diagrams/sketches/graphs it must be dark (HB or B).Write your answers for this paper in the Decision Mathematics black ink or ball-point pen.
• answer
... [Show More] book provided.Fill in the boxes at 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 answer book provided
• – You should show sufficient working to make your methods clear. there may be more space than you need. • Answers without working may not gain full credit.Inexact answers should be given to three significant figures unless otherwise stated.
Information
••• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.There are 8 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.Good luck with your examination. Turn over
P66801A *P66801A*
©2021 Pearson Education Ltd. 1/1/1/1/
Figure 1
A Hamiltonian cycle for the graph in Figure 1 begins C, V, E, X, A, W, ….
(a) Complete the Hamiltonian cycle.
(1)
(b) Hence use the planarity algorithm to determine whether the graph shown in Figure 1 is planar. You must make your working clear and justify your answer.
(3)
(Total for Question 1 is 4 marks)
2
Figure 2
A project is modelled by the activity network shown in Figure 2. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, to complete the corresponding activity.
(a) Complete Diagram 1 in the answer book to show the early event times and the late event times.
(4)
Each activity requires one worker and the project must be completed in the shortest possible time using as few workers as possible.
(b) Calculate a lower bound for the number of workers needed to complete the project in the shortest possible time. You must show your working.
(2)
(c) Schedule the activities using Grid 1 in the answer book.
(3)
(Total for Question 2 is 9 marks)
3
A B C D E F G H
A – 24 42 48 34 37 32 22
B 24 – 40 35 30 41 39 44 [Show Less]