Exam (elaborations)
AS & A Level FURTHER MATHEMATICS 9231/23 Paper 2 Further Pure Mathematics 2 May/June 2023 AUTHENTIC MARKING SCHEME ATTAHED
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FURTHER MATHEMATICS
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FURTHER MATHEMATICS
AS & A Level FURTHER MATHEMATICS 9231/23 Paper 2 Further Pure Mathematics 2 May/June 2023 AUTHENTIC MARKING SCHEME ATTAHED
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Cambridge International AS & A Level
* 1 7 9 3 6 9 4 5 4 1 *
FURTHER MATHEMATICS 9231/23
Paper 2 Further Pure Mathematics 2 May/June 2023
2 hours
You must answer on the question paper.
You will need: List of formulae (MF19)
INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● If additional space is needed, you should use the lined page at the end of this booklet; the question
number or numbers must be clearly shown.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
INFORMATION
● The total mark for this paper is 75.
● The number of marks for each question or part question is shown in brackets [ ].
This document has 16 pages. Any blank pages are indicated.
DC (RW/CB) 311419/2
© UCLES 2023 [Turn over
, 2
BLANK PAGE
© UCLES 2023 9231/23/M/J/23
, 3
1 (a) Find the Maclaurin series for sin -1 x up to and including the term in x 3 . [5]
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1
1
(b) Deduce an approximation to y 0
5
1 - u2
du , giving your answer as a fraction. [1]
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© UCLES 2023 9231/23/M/J/23 [Turn over
, 4
2 The variables x and y are related by the differential equation
d2x dx
+ 5 + x = t 2 + 10t + 13.
6
dt 2 dt
(a) Find the general solution for x in terms of t. [6]
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(b) State an approximate solution for large positive values of t. [1]
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© UCLES 2023 9231/23/M/J/23