Approximating functions: OCR MEI A‑Level Further Maths questions

OCR MEI A-Level Further Maths past-paper questions on 6.4 Approximating functions, 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.

All 18 questions on Approximating functions, as a list

June 2025, Numerical Methods, Q8 (10 marks): Following an injury an athlete returns to training in preparation for a regional competition. At the end of each week the athlete’s trainer records the time, t
June 2025, AS Numerical Methods, Q2 (4 marks): The table gives three values of x and the associated values of y. x 2 3 1 - y 0.18 0.45 .3 39 - Use Lagrange’s form of the interpolating polynomial to construct
June 2025, AS Numerical Methods, Q7 (10 marks): A student makes a cup of tea and investigates how long it takes to reach room temperature. The student places the cup of tea on a table in the kitchen and recor
June 2024, Numerical Methods, Q4 (10 marks): Between 1946 and 2012 the mean monthly maximum temperature of the water surface of a lake in northern England has been recorded by environmental scientists. Som
June 2024, AS Numerical Methods, Q1 (3 marks): The difference table shows some values of x and the associated values of y. x y y 2 3 y y D D D 0 0.8 1 0.7 2 0.1 3 11.3 4 70.5 5 250.6 (a) Complete the copy of
June 2024, AS Numerical Methods, Q3 (8 marks): Following an injury a professional footballer has to undergo a rehabilitation programme before she can resume playing. As part of the programme she is required
June 2023, Numerical Methods, Q2 (8 marks): A car tyre has a slow puncture. Initially the tyre is inflated to a pressure of 34.5 psi. The pressure is checked after 3 days and then again after 5 days. The
June 2023, AS Numerical Methods, Q2 (4 marks): The table gives three values of x and the associated values of y. x 3 5 8 y 9.26 19.3 37.96 Use Lagrange’s method to construct the interpolating polynomial of d
June 2023, AS Numerical Methods, Q6 (9 marks): After taking his pet dog to the vet for a check-up, a dog owner is advised that the dog is too heavy and must therefore go on a special diet. The owner records
June 2022, Numerical Methods, Q7 (14 marks): Sam decided to go on a high-protein diet. Sam’s mass in kg, M, after t days of following the diet is recorded in Fig. 7.1. t 0 10 20 30 M 88.3 80.05 78.7 78.85
June 2022, AS Numerical Methods, Q7 (13 marks): Azmi placed a container of liquid in a refrigerator unit in a laboratory. Initially the temperature of the liquid was 22 °C. Azmi recorded the temperature, y °C
November 2021, Numerical Methods, Q2 (6 marks): The table shows some values of x and the associated values of ( )x f . x 1 2 3 4 5 f(x) ‒0.65 ‒0.35 1.77 5.71 11.47 (a) Complete the difference table in the Pri
November 2021, AS Numerical Methods, Q1 (5 marks): The table shows 3 values of x and the associated values of ( ) f x . x -1 1 2 f x ( ) 0.7 -3.56 -4.94 (a) Use Lagrange’s method to construct the interpolating p
November 2020, Numerical Methods, Q2 (5 marks): Fig. 2 shows 3 values of x and the associated values of a function, ( )x f . x 1 2 5 5 16.6 76.6 f ( )x Fig. 2 Find a polynomial p ( )x of degree 2 to approxima
November 2020, AS Numerical Methods, Q3 (7 marks): Fig. 3 shows three values of x and the associated values of ( )x f . x 1 2 5 2.53 7.71 47.37 f ( )x Fig. 3 (a) Use Lagrange’s method to construct the interpolat
June 2019, Numerical Methods, Q3 (11 marks): In the first week of an outbreak of influenza, 9 patients were diagnosed with the virus at a medical practice in Pencaster. Records were kept of y, the total nu
June 2019, AS Numerical Methods, Q7 (18 marks): 8E+17 8E+17 1.0737E+179 1.0737E+179 0 #NUM! #NUM! Fig. 5 The formulae in cells E2 and F2 are =D2 - C2 and =C2*D2 respectively. Equivalent formulae are entered i
June 2018, AS Numerical Methods, Q5 (13 marks): The value of shares in Sunfield plc was £2.21 per unit on the first day it came under new management. One week later the value of one unit of shares was £4.00 a

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