Pearson Edexcel GCE Decision Mathematics D1

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Pearson Edexcel GCEDecision Mathematics D1Advanced/Advanced SubsidiaryFriday 17 June 2016 – AfternoonTime: 1 hour 30 minutesPaper Reference6689/01You must have:D1 Answer BookCandidates may use any calculator allowed by the regulations of theJoint Council for Qualifications. Calculators must not have the facilityfor symbolic algebra manipulation, differentiation and integration, orhave retrievable mathematical formulae stored in them.Instructionsblack ink or ball-point pen. UseIf 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, centrenumber and candidate number.Answer all questions and ensure that your answers to parts of questions are clearlylabelled.Answerthe questions in the D1 answer book provided – there maybe more space than you need.You should show sufficient working to make your methods clear. Answers withoutworking may not gain full credit.Whenacalculator degree of accuracy.is used, the answer should be given to an appropriate Do not return the question paper with the answer book.InformationThe total mark for this paper is 75. Themarks for each question are shown in brackets– use this as a guide as to how much time to spend on each question.Adviceeach question carefully before you start to answer it. ReadTry to answer every question. Check your answers if you have time at the end.P46678A 2016 Pearson Education Ltd.1/1/1/1/e2*P46678A*Turn over

Write your answers in the D1 answer book for this paper.1.LALAMBMBNCNCPDPDTETEFigure 1Figure 2(a) Define the term ‘bipartite graph’.(2)Figure 1 shows the possible allocations of five people, Larry (L), Monisha (M), Nina (N), Phil (P)and Theo (T), to five activities, A, B, C, D and E.Figure 2 shows an initial matching.(b) Starting from this initial matching, use the maximum matching algorithm to find a completematching. You should list the alternating path you use and state your complete matching.(3)(Total 5 marks)P46678A2

2.Draw the activity network described in the precedence table below, using activity on arc and exactlythree dummies.ActivityImmediately preceding activitiesA–B–CADAEBFBGA, E, FHFICJD, GKD, G(Total 5 marks)P46678A3Turn over

3.59451855471163171542(a) The list of numbers above is to be sorted into descending order. Perform a quick sort to obtainthe sorted list. You should show the result of each pass and identify your pivots clearly.(4)The numbers in the list represent the lengths, in cm, of some pieces of copper wire. The copperwire is sold in one metre lengths.(b) Use the first-fit decreasing bin packing algorithm to determine how these pieces could be cutfrom one metre lengths. (You should ignore wastage due to cutting.)(3)(c) Determine whether your solution to (b) is optimal. Give a reason for your answer.(2)(Total 9 marks)P46678A4

4.A5B1317EC2115D133110F42H7G914J231517KFigure 3Figure 3 represents a network of tram tracks. The number on each edge represents the length,in miles, of the corresponding track. One day, Sarah wishes to travel from A to F. She wishes tominimise the distance she travels.(a) Use Dijkstra’s algorithm to find the shortest path from A to F. State your path and its length.(6)On another day, Sarah wishes to travel from A to F via J.(b) Find a route of minimal length that goes from A to F via J and state its length.(2)(c) Use Prim’s algorithm, starting at G, to find the minimum spanning tree for the network.You must clearly state the order in which you select the edges of your tree.(3)(d) State the length, in miles, of the minimum spanning tree.(1)(Total 12 marks)P46678A5Turn over

5.StartInput x and yt 0YesIs x odd?x2y 2yx x–1y yt t yx Not tNoIs x 0?YesOutput tStopFigure 4An algorithm is described by the flow chart shown in Figure 4.Given that x 27 and y 5,(a) complete the table in the answer book to show the results obtained at each step when thealgorithm is applied. Give the final output.(4)The numbers 122 and1are to be used as inputs for the algorithm described by the flow chart.2(b) (i) State, giving a reason, which number should be input as x.(ii) State the output.(3)(Total 7 marks)P46678A6

e 5[The total weight of the network is 384]Figure 5 models a network of corridors in an office complex that need to be inspected by a securityguard. The number on each arc is the length, in metres, of the corresponding section of corridor.Each corridor must be traversed at least once and the length of the inspection route must beminimised. The guard must start and finish at vertex A.(a) Use the route inspection algorithm to find the length of the shortest inspection route. State thearcs that should be repeated. You should make your method and working clear.(5)It is now possible for the guard to start at one vertex and finish at a different vertex. An inspectionroute that traverses each corridor at least once is still required.(b) Explain why the inspection route should start at a vertex with odd degree.(2)The guard decides to start the inspection route at F and the length of the inspection route must stillbe minimised.(c) Determine where the guard should finish. You must give reasons for your answer.(2)(d) State a possible route and its length.(2)(Total 11 marks)P46678A7Turn over

