Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
reference 9FM0/3A
Paper
Time 1 hour 30 minutes
Further Mathematics
Advanced
PAPER 3A: Further Pure Mathematics 1
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
A-LEVEL Pearson Edexcel LEVEL 3
GCE
In A Level Further Mathematics
(9FM0)
Paper 3A Further Pure
Mathematics 1 Exam Question
paper
(AUTHENTIC MARKING SCHEME
ATTACHED)
Q:1/1/1/1/ *P65497A0132*
P65497A
©2022 Pearson Education Ltd.
, x2 y2
1. An ellipse has equation 1 and eccentricity e 1
16 4
A hyperbola has equation x2 y2 1 and eccentricity e 2
a2 b2
Given that e 1 × e 2 = 1
(a) show that a 2 = 3b 2
(4)
Given also that the coordinates of the foci of the ellipse are the same as the coordinates
of the foci of the hyperbola,
(b) determine the equation of the hyperbola.
(3)
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2
*P65497A0232*
,Question 1 continued
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(Total for Question 1 is 7 marks)
3
*P65497A0332* Turn over
, 2. During 2029, the number of hours of daylight per day in London, H, is modelled by
the equation
x – 4 cos x + 11.5
H = 0.3 sin 0 x < 365
60 60
where x is the number of days after 1st January 2029 and the angle is in radians.
(a) Show that, according to the model, the number of hours of daylight in London on
the 31st January 2029 will be 8.13 to 3 significant figures.
(1)
x
(b) Use the substitution t tan to show that H can be written as
120
H at 2 bt c
2
1 t
where a, b and c are constants to be determined.
(2)
(c) Hence determine, according to the model, the date of the first day of 2029 when
there will be at least 12 hours of daylight in London.
(4)
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4
*P65497A0432*
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
reference 9FM0/3A
Paper
Time 1 hour 30 minutes
Further Mathematics
Advanced
PAPER 3A: Further Pure Mathematics 1
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
A-LEVEL Pearson Edexcel LEVEL 3
GCE
In A Level Further Mathematics
(9FM0)
Paper 3A Further Pure
Mathematics 1 Exam Question
paper
(AUTHENTIC MARKING SCHEME
ATTACHED)
Q:1/1/1/1/ *P65497A0132*
P65497A
©2022 Pearson Education Ltd.
, x2 y2
1. An ellipse has equation 1 and eccentricity e 1
16 4
A hyperbola has equation x2 y2 1 and eccentricity e 2
a2 b2
Given that e 1 × e 2 = 1
(a) show that a 2 = 3b 2
(4)
Given also that the coordinates of the foci of the ellipse are the same as the coordinates
of the foci of the hyperbola,
(b) determine the equation of the hyperbola.
(3)
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2
*P65497A0232*
,Question 1 continued
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(Total for Question 1 is 7 marks)
3
*P65497A0332* Turn over
, 2. During 2029, the number of hours of daylight per day in London, H, is modelled by
the equation
x – 4 cos x + 11.5
H = 0.3 sin 0 x < 365
60 60
where x is the number of days after 1st January 2029 and the angle is in radians.
(a) Show that, according to the model, the number of hours of daylight in London on
the 31st January 2029 will be 8.13 to 3 significant figures.
(1)
x
(b) Use the substitution t tan to show that H can be written as
120
H at 2 bt c
2
1 t
where a, b and c are constants to be determined.
(2)
(c) Hence determine, according to the model, the date of the first day of 2029 when
there will be at least 12 hours of daylight in London.
(4)
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4
*P65497A0432*
