Cambridge International AS & A Level
CANDIDATE
NAME
CENTRE CANDIDATE
NUMBER NUMBER
*2968750175*
MATHEMATICS 9709/31
Paper 3 Pure Mathematics 3 May/June 2023
1 hour 50 minutes
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 20 pages. Any blank pages are indicated.
JC23 06_9709_31/2R
© UCLES 2023 [Turn over
, 2
1 Solve the equation
3e2x − 4e−2x = 5.
Give the answer correct to 3 decimal places. [3]
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© UCLES 2023 9709/31/M/J/23
, 3
2 (a) Sketch the graph of y = !2x + 3!. [1]
(b) Solve the inequality 3x + 8 > !2x + 3!. [3]
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© UCLES 2023 9709/31/M/J/23 [Turn over
, 4
$
3 Find the coefficient of x3 in the binomial expansion of "3 + x# 1 + 4x. [4]
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© UCLES 2023 9709/31/M/J/23
CANDIDATE
NAME
CENTRE CANDIDATE
NUMBER NUMBER
*2968750175*
MATHEMATICS 9709/31
Paper 3 Pure Mathematics 3 May/June 2023
1 hour 50 minutes
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 20 pages. Any blank pages are indicated.
JC23 06_9709_31/2R
© UCLES 2023 [Turn over
, 2
1 Solve the equation
3e2x − 4e−2x = 5.
Give the answer correct to 3 decimal places. [3]
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© UCLES 2023 9709/31/M/J/23
, 3
2 (a) Sketch the graph of y = !2x + 3!. [1]
(b) Solve the inequality 3x + 8 > !2x + 3!. [3]
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© UCLES 2023 9709/31/M/J/23 [Turn over
, 4
$
3 Find the coefficient of x3 in the binomial expansion of "3 + x# 1 + 4x. [4]
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© UCLES 2023 9709/31/M/J/23