7.D(w)55E(4)A(5)0B(7)301730L(5)G(7)9017 K(13)30M(6)17H(8)30y9I(12)F (5)N(8)C(3)x3zJ(10)22Figure 6The network in Figure 6 shows the activities that need to be undertaken by a company to completea project. Each activity is represented by an arc and the duration, in days, is shown in brackets.Each activity requires exactly one worker. The early event times and late event times are shown ateach vertex.Given that the total float on activity D is 1 day,(a) find the values of w, x, y and z.(3)(b) On Diagram 1 in the answer book, draw a cascade (Gantt) chart for the project.(4)(c) Use your cascade chart to determine a lower bound for the minimum number of workersneeded to complete the project in the shortest possible time. You must make specific referenceto times and activities.(2)It is decided that the company may use up to 36 days to complete the project.(d) On Diagram 2 in the answer book, construct a scheduling diagram to show how the project canbe completed within 36 days using as few workers as possible.(3)(Total 12 marks)P46678A8

8.Charlie needs to buy storage containers.There are two different types of storage container available, standard and deluxe.Standard containers cost 20 and deluxe containers cost 65. Let x be the number of standardcontainers and y be the number of deluxe containers.The maximum budget available is 520(a) Write down an inequality, in terms of x and y, to model this constraint.(1)Three further constraints are:x.2–x 24y . 247x 8y - 112(b) Add lines and shading to Diagram 1 in the answer book to represent all four constraints.Hence determine the feasible region and label it R.(4)The capacity of a deluxe container is 50% greater than the capacity of a standard container.Charlie wishes to maximise the total capacity.(c) State an objective function, in terms of x and y.(1)(d) Use the objective line method to find the optimal vertex, V, of the feasible region. You mustmake your objective line clear and label the optimal vertex V.(3)(e) Calculate the exact coordinates of vertex V.(2)(f) Determine the number of each type of container that Charlie should buy. You must make yourmethod clear and calculate the cost of purchasing the storage containers.(3)(Total 14 marks)TOTAL FOR PAPER: 75 MARKSENDP46678A9

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Write your name hereSurnameOther namesPearsonEdexcel GCECentre NumberCandidate NumberDecision Mathematics D1Advanced/Advanced SubsidiaryFriday 17 June 2016 – AfternoonTime: 1 hour 30 minutesAnswer BookDo not return the question paper with the answer book.Paper Reference6689/01Total MarksTurn overP46678A 2016 Pearson Education Ltd.1/1/1/1/e2*P46678A0116*

Leaveblank1.ALAMBMBNCNCPDPDTETEFigure 1DO NOT WRITE IN THIS AREALFigure 2DO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA(Total 5 marks)2*P46678A0216*Q1

DO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREALeaveblank2.Q2(Total 5 marks)*P46678A0316*3Turn over

Leaveblank3.59451855471163171542DO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA4*P46678A0416*DO NOT WRITE IN THIS AREA

LeaveblankDO NOT WRITE IN THIS AREAQuestion 3 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREAQ3(Total 9 marks)*P46678A0516*5Turn over

exOrder oflabellingFinalvalueDO NOT WRITE IN THIS AREA14JH4GDO NOT WRITE IN THIS AREAAWorking values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Length of shortest path:6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .*P46678A0616*DO NOT WRITE IN THIS AREAShortest path:

LeaveblankDO NOT WRITE IN THIS AREAQuestion 4 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREAQ4(Total 12 marks)*P46678A0716*7Turn over

Leaveblank5.(a)You may not need to use all the rows in this table.xytIs x odd?2750YesIs x 0?DO NOT WRITE IN THIS AREAIt may not be necessary to complete all boxes in each row.DO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA8*P46678A0816*

LeaveblankDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREAQuestion 5 continuedFinal output(b)DO NOT WRITE IN THIS AREAQ5(Total 7 marks)*P46678A0916*9Turn over

DO NOT WRITE IN THIS AREA1715JFigure 5[The total weight of the network is 384]DO NOT WRITE IN THIS AREA10*P46678A01016*DO NOT WRITE IN THIS AREA

DO NOT WRITE IN THIS AREAQuestion 6 continuedLeaveblankDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREAQ6(Total 11 marks)*P46678A01116*11Turn over

Leaveblank7.(a)(b)02468101214161820222426283032DO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA12*P46678A01216*DO NOT WRITE IN THIS AREADiagram 1

Leaveblank(c)(d)02468101214 1618202224 262830 323436 38DO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREAQuestion 7 continuedDiagram 2Q7(Total 12 marks)*P46678A01316*13Turn over

Leaveblank8.DO NOT WRITE IN THIS AREAy16 –14 –12 –10 –8–DO NOT WRITE IN THIS ��2–242832xDiagram 114*P46678A01416*DO NOT WRITE IN THIS AREA

LeaveblankDO NOT WRITE IN THIS AREAQuestion 8 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA*P46678A01516*15Turn over

LeaveblankQuestion 8 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA(Total 14 marks)TOTAL FOR PAPER: 75 MARKSEND16*P46678A01616*Q8DO NOT WRITE IN THIS AREA

Answer the questions in the D1 answer book provided – there may be more space than you need. . 13 7 21 9 J H 17 5 C 13 14 K 2 23 17 15 10 4 31. P46678A 6 5. . Edexcel GCE Decision Mathematics D1 Advanced/Advanced Subsidiary P46678A 2016 Pearson Education Ltd. 1/1/1/1/e2

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