods, Q5 (11 marks): y 5 ( )x x Arthur uses a spreadsheet to approximate f d using the trapezium rule. Some of the output is shown in Fig. 5.1. 0 C D E F 3 x y 4 T 5 0 1.732051 6 1
- June 2019, Numerical Methods, Q6 (10 marks): y x 6 The spreadsheet output in Fig. 6 shows approximations to x - d x found using the midpoint 0 rule, denoted by Mn, and the trapezium rule, denoted by Tn. A
- June 2019, AS Numerical Methods, Q4 (5 marks): = ^ h . x 4 Fig. 4.1 shows the graph of y 0 8 . x y 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 x 0 0.5 1 1.5 2 2.5 3 3.5 Fig. 4.1 ^ h for various values x Fig. 4.2 shows som
- June 2019, AS Numerical Methods, Q8 (12 marks): ^ h 1 y 8 Fig. 8.1 shows estimates of sin x d x found using the trapezium rule, denoted by Tn, together 0 with some further analysis of these estimates. n Tn di
- June 2018, AS Numerical Methods, Q2 (4 marks): The table in Fig. 2 shows some values of log x 3 which are correct to 6 decimal places. x 2 2.25 2.5 2.75 3 log3x 0.630930 0.738140 0.834044 0.920799 1 Fig. 2 3
- June 2018, AS Numerical Methods, Q7 (12 marks): x 2 7 Fig. 7.1 shows part of the curve y 2 x + . 3 = - y 6 5 4 3 2 1 0 x 0 1 2 3 4 5 Fig. 7.1 7 ^ h y 4 x 2 (i) State, with a reason, whether using the trapeziu
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