Pearson Edexcel Level 3 GCE
Friday 17 Mathematics
Further May 2024 � �
Advanced Subsidiary
Afternoon
Paper
Further Mathematics options reference 8FM0/27
27: Decision Mathematics 1
(Part of options D, F, H and K)
Pearson Edexcel GCE
In AS Further Mathematics (8FM0)Paper 27 Decision Mathematics 1
You must have:
Mathematical Formulae and Statistical Tables (Green), calculator,
D1 Answer Book (enclosed)
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.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of the answer book with your name, centre number
• Answer
and candidate number.
all questions and ensure that your answers to parts of questions are
• Answer
clearly labelled.
the questions in the answer book provided
• You
– there may be more space than you need.
should show sufficient working to make your methods clear.
• Inexact
Answers without working may not gain full credit.
answers should be given to three significant figures unless
• Do not return the question paper with the D1 Answer Book.
otherwise stated.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The total mark for this part of the examination is 40. There are 4 questions.
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
, BLANK PAGE
2
,1.
4 6.5 7 1.3 2 5 1.5 6 4.5 6 1
The list of eleven numbers shown above is to be sorted into descending order.
(a) Carry out a quick sort to produce the sorted list. You should show the result of each
pass and identify the pivots clearly.
(3)
(b) Use the first‑fit decreasing bin packing algorithm to pack the numbers into bins of
size 10
(3)
(c) Determine whether your answer to part (b) uses the minimum number of bins. You
must justify your answer.
(2)
A different list of eleven numbers is to be sorted into descending order using a bubble
sort. The list after the second pass is
4.5 5.6 3.8 6.7 5.4 1.6 4.8 9.1 3.3 1.7 1.5
(d) Explain how you know that at least one of the first two passes of the bubble sort
was not carried out correctly.
(1)
(Total for Question 1 is 9 marks)
3
, 2. A company manages an awards evening.
The table below lists the activities required to set up the room for the evening, and their
immediately preceding activities. Each activity requires exactly one person.
Activity Immediately preceding activities
A ‑
B A
C A
D C
E C
F B, D, E
G E
H B
J H, F, G
Figure 1 shows a partially completed activity network used to model the project. Each
activity is represented by an arc.
B
A
D
C
Figure 1
(a) Add the remaining five activities to Diagram 1 in the answer book to complete the
activity network, using exactly two dummies.
(3)
4
Friday 17 Mathematics
Further May 2024 � �
Advanced Subsidiary
Afternoon
Paper
Further Mathematics options reference 8FM0/27
27: Decision Mathematics 1
(Part of options D, F, H and K)
Pearson Edexcel GCE
In AS Further Mathematics (8FM0)Paper 27 Decision Mathematics 1
You must have:
Mathematical Formulae and Statistical Tables (Green), calculator,
D1 Answer Book (enclosed)
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.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of the answer book with your name, centre number
• Answer
and candidate number.
all questions and ensure that your answers to parts of questions are
• Answer
clearly labelled.
the questions in the answer book provided
• You
– there may be more space than you need.
should show sufficient working to make your methods clear.
• Inexact
Answers without working may not gain full credit.
answers should be given to three significant figures unless
• Do not return the question paper with the D1 Answer Book.
otherwise stated.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The total mark for this part of the examination is 40. There are 4 questions.
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
, BLANK PAGE
2
,1.
4 6.5 7 1.3 2 5 1.5 6 4.5 6 1
The list of eleven numbers shown above is to be sorted into descending order.
(a) Carry out a quick sort to produce the sorted list. You should show the result of each
pass and identify the pivots clearly.
(3)
(b) Use the first‑fit decreasing bin packing algorithm to pack the numbers into bins of
size 10
(3)
(c) Determine whether your answer to part (b) uses the minimum number of bins. You
must justify your answer.
(2)
A different list of eleven numbers is to be sorted into descending order using a bubble
sort. The list after the second pass is
4.5 5.6 3.8 6.7 5.4 1.6 4.8 9.1 3.3 1.7 1.5
(d) Explain how you know that at least one of the first two passes of the bubble sort
was not carried out correctly.
(1)
(Total for Question 1 is 9 marks)
3
, 2. A company manages an awards evening.
The table below lists the activities required to set up the room for the evening, and their
immediately preceding activities. Each activity requires exactly one person.
Activity Immediately preceding activities
A ‑
B A
C A
D C
E C
F B, D, E
G E
H B
J H, F, G
Figure 1 shows a partially completed activity network used to model the project. Each
activity is represented by an arc.
B
A
D
C
Figure 1
(a) Add the remaining five activities to Diagram 1 in the answer book to complete the
activity network, using exactly two dummies.
(3)
4
