Pearson Edexcel Level 3 GCE
Tuesday 16 June 2026
Afternoon (Time: 1 hour 30 minutes)
Paper
reference 9FM0/3D
Further Mathematics
Advanced
PAPER 3D: Decision Mathematics 1
You must have:
Mathematical Formulae and Statistical Tables (Green), calculator,
Decision Mathematics Answer Book (enclosed)
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).
• Write your answers for this paper in the Decision Mathematics answer book
provided.
• Fill in the boxes at the top of the answer book with your name, centre number
and candidate number.
•• Do not return the question paper with the answer book.
Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
• Answer the questions in the answer book 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
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 8 questions in this question paper. The total mark for this paper is 75.
• – use this asfora guide
The marks each question are shown in brackets
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
P79396A
©2026 Pearson Education Ltd.
P:1/1/1/1/1/
*P79396A*
,1.
61 53 64 41 40 73 42 60 70 65 72 37
(a) Use quick sort to sort the twelve numbers in the list above into ascending order.
You should show the result of each pass and identify your pivots clearly.
(4)
B 40 C
60
61 D
41 42
65
37
A H
70
64 E
53 73
72
G
F
Figure 1
The nodes in the network in Figure 1 represent the power sockets in an office. The
value on each arc represents the cost (in pounds) of connecting a cable between the
corresponding power sockets.
(b) (i) Using Kruskal’s algorithm, find a minimum spanning tree for the network,
clearly showing the order in which you consider and select the arcs.
(ii) State the minimum total cost of connecting the power sockets.
(4)
(Total for Question 1 is 8 marks)
2 P79396A
,2.
120 C
B
140
140 310
190
250
F 120
A I
240
D 330 220
150 110 H
200 320
110
E
170
G
Figure 2
[The total weight of the network is 3120]
Figure 2 represents a network of underground pipes with nine access points, A, B, C,
D, E, F, G, H and I. The number on each arc represents the length, in metres, of the
corresponding pipe.
The pipes are to be inspected by a robot. The robot must travel along each pipe at least
once. The length of the inspection route must be minimised. The inspection route will
start and finish at A.
(a) (i) By considering the pairings of all relevant nodes, find the length of the
robot’s route.
(ii) State the arcs which will need to be repeated.
(5)
It is now decided that the robot can start and finish at different access points. The length
of the route must still be minimised and each pipe must be travelled along at least once.
(b) Determine where the route should start and finish. You must justify your answer.
(2)
(Total for Question 2 is 7 marks)
P79396A 3
Turn over
, 3.
21 18 4 15 20
8
5 23 19 10
The ten distinct numbers in the list above are to be packed into bins of size 36
(a) (i) Explain why it is not possible to pack these numbers into fewer than five bins.
(ii) Use the first‑fit bin packing algorithm to pack the ten numbers into bins of
size 36
(3)
Bin packing algorithms have quadratic order.
A computer takes 1.62 seconds to place 600 items into bins.
(b) Estimate the time required for the computer to place 10 800 items into bins.
(2)
(Total for Question 3 is 5 marks)
4 P79396A
Tuesday 16 June 2026
Afternoon (Time: 1 hour 30 minutes)
Paper
reference 9FM0/3D
Further Mathematics
Advanced
PAPER 3D: Decision Mathematics 1
You must have:
Mathematical Formulae and Statistical Tables (Green), calculator,
Decision Mathematics Answer Book (enclosed)
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).
• Write your answers for this paper in the Decision Mathematics answer book
provided.
• Fill in the boxes at the top of the answer book with your name, centre number
and candidate number.
•• Do not return the question paper with the answer book.
Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
• Answer the questions in the answer book 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
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 8 questions in this question paper. The total mark for this paper is 75.
• – use this asfora guide
The marks each question are shown in brackets
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
P79396A
©2026 Pearson Education Ltd.
P:1/1/1/1/1/
*P79396A*
,1.
61 53 64 41 40 73 42 60 70 65 72 37
(a) Use quick sort to sort the twelve numbers in the list above into ascending order.
You should show the result of each pass and identify your pivots clearly.
(4)
B 40 C
60
61 D
41 42
65
37
A H
70
64 E
53 73
72
G
F
Figure 1
The nodes in the network in Figure 1 represent the power sockets in an office. The
value on each arc represents the cost (in pounds) of connecting a cable between the
corresponding power sockets.
(b) (i) Using Kruskal’s algorithm, find a minimum spanning tree for the network,
clearly showing the order in which you consider and select the arcs.
(ii) State the minimum total cost of connecting the power sockets.
(4)
(Total for Question 1 is 8 marks)
2 P79396A
,2.
120 C
B
140
140 310
190
250
F 120
A I
240
D 330 220
150 110 H
200 320
110
E
170
G
Figure 2
[The total weight of the network is 3120]
Figure 2 represents a network of underground pipes with nine access points, A, B, C,
D, E, F, G, H and I. The number on each arc represents the length, in metres, of the
corresponding pipe.
The pipes are to be inspected by a robot. The robot must travel along each pipe at least
once. The length of the inspection route must be minimised. The inspection route will
start and finish at A.
(a) (i) By considering the pairings of all relevant nodes, find the length of the
robot’s route.
(ii) State the arcs which will need to be repeated.
(5)
It is now decided that the robot can start and finish at different access points. The length
of the route must still be minimised and each pipe must be travelled along at least once.
(b) Determine where the route should start and finish. You must justify your answer.
(2)
(Total for Question 2 is 7 marks)
P79396A 3
Turn over
, 3.
21 18 4 15 20
8
5 23 19 10
The ten distinct numbers in the list above are to be packed into bins of size 36
(a) (i) Explain why it is not possible to pack these numbers into fewer than five bins.
(ii) Use the first‑fit bin packing algorithm to pack the ten numbers into bins of
size 36
(3)
Bin packing algorithms have quadratic order.
A computer takes 1.62 seconds to place 600 items into bins.
(b) Estimate the time required for the computer to place 10 800 items into bins.
(2)
(Total for Question 3 is 5 marks)
4 P79396A
