Pearson Edexcel Level 3 GCE
reference9FM0/3D
Paper
Time 1 hour 30 minutes
Further Mathematics
Advanced
PAPER 3D: Decision Mathematics 1
You must have:
Mathematical Formulae and Statistical Tables (Green),
calculator, Decision Mathematics Answer Book (enclosed)
A-Level Pearson Edexcel Level 3 GCE
AL Further Mathematics (9FM0) advanced
Paper 3D Decision Mathematics 1
summer Exam Question paper
(AUTHENTIC MARKING SCHEME)
1/1/1/1/ *P72094A*
P72094A
,1. A gardener needs the following lengths of string. All lengths are in metres.
4.3 6.1 5.1 4.7 2.5 5.9 3.4 1.7 2.1 0.4 1.3
She cuts the lengths from balls of string. Each ball contains 10 m of string.
(a) Calculate a lower bound for the number of balls of string the
gardener needs. You must make your method clear.
(2)
(b)Use the first-fit bin packing algorithm to determine how the
lengths could be cut from the balls of string.
(3)
(Total for Question 1 is 5 marks)
2 P72094A
, 2.
B 23
8 4 H
16
9 3 E 33
A 18 23
C 31 6
17
10 J K
F
14 10 10
14 25
D 25 G
Figure 1
[The total weight of the network is 299]
Figure 1 represents a network of cycle tracks between 10 landmarks, A, B, C, D, E, F,
G, H, J and K. The number on each edge represents the length, in kilometres, of the
corresponding track.
One day, Blanche wishes to cycle from A to K. She wishes to minimise the distance
she travels.
(a) (i) Use Dijkstra’s algorithm to find the shortest path from A to K.
(ii) State the length of the shortest path from A to K.
(6)
The cycle tracks between the landmarks now need to be inspected. Blanche must travel
along each track at least once. She wishes to minimise the length of her inspection
route. Blanche will start her inspection route at D and finish at E.
(b) (i) State the edges that will need to be traversed twice.
(ii) Find the length of Blanche’s route.
(2)
It is now decided to start the inspection route at A and finish at K. Blanche must
minimise the length of her route and travel along each track at least once.
(c) By considering the pairings of all relevant nodes, find the length of Blanche’s new
route. You must make your method and working clear.
(5)
(Total for Question 2 is 13 marks)
P72094A 3
Turn over
, 3. The initial distance matrix (Table 1) shows the lengths, in metres, of
the corridors connecting six classrooms, A, B, C, D, E and F, in a
school. For safety reasons, some of the corridors are one-way only.
A B C D E F
A – 12 32 24 29 11
B 12 – 17 8 ∞ ∞
C 32 17 – 4 12 ∞
D 24 ∞ 4 – ∞ 13
E ∞ ∞ 12 18 – 12
F 11 ∞ ∞ 13 12 –
Table 1
(a) By adding the arcs from vertex A, along with their weights,
complete the drawing of this network on Diagram 1 in the answer
book.
(2)
Floyd’s algorithm is to be used to find the complete network of
shortest distances between the six classrooms.
The distance matrix after two iterations of Floyd’s algorithm is shown in Table 2.
A B C D E F
A – 12 29 20 29 11
B 12 – 17 8 41 23
C 29 17 – 4 12 40
D 24 36 4 – 53 13
E ∞ ∞ 12 18 – 12
F 11 23 40 13 12 –
Table 2
(b)Perform the next two iterations of Floyd’s algorithm that follow
from Table 2. You should show the distance matrix after each
iteration.
(4)
4 P72094A
reference9FM0/3D
Paper
Time 1 hour 30 minutes
Further Mathematics
Advanced
PAPER 3D: Decision Mathematics 1
You must have:
Mathematical Formulae and Statistical Tables (Green),
calculator, Decision Mathematics Answer Book (enclosed)
A-Level Pearson Edexcel Level 3 GCE
AL Further Mathematics (9FM0) advanced
Paper 3D Decision Mathematics 1
summer Exam Question paper
(AUTHENTIC MARKING SCHEME)
1/1/1/1/ *P72094A*
P72094A
,1. A gardener needs the following lengths of string. All lengths are in metres.
4.3 6.1 5.1 4.7 2.5 5.9 3.4 1.7 2.1 0.4 1.3
She cuts the lengths from balls of string. Each ball contains 10 m of string.
(a) Calculate a lower bound for the number of balls of string the
gardener needs. You must make your method clear.
(2)
(b)Use the first-fit bin packing algorithm to determine how the
lengths could be cut from the balls of string.
(3)
(Total for Question 1 is 5 marks)
2 P72094A
, 2.
B 23
8 4 H
16
9 3 E 33
A 18 23
C 31 6
17
10 J K
F
14 10 10
14 25
D 25 G
Figure 1
[The total weight of the network is 299]
Figure 1 represents a network of cycle tracks between 10 landmarks, A, B, C, D, E, F,
G, H, J and K. The number on each edge represents the length, in kilometres, of the
corresponding track.
One day, Blanche wishes to cycle from A to K. She wishes to minimise the distance
she travels.
(a) (i) Use Dijkstra’s algorithm to find the shortest path from A to K.
(ii) State the length of the shortest path from A to K.
(6)
The cycle tracks between the landmarks now need to be inspected. Blanche must travel
along each track at least once. She wishes to minimise the length of her inspection
route. Blanche will start her inspection route at D and finish at E.
(b) (i) State the edges that will need to be traversed twice.
(ii) Find the length of Blanche’s route.
(2)
It is now decided to start the inspection route at A and finish at K. Blanche must
minimise the length of her route and travel along each track at least once.
(c) By considering the pairings of all relevant nodes, find the length of Blanche’s new
route. You must make your method and working clear.
(5)
(Total for Question 2 is 13 marks)
P72094A 3
Turn over
, 3. The initial distance matrix (Table 1) shows the lengths, in metres, of
the corridors connecting six classrooms, A, B, C, D, E and F, in a
school. For safety reasons, some of the corridors are one-way only.
A B C D E F
A – 12 32 24 29 11
B 12 – 17 8 ∞ ∞
C 32 17 – 4 12 ∞
D 24 ∞ 4 – ∞ 13
E ∞ ∞ 12 18 – 12
F 11 ∞ ∞ 13 12 –
Table 1
(a) By adding the arcs from vertex A, along with their weights,
complete the drawing of this network on Diagram 1 in the answer
book.
(2)
Floyd’s algorithm is to be used to find the complete network of
shortest distances between the six classrooms.
The distance matrix after two iterations of Floyd’s algorithm is shown in Table 2.
A B C D E F
A – 12 29 20 29 11
B 12 – 17 8 41 23
C 29 17 – 4 12 40
D 24 36 4 – 53 13
E ∞ ∞ 12 18 – 12
F 11 23 40 13 12 –
Table 2
(b)Perform the next two iterations of Floyd’s algorithm that follow
from Table 2. You should show the distance matrix after each
iteration.
(4)
4 P72094A
