Maths 28
Pearson Edexcel Level
3 GCE
Friday 16 May 2025
8FM0/
Afterno Paper
on referen
ce
Further Mathematics
🟐 🟐
Advanced Subsidiary 28
Further Mathematics
options 28: Decision
Mathematics 2 (Part of
option K only)
You must have:
Mathematical Formulae and Statistical Tables (Green), calculator,
D2 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
• If pencil is used for diagrams/sketches/graphs it must be dark
• Fill
pen. in the boxes at the top of the answer book with your
(HB or B). centre number and candidate number.
• Answer
name,
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.
• Do not return the question paper with the D2 Answer Book.
Information
• A booklet ‘Mathematical Formulae and Statistical Tables’ is
• The total mark for this part of the examination is 40. There are 4
• The marks –for
provided.
questions. each
use thisquestion
as a guideareas
shown in much time to spend
to how
on each question.
brackets
Advice
• Read each question carefully before you start to answer it.
• Try to answer every
• Check your answers if you have time at the end.
question.
Turn over
Maths 28
,P74076A
©2025 Pearson
Education Ltd. Y:1/1/1/
, 1. Five workers, A, B, C, D and E, are each to be assigned to one of five tasks, J, K, L,
M and N. Each task must be assigned to exactly one worker and each worker must do
exactly one task.
Worker C cannot do task L and worker D cannot do task K.
The profit, in pounds, that each worker will make while assigned to each task is shown
in the table below.
J K L M N
A 38 33 40 35 32
B 26 24 27 25 23
C 33 29 – 30 27
D 36 – 41 37 33
E 32 27 31 29 25
The Hungarian algorithm is to be used to find the maximum total profit that can be
earned by the five workers.
(a) Explain how the contents of the table must be modified to allow the algorithm to be
used.
(2)
(b) Reducing rows first, use the Hungarian algorithm to obtain the maximum total
profit. You should explain how any initial row and column reductions are made and
also how you determine if the table is optimal at each stage.
(7)
(Total for Question 1 is 9 marks)
2 P74076
A
■■■■
Pearson Edexcel Level
3 GCE
Friday 16 May 2025
8FM0/
Afterno Paper
on referen
ce
Further Mathematics
🟐 🟐
Advanced Subsidiary 28
Further Mathematics
options 28: Decision
Mathematics 2 (Part of
option K only)
You must have:
Mathematical Formulae and Statistical Tables (Green), calculator,
D2 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
• If pencil is used for diagrams/sketches/graphs it must be dark
• Fill
pen. in the boxes at the top of the answer book with your
(HB or B). centre number and candidate number.
• Answer
name,
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.
• Do not return the question paper with the D2 Answer Book.
Information
• A booklet ‘Mathematical Formulae and Statistical Tables’ is
• The total mark for this part of the examination is 40. There are 4
• The marks –for
provided.
questions. each
use thisquestion
as a guideareas
shown in much time to spend
to how
on each question.
brackets
Advice
• Read each question carefully before you start to answer it.
• Try to answer every
• Check your answers if you have time at the end.
question.
Turn over
Maths 28
,P74076A
©2025 Pearson
Education Ltd. Y:1/1/1/
, 1. Five workers, A, B, C, D and E, are each to be assigned to one of five tasks, J, K, L,
M and N. Each task must be assigned to exactly one worker and each worker must do
exactly one task.
Worker C cannot do task L and worker D cannot do task K.
The profit, in pounds, that each worker will make while assigned to each task is shown
in the table below.
J K L M N
A 38 33 40 35 32
B 26 24 27 25 23
C 33 29 – 30 27
D 36 – 41 37 33
E 32 27 31 29 25
The Hungarian algorithm is to be used to find the maximum total profit that can be
earned by the five workers.
(a) Explain how the contents of the table must be modified to allow the algorithm to be
used.
(2)
(b) Reducing rows first, use the Hungarian algorithm to obtain the maximum total
profit. You should explain how any initial row and column reductions are made and
also how you determine if the table is optimal at each stage.
(7)
(Total for Question 1 is 9 marks)
2 P74076
A
■■■■
