plumiNumerical differentiation: OCR MEI A‑Level Further Maths questions
OCR MEI A-Level Further Maths past-paper questions on 6.2 Numerical differentiation, 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 21 questions on Numerical differentiation, as a list
- June 2025, Numerical Methods, Q1 (4 marks): The table shows some values of x and the associated values of ( ) f x . x 1.9 2.0 2.1 0.216 92 0.2 0.184 84 f ( )x (a) Determine an estimate of f 2 0 ( . ) usin
- June 2025, AS Numerical Methods, Q4 (8 marks): A student is using a spreadsheet to investigate the curve y f ( ) x at the point where x 2 . Some = = of the spreadsheet output is shown below. Table 4.1 shows
- June 2025, AS Numerical Methods, Q8 (7 marks): Table 8.1 shows some values of x and the associated values of ( )x f . Table 8.1 x 0.5 0.9 1.3 f ( )x 1.414 21 1.099 47 0.711 01 (a) Use the central difference
- June 2024, Numerical Methods, Q1 (4 marks): The table shows some values of x, together with the associated values of a function, ( )x f . x 1.9 2 2.1 0.5842 0.6309 0.6753 f ( )x (a) Use the information in
- June 2024, Numerical Methods, Q6 (10 marks): Table 6.1 shows some values of x and the associated values of a function, y f ( ) x . = Table 6.1 x 1.5 1 2 0.840 89 1 1.189 21 f ( )x (a) Explain why it is not
- June 2024, AS Numerical Methods, Q5 (10 marks): Table 5.1 shows some values of x and the associated values of ( )x f . Table 5.1 x 5 5.0001 5.001 5.01 5.1 f(x) 12.182 494 12.183 103 12.188 587 12.243 559 12.8
- June 2024, AS Numerical Methods, Q6 (11 marks): The equation log x x 5 0 has two roots, a and b. 3 - = You are given that 1 1 1 2 . a x n (a) Use the iterative formula x x x and x g ( ) , where ( g ) 3 2 , to
- June 2023, Numerical Methods, Q3 (6 marks): The diagram shows the graph of y f ( ) x for values of x from 1 to 3.5. = y 2.5 2 1.5 1 0.5 x 0 0.5 1 1.5 2 2.5 3 3.5 The table shows some values of x and the a
- June 2023, Numerical Methods, Q7 (6 marks): d , when x y 7 y x , is given in Table 7.1. The value of a function, f ( ) , and its gradient function, x 2 = = d Table 7.1 d y x f ( )x d x 2 6 .2 8 - (a) Dete
- June 2023, AS Numerical Methods, Q8 (9 marks): Table 8.1 shows some values of x and the associated values of a function ( )x f . Table 8.1 x 1.2 2 2.8 ( )x 0.9638087 1.3258177 1.4439304 f (a) Use the forward
- June 2022, Numerical Methods, Q2 (7 marks): The table shows some values of x and the associated values of y f ( ) x . = x 2.75 3 3.25 f(x) 0.920799 1 1.072858 d y at x (a) Calculate an estimate of d = usi
- June 2022, AS Numerical Methods, Q2 (6 marks): The table shows some values of x and the associated values of y = f (x). x 1.98 1.99 2 2.01 2.02 f (x) 1.10311648 1.10514069 1.10714872 1.10914075 1.11111695 d
- November 2021, Numerical Methods, Q4 (6 marks): The table shows some values of x and the associated values of ( )x f . x 4 4.0001 4.001 4.01 4.1 4 4.0002386 4.0023871 4.0239468 4.2472072 f ( )x (a) Calculate
- November 2021, AS Numerical Methods, Q2 (6 marks): The table shows 2 values of x and the associated values of (fx . The values of x are exact and the ) values of ( ) f x have been rounded to 3 decimal places. x
- November 2021, AS Numerical Methods, Q3 (5 marks): The table shows 3 values of x and the associated values of ( ) f x . x 2 2.05 2.1 f x ( ) 1.386294 1.471572 1.558068 (a) Use the forward difference method to fi
- November 2021, AS Numerical Methods, Q7 (12 marks): x 2 7 The equation ( ) f x 0 where ( ) f x 0 9 . x - - has a root a, such that x 1 .1 87 . = = . a # x 1 + n Sundip is considering using the iterative formula x
- November 2020, Numerical Methods, Q5 (34 marks): You are given that 3 x x 25 + g ( )x . = 2 Fig. 5.1 shows two values of x and the associated values of ( )x g . x 1.45 1.55 g ( )x 1.49468 1.49949 Fig. 5.1 (a)
- November 2020, AS Numerical Methods, Q1 (9 marks): Fig. 1.1 shows the graph of y f ( ) x for 0 x G . 1 = G y 1.2 1.0 0.8 0.6 0.4 0.2 0 x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fig. 1.1 Fig. 1.2 shows three va
- June 2019, Numerical Methods, Q5 (12 marks): Fig. 5 shows spreadsheet output concerning the estimation of the derivative of a function ( )x f at x 2 using the forward difference method. = A B C D 1 h est
- June 2019, AS Numerical Methods, Q2 (8 marks): You are given that ( ) f x log ( 2 x 1 ) . = + 10 (a) Calculate the absolute error when ( ) f 5 is used to approximate ( . f 4 98 . ) [2] (b) Hence find an appr
- June 2018, AS Numerical Methods, Q3 (8 marks): The spreadsheet output in Fig. 3 shows Table 1 and Table 2. A B C D E F G 1 x 2 2.1 2.01 2.001 2.0001 2.00001 2 f(x) 0.64 0.625876972 0.638573473 0.639857204 0.
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