Edexcel as level further mathematics question paper 27 may 2023

Pearson Edexcel Level 3 GCE Friday 19 May 2023 Afternoon Paper reference 8FM0/27 Further Mathematics Advanced Subsidiary Further Mathematics options 27: Decision Mathematics 1 (Part of options D, F, H and K) 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. • 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 answers should be given to three significant figures unless otherwise stated. • Do not return the question paper with the D1 Answer Book. Information • A booklet ‘Mathematical Formulae and Statistical Tables’ is provided. • The total mark for this part of the examination is 40. There are 5 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 question. • Check your answers if you have time at the end.2 P72813A  Answer ALL questions. Write your answers in the answer book provided. 1. 56 The list of eleven numbers shown above is to be sorted into descending order. Carry out a quick sort to produce the sorted list. You should show the result of each pass and identify the pivots clearly. (Total for Question 1 is 4 marks) 3 Turn over P72813A 2. A(6) B(10) C(7) D(7) E(8) F(11) G(5) H(9) I(2) J(6) K(9) L(5) 1 3 7 4 6 8 2 5 Figure 1 A project is modelled by the activity network shown in Figure 1. The activities are represented by the arcs. The number in brackets on each arc gives the time required, in hours, to complete the corresponding activity. The numbers in circles are the event numbers. Each activity requires one worker, and the project is to be completed in the shortest possible time. (a) Explain the significance of the dummy activity from event 3 to event 4 (1) (b) Complete Diagram 1 in the answer book to show the early event times and the late event times. (3) (c) State the critical activities. (1) (d) Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working. (1) (e) Draw a Gantt chart for this project on Grid 1 in the answer book. (4) (Total for Question 2 is 10 marks