OCR 2023 GCE FURTHER MATHEMATICS B (MEI) Y413/01: MEI MODELLING WITH ALGORITHMS AS LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

FURTHER MATHEMATICS B (MEI) MEI MODELLING WITH ALGORITHMS OCR 2023 GCE FURTHER MATHEMATICS B (MEI) Y413/01: MEI MODELLING WITH ALGORITHMS AS LEVEL QUESTION PAPER & MARK SCHEME (MERGED) You must have: •the Printed Answer Booklet •the Formulae Booklet for Further Mathematics B (MEI) •a scientific or graphical calculator QP Oxford Cambridge and RSA Friday 26 May 2023 – Afternoon AS Level Further Mathematics B (MEI) Y413/01 Modelling with Algorithms Time allowed: 1 hour 15 minutes INSTRUCTIONS • Use black ink. You can use an HB pencil, but only for graphs and diagrams. • Write your answer to each question in the space provided in the Printed Answer Booklet . If you need extra space use the lined pages at the end of the Printed Answer Booklet. The question numbers must be clearly shown. • Fill in the boxes on the front of the Printed Answer Booklet. • Answer all the questions. • Where appropriate, your answer should be supported with working. Marks might be given for using a correct method, even if your answer is wrong. • Give your final answers to a degree of accuracy that is appropriate to the context. • Do not send this Question Paper for marking. Keep it in the centre or recycle it. INFORMATION • The total mark for this paper is 60. • The marks for each question are shown in brackets [ ]. • This document has 12 pages. ADVICE • Read each question carefully before you start your answer. 2 © OCR 2023 Y413/01 Jun23 10 C E 2 1 6 11 2 17 8 H 5 G 4 J 2 12 13 10 10 10 5 7 D F 6 1 Fig. 1.1 I A B K a The diagram in Fig. 1.1 represents a system of pipes through which a fluid can flow from two sources to three sinks. It also shows a cut a. The weights on the arcs show the capacities of the pipes in gallons per minute. (a) Add a supersource S and a supersink T to the network in the Printed Answer Booklet, giving appropriate weightings and directions to the connecting arcs. [2] (b) Calculate the capacity of the cut a. [1] 3 Turn over © OCR 2023 Y413/01 Jun23 10 C E 2 1 6 4 2 15 8 1 H 0 G 4 J 12 13 6 0 3 10 7 D F 2 The diagram in Fig. 1.2 shows a feasible flow through the network. Fig. 1.2 I A B K (c) Write down the amount of fluid, in gallons per minute, that Fig. 1.2 shows flowing from the sources to the sinks. [1] (d) Prove that the flow shown in Fig. 1.2 is the maximum possible flow through the network. [2]