Pearson Edexcel Level 3 GCE
Further Mathematics
Advanced Subsidiary Further Mathematics options 28:
Decision Mathematics 2 ((Part of option K only))
You must have:
Mathematical Formulae and Statistical Tables (Green), 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). Fill in the boxes at the top of the answer book with your name,
centre number and candidate number.
• 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
stated.
answers should be given to three significant figures unless otherwise
• Do not return the question paper with the D2 Answer Book.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
total mark for this part of the examination is 40. There are 4 questions.
• 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
• Check your answers if you have time at the
• end. Good luck with your examination.
question.
Turn over
P66795A
©2021 Pearson Education Ltd.
1/1/1/1/1/
, Write your answers in the answer book provided.
1. Five workers, A, B, C, D and E, are available to complete four tasks, P, Q, R and S.
Each task must be assigned to exactly one worker and each worker can do at most one task.
Worker B cannot be assigned to task R.
The amount, in pounds, that each worker will earn if they are assigned to each task is shown in the
table below.
P Q R S
A 55 56 58 57
B 60 61 – 64
C 59 60 62 63
D 64 66 71 69
E 65 68 72 66
The Hungarian algorithm is to be used to find the maximum total amount that can be earned by the
five workers.
(a) Explain how the table should be modified to allow the Hungarian algorithm to be used, giving
reasons for your answer.
(2)
(b) Reducing rows first, use the Hungarian algorithm to obtain the maximum possible total
earnings. You should explain how any initial row and column reductions were made and how
you determined if the table was optimal at each stage.
(7)
(Total for Question 1 is 9 marks)
P66795A 2
Further Mathematics
Advanced Subsidiary Further Mathematics options 28:
Decision Mathematics 2 ((Part of option K only))
You must have:
Mathematical Formulae and Statistical Tables (Green), 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). Fill in the boxes at the top of the answer book with your name,
centre number and candidate number.
• 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
stated.
answers should be given to three significant figures unless otherwise
• Do not return the question paper with the D2 Answer Book.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
total mark for this part of the examination is 40. There are 4 questions.
• 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
• Check your answers if you have time at the
• end. Good luck with your examination.
question.
Turn over
P66795A
©2021 Pearson Education Ltd.
1/1/1/1/1/
, Write your answers in the answer book provided.
1. Five workers, A, B, C, D and E, are available to complete four tasks, P, Q, R and S.
Each task must be assigned to exactly one worker and each worker can do at most one task.
Worker B cannot be assigned to task R.
The amount, in pounds, that each worker will earn if they are assigned to each task is shown in the
table below.
P Q R S
A 55 56 58 57
B 60 61 – 64
C 59 60 62 63
D 64 66 71 69
E 65 68 72 66
The Hungarian algorithm is to be used to find the maximum total amount that can be earned by the
five workers.
(a) Explain how the table should be modified to allow the Hungarian algorithm to be used, giving
reasons for your answer.
(2)
(b) Reducing rows first, use the Hungarian algorithm to obtain the maximum possible total
earnings. You should explain how any initial row and column reductions were made and how
you determined if the table was optimal at each stage.
(7)
(Total for Question 1 is 9 marks)
P66795A 2
