Cambridge International AS & A Level
CANDIDATE
NAME
CENTRE CANDIDATE
NUMBER NUMBER
*2330973605*
MATHEMATICS 9709/12
Paper 1 Pure Mathematics 1 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_12/2R
© UCLES 2023 [Turn over
, 2
dy 4
1 The equation of a curve is such that = for x > 3. The curve passes through the point
dx !x − 3"3
!4, 5".
Find the equation of the curve. [3]
y 1 d
................................................................................................................................................................
43
................................................................................................................................................................
4 n 353 oh
................................................................................................................................................................
................................................................................................................................................................
g
III
................................................................................................................................................................
................................................................................................................................................................
7
to
1
y 4
................................................................................................................................................................
g
................................................................................................................................................................
5 I C
................................................................................................................................................................
................................................................................................................................................................
7
................................................................................................................................................................
................................................................................................................................................................
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© UCLES 2023 9709/12/M/J/23
, 3
2 The coefficient of x4 in the expansion of !x + a"6 is p and the coefficient of x2 in the expansion of
!ax + 3"4 is q. It is given that p + q = 276.
Find the possible values of the constant a. [4]
................................................................................................................................................................
atr s Cy a n 15A n
................................................................................................................................................................
................................................................................................................................................................
tan Cz 3 an 54dm
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
1592 5492 276
................................................................................................................................................................
a 4
................................................................................................................................................................
a 12
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© UCLES 2023 9709/12/M/J/23 [Turn over
CANDIDATE
NAME
CENTRE CANDIDATE
NUMBER NUMBER
*2330973605*
MATHEMATICS 9709/12
Paper 1 Pure Mathematics 1 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_12/2R
© UCLES 2023 [Turn over
, 2
dy 4
1 The equation of a curve is such that = for x > 3. The curve passes through the point
dx !x − 3"3
!4, 5".
Find the equation of the curve. [3]
y 1 d
................................................................................................................................................................
43
................................................................................................................................................................
4 n 353 oh
................................................................................................................................................................
................................................................................................................................................................
g
III
................................................................................................................................................................
................................................................................................................................................................
7
to
1
y 4
................................................................................................................................................................
g
................................................................................................................................................................
5 I C
................................................................................................................................................................
................................................................................................................................................................
7
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
© UCLES 2023 9709/12/M/J/23
, 3
2 The coefficient of x4 in the expansion of !x + a"6 is p and the coefficient of x2 in the expansion of
!ax + 3"4 is q. It is given that p + q = 276.
Find the possible values of the constant a. [4]
................................................................................................................................................................
atr s Cy a n 15A n
................................................................................................................................................................
................................................................................................................................................................
tan Cz 3 an 54dm
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
1592 5492 276
................................................................................................................................................................
a 4
................................................................................................................................................................
a 12
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
© UCLES 2023 9709/12/M/J/23 [Turn over
