Ocr 2024
OXFORD CAMBRDGE
AND RSA 2024
[Type the document subtitle]
OCR 2024
2024
[Type the company address]
, Oxford Cambridge and RSA
Friday 14 June 2024 – AfternoonAS Level
Further Mathematics B (MEI) Y414/01 Numerical
Methods
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(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 AnswerBooklet. 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 begiven
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 8 pages.
ADVICE
• Read each question carefully before you start your answer.
OCR is an exempt
,Charity
Turn over
, 2
1 The difference table shows some values of x and the associated values of y.
x y Dy D2 y D3 y
0 0.8
1 0.7
2 0.1
3 11.3
4 70.5
5 250.6
(a) Complete the copy of the difference table in the Printed Answer Booklet. [2]
(b) Explain whether a cubic polynomial would be suitable to model the relationship between
y and x. [1]
2 A spreadsheet is used to find the approximate value of r +e. The output is shown in the table.
A B
1 r 3.141 593
2 e 2.718 282
3 r +e 5.859 874
The formula in cell B1 is = PI() .
The formula in cell B2 is = EXP(1)
and the formula in cell B3 is = BI +B2 .
(a) Show that the approximations to r and e displayed in cells B1 and B2 respectively have both
been rounded. [1]
(b) Find the relative error when 3.141 593 is used to approximate r. [2]
© OCR 2024 Y414/01 Jun24
OXFORD CAMBRDGE
AND RSA 2024
[Type the document subtitle]
OCR 2024
2024
[Type the company address]
, Oxford Cambridge and RSA
Friday 14 June 2024 – AfternoonAS Level
Further Mathematics B (MEI) Y414/01 Numerical
Methods
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(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 AnswerBooklet. 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 begiven
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 8 pages.
ADVICE
• Read each question carefully before you start your answer.
OCR is an exempt
,Charity
Turn over
, 2
1 The difference table shows some values of x and the associated values of y.
x y Dy D2 y D3 y
0 0.8
1 0.7
2 0.1
3 11.3
4 70.5
5 250.6
(a) Complete the copy of the difference table in the Printed Answer Booklet. [2]
(b) Explain whether a cubic polynomial would be suitable to model the relationship between
y and x. [1]
2 A spreadsheet is used to find the approximate value of r +e. The output is shown in the table.
A B
1 r 3.141 593
2 e 2.718 282
3 r +e 5.859 874
The formula in cell B1 is = PI() .
The formula in cell B2 is = EXP(1)
and the formula in cell B3 is = BI +B2 .
(a) Show that the approximations to r and e displayed in cells B1 and B2 respectively have both
been rounded. [1]
(b) Find the relative error when 3.141 593 is used to approximate r. [2]
© OCR 2024 Y414/01 Jun24
