Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 19 June 2026
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/3A
Further Mathematics
Advanced
PAPER 3A: Further Pure Mathematics 1
You must have: Total Marks
Mathematical Formulae and Statistics Tables (Green), calculator
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
Instructions
•• Use black ink or ball-point pen.
•
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the boxes at the top of this page with your name,
••
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are clearly labelled.
Answer the questions in the spaces provided
•
– there may be more space than you need.
You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
• Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
There are 9 questions in this question paper. The total mark for this paper is 75.
The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
•
Try to answer every question.
Check your answers if you have time at the end.
Turn over
P74079A
©2026 Pearson Education Ltd.
P:1/1/1/1/1/1/1/1/
*P74079A0132*
,1.
y
H
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
P
O x
Q
l
Figure 1
Figure 1 shows a rectangular hyperbola H with parametric equations
t 1
x y t
0
6 6t
The line l with equation 3 x 15 y 2
0 intersects H at the point P and at the point Q,
as shown in Figure 1.
(a) Show that the points of intersection of l and H satisfy the equation
t 2 4t 5
0
(2)
(b) Hence, or otherwise, determine the coordinates of P and Q.
(4)
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2
*P74079A0232*
, Question 1 continued
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(Total for Question 1 is 6 marks)
3
*P74079A0332* Turn over
, 2. The line l has vector equation
2
4
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
r
1
3 0
3
2
The plane Π contains the line l and the point A (3, 2, 1)
(a) Determine a vector equation for Π, giving your answer in the form r a λb μc
where λ and μ are scalar parameters.
(3)
(b) Determine a vector equation for the line of intersection of Π with the x-y plane.
Give your answer in the form r = p + tq where t is a scalar parameter.
(3)
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4
*P74079A0432*
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 19 June 2026
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/3A
Further Mathematics
Advanced
PAPER 3A: Further Pure Mathematics 1
You must have: Total Marks
Mathematical Formulae and Statistics Tables (Green), calculator
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
Instructions
•• Use black ink or ball-point pen.
•
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the boxes at the top of this page with your name,
••
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are clearly labelled.
Answer the questions in the spaces provided
•
– there may be more space than you need.
You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
• Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
There are 9 questions in this question paper. The total mark for this paper is 75.
The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
•
Try to answer every question.
Check your answers if you have time at the end.
Turn over
P74079A
©2026 Pearson Education Ltd.
P:1/1/1/1/1/1/1/1/
*P74079A0132*
,1.
y
H
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
P
O x
Q
l
Figure 1
Figure 1 shows a rectangular hyperbola H with parametric equations
t 1
x y t
0
6 6t
The line l with equation 3 x 15 y 2
0 intersects H at the point P and at the point Q,
as shown in Figure 1.
(a) Show that the points of intersection of l and H satisfy the equation
t 2 4t 5
0
(2)
(b) Hence, or otherwise, determine the coordinates of P and Q.
(4)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P74079A0232*
, Question 1 continued
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DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
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(Total for Question 1 is 6 marks)
3
*P74079A0332* Turn over
, 2. The line l has vector equation
2
4
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
r
1
3 0
3
2
The plane Π contains the line l and the point A (3, 2, 1)
(a) Determine a vector equation for Π, giving your answer in the form r a λb μc
where λ and μ are scalar parameters.
(3)
(b) Determine a vector equation for the line of intersection of Π with the x-y plane.
Give your answer in the form r = p + tq where t is a scalar parameter.
(3)
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4
*P74079A0432*
