Pearson Edexcel International Advanced Level
Wednesday 10 January 2024
Morning (Time: 1 hour 30 minutes)
Paper
reference WDM11/01
Mathematics
International Advanced Subsidiary/Advanced Level
Decision Mathematics D1
You must have:
Decision Mathematics Answer Book (enclosed), calculator
Candidates may use any calculator allowed 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).
Coloured pencils and highlighter pens must not be used.
• Fill in the boxes on 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 D1 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
•• There are 7 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.
If you change your mind about an answer, cross it out and put your new answer and
any working underneath.
, Write your answers in the D1 answer book for this paper.
1.
D(5)
E(2)
L(12)
A(4)
B(3) G(5) J(6)
C(7) F(6)
H(6) K(5)
I(6)
Figure 1
A project is modelled by the activity network shown in Figure 1. The activities are
represented by the arcs. The number in brackets on each arc gives the time, in hours, to
complete the corresponding activity. Each activity requires one worker. The project is to
be completed in the shortest possible time using as few workers as possible.
(a) Complete Diagram 1 in the answer book to show the early event times and the late
event times.
(4)
(b) Calculate the total float for activity D. You must make the numbers used in your
calculation clear.
(1)
(c) Calculate a lower bound for the minimum number of workers required to complete
the project in the shortest possible time. You must show your working.
(2)
(d) Draw a cascade chart for this project on Grid 1 in the answer book.
(4)
(e) Use your cascade chart to determine the minimum number of workers needed to
complete the project in the shortest possible time. You must make specific reference
to time and activities. (You do not need to provide a schedule of the activities.)
(2)
(Total for Question 1 is 13 marks)
2 P73481A
,2.
A B C D E F G H
A – 34 29 35 28 30 37 38
B 34 – 32 28 39 40 32 39
C 29 32 – 27 33 39 34 31
D 35 28 27 – 35 38 41 36
E 28 39 33 35 – 36 33 40
F 30 40 39 38 36 – 34 39
G 37 32 34 41 33 34 – 35
H 38 39 31 36 40 39 35 –
Table 1
Table 1 represents a network that shows the travel times, in minutes, between eight
towns, A, B, C, D, E, F, G and H.
(a) Use Prim’s algorithm, starting at A, to find the minimum spanning tree for this
network. You must clearly state the order in which you select the edges of your tree.
(3)
(b) State the weight of the minimum spanning tree.
(1)
A B C D E F G H
J 33 37 41 35 x 40 28 42
Table 2
Table 2 shows the travel times, in minutes, between town J and towns A, B, C, D, E, F,
G and H.
The journey time between towns E and J is x minutes where x > 28
A salesperson needs to visit all of the nine towns, starting and finishing at J.
The salesperson wishes to minimise the total time spent travelling.
(c) Starting at J, use the nearest neighbour algorithm to find an upper bound for
the duration of the salesperson’s route. Write down the route that gives this
upper bound.
(2)
Using the nearest neighbour algorithm, starting at E, an upper bound of 291 minutes for
the salesperson’s route was found.
(d) State the best upper bound that can be obtained by using this information and your
answer to (c). Give the reason for your answer.
(1)
Starting by deleting J and all of its arcs, a lower bound of 264 minutes for the duration
of the salesperson’s route was found.
(e) Determine the value of x. You must make your method and working clear.
(3)
(Total for Question 2 is 10 marks)
P73481A 3
Turn over
, 3.
B 28 E
47
H
17 8 38
20 5
28 C 25 F 40
A J
10 12
39 55 11 18
20
D 37 G
Figure 2
[The total weight of the network is 458]
Figure 2 represents a network of roads between nine towns, A, B, C, D, E, F, G, H and J.
The number on each edge represents the length, in kilometres, of the corresponding road.
(a) (i) Use Dijkstra’s algorithm to find the shortest path from A to J.
(ii) State the length of the shortest path from A to J.
(6)
The roads between the towns must be inspected. Claude must travel along each road at
least once. Claude will start the inspection route at A and finish at J. Claude wishes to
minimise the length of the inspection route.
(b) By considering the pairings of all relevant nodes, find the length of Claude’s route.
State the arcs that will need to be traversed twice.
(5)
If Claude does not start the inspection route at A and finish at J, a shorter inspection
route is possible.
(c) Determine the two towns at which Claude should start and finish so that the
route has minimum length. Give a reason for your answer and state the length of
this route.
(3)
(Total for Question 3 is 14 marks)
4 P73481A
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