Oxford Cambridge and RSA
Examinations GCE Further
Mathematics B MEIY434/01:
Numerical methods
A Level
Question paper with marking scheme
(merged)
, Oxford Cambridge and RSA
Thursday 22 June 2023 – Afternoon
A Level Further Mathematics B (MEI)
Y434/01 Numerical Methods
Time allowed: 1 hour 15 minutes
* 9 9 7 2 7 9 8 3 1 2 *
You must have:
• the Printed Answer Booklet
QP
• the Formulae Booklet for Further Mathematics B
(MEI)
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined pages at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2023 [A/508/5598] OCR is an exempt Charity
DC (PQ/JG) 326282/6 Turn over
, 2
1 You are given that (x1, y1) = (0.9, 2.3) and (x2, y2) = (1.1, 2.7) .
The values of x1 and x2 have been rounded to 1 decimal place.
(a) Determine the range of possible values of x2 - x 1 . [2]
The values of y 1 and y2 have been chopped to 1 decimal place.
(b) Determine the range of possible values of y 2 - y 1 . [2]
y2 - y1
You are given that m = .
x2 - x1
(c) Determine the range of possible values of m. [2]
(d) Explain why your answer to part (c) is much larger than your answer to part (a) and your
answer to part (b). [1]
2 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 time t in days and the pressure, P psi, are
shown in the table below. You are given that the pressure in a car tyre is measured in pounds per
square inch (psi).
t 0 3 5
P 34.5 29.4 27.0
The owner of the car believes the relationship between P and t may be modelled by a polynomial.
(a) Explain why it is not possible to use Newton’s forward difference interpolation method for
these data. [1]
(b) Use Lagrange’s form of the interpolating polynomial to find an interpolating polynomial of
degree 2 for these data. [4]
The car owner uses the polynomial found in part (b) to model the relationship between P and t.
Subsequently it is found that when t = 6 , P = 26.0 and when t = 10 , P = 24.4 .
(c) Determine whether the owner’s model is a good fit for these data. [2]
(d) Explain why the model would not be suitable in the long term. [1]
© OCR 2023 Y434/01 Jun23
, 3
3 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 associated values of y.
x 1.5 2 2.5
y 1.682137 2.094395 2.318559
dy
(a) Use the forward difference method to calculate an approximation to at x = 2 . [2]
dx
dy
(b) Use the central difference method to calculate an approximation to at x = 2 . [2]
dx
(c) On the copy of the diagram in the Printed Answer Booklet, show how the central difference
dy
method gives the approximation to at x = 2 which was found in part (b). [1]
dx
(d) Explain whether your answer to part (a) or your answer to part (b) is likely to give a better
dy
approximation to at x = 2 . [1]
dx
© OCR 2023 Y434/01 Jun23 Turn over
Examinations GCE Further
Mathematics B MEIY434/01:
Numerical methods
A Level
Question paper with marking scheme
(merged)
, Oxford Cambridge and RSA
Thursday 22 June 2023 – Afternoon
A Level Further Mathematics B (MEI)
Y434/01 Numerical Methods
Time allowed: 1 hour 15 minutes
* 9 9 7 2 7 9 8 3 1 2 *
You must have:
• the Printed Answer Booklet
QP
• the Formulae Booklet for Further Mathematics B
(MEI)
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined pages at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2023 [A/508/5598] OCR is an exempt Charity
DC (PQ/JG) 326282/6 Turn over
, 2
1 You are given that (x1, y1) = (0.9, 2.3) and (x2, y2) = (1.1, 2.7) .
The values of x1 and x2 have been rounded to 1 decimal place.
(a) Determine the range of possible values of x2 - x 1 . [2]
The values of y 1 and y2 have been chopped to 1 decimal place.
(b) Determine the range of possible values of y 2 - y 1 . [2]
y2 - y1
You are given that m = .
x2 - x1
(c) Determine the range of possible values of m. [2]
(d) Explain why your answer to part (c) is much larger than your answer to part (a) and your
answer to part (b). [1]
2 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 time t in days and the pressure, P psi, are
shown in the table below. You are given that the pressure in a car tyre is measured in pounds per
square inch (psi).
t 0 3 5
P 34.5 29.4 27.0
The owner of the car believes the relationship between P and t may be modelled by a polynomial.
(a) Explain why it is not possible to use Newton’s forward difference interpolation method for
these data. [1]
(b) Use Lagrange’s form of the interpolating polynomial to find an interpolating polynomial of
degree 2 for these data. [4]
The car owner uses the polynomial found in part (b) to model the relationship between P and t.
Subsequently it is found that when t = 6 , P = 26.0 and when t = 10 , P = 24.4 .
(c) Determine whether the owner’s model is a good fit for these data. [2]
(d) Explain why the model would not be suitable in the long term. [1]
© OCR 2023 Y434/01 Jun23
, 3
3 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 associated values of y.
x 1.5 2 2.5
y 1.682137 2.094395 2.318559
dy
(a) Use the forward difference method to calculate an approximation to at x = 2 . [2]
dx
dy
(b) Use the central difference method to calculate an approximation to at x = 2 . [2]
dx
(c) On the copy of the diagram in the Printed Answer Booklet, show how the central difference
dy
method gives the approximation to at x = 2 which was found in part (b). [1]
dx
(d) Explain whether your answer to part (a) or your answer to part (b) is likely to give a better
dy
approximation to at x = 2 . [1]
dx
© OCR 2023 Y434/01 Jun23 Turn over
