Free-Standing Mathematics Qualification Advanced Level June Use black ink or black ball-point pen. Pencil should only be used for drawing.

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1 Free-Standing Mathematics Qualification Advanced Level June 2015 Using and Applying 64/2 Decision Mathematics Unit 14 Tuesday 12 May pm to 3.00 pm For this paper you must have: a clean copy of the Data Sheet (enclosed) a calculator a ruler. Time allowed 1 hour 30 minutes Instructions Use black ink or black ball-point pen. Pencil should only be used for drawing. Fill in the boxes at the top of this page. Answer all questions. Write the question part reference (eg, (i) etc) in the left-hand margin. You must answer each question in the space provided for that question. If you require extra space, use an AQA supplementary answer book; do not use the space provided for a different question. Do not write outside the box around each page. Show all necessary working; otherwise marks for method may be lost. Do all rough work in this book. Cross through any work that you do not want to be marked. The final answer to questions requiring the use of tables or calculators should be given to three significant figures, unless stated otherwise. You may not refer to the copy of the Data Sheet that was available prior to this examination. A clean copy is enclosed for your use. Condensed Information The marks for questions are shown in brackets. The maximum mark for this paper is 60. You may use either a scientific calculator or a graphics calculator. Advice You do not necessarily need to use all the space provided. P0735/Jun15/E3 64/2

2 2 1 Some students are travelling by car to visit a university when they realise they have a flat tyre. The work involved in changing the wheel has been divided into a number of tasks, as shown in the table below. Activity Immediate predecessor A: Find the wheel that needs changing 0.5 B: Unlock boot 0.25 C: Get tool kit and jack from boot B 1 D: Get spare wheel from boot B 1 E: Fix jack under car and jack up A, C 2 F: Loosen wheel nuts A, C 1 G: Remove wheel nuts E, F 1.5 H: Replace wheel on axle D, G 1 I: Tighten wheel nuts by hand H 1.25 J: Lower jack H 1 K: Fully tighten wheel nuts I, J 1.5 L: Replace tool kit and jack in boot K 1 M: Put punctured wheel in boot K 1.25 N: Lock boot L, M 0.5 Duration (minutes) (c) (d) Construct an activity network for the work involved. Find the earliest start time for each activity. Find the latest finish time for each activity. Find the critical path. [3 marks] (e) (f) Given that all activities start as early as possible, draw a cascade (Gantt) diagram for the work involved. Use the grid on page 3. Given that the driver of the car completes all of the tasks on her own, find the minimum time for the driver to change the wheel. (02)

3 3 0 Duration (minutes) 20 (03) Turn over s

4 4 2 The diagram below shows a network of roads connecting some towns in South Wales. The number on each edge shows the time, in minutes, to drive between each pair of towns. Megan lives in Cardiff and wishes to drive to Abergavenny. Use Dijkstra s algorithm on the diagram below to find the minimum travelling time from Cardiff (CA) to Abergavenny (AG). Show all temporary labels. State the corresponding route. [6 marks] Before Megan leaves home, she finds out that the roads from Blaenavon (BL) to Abergavenny (AG) and from Goetre (GO) to Abergavenny (AG) are closed due to snow. Find the new minimum travelling time from Cardiff (CA) to Abergavenny (AG). State the corresponding route. [3 marks] 11 AG HE 12 CE BL 14 SW 3 PP 8 GO 7 6 LT RA 8 US NU NA 11 NE 12 CA PB (04)

5 5 3 The diagram shows a network of roads connecting some towns in South Wales. The number on each edge shows the time, in minutes, to drive between each pair of towns. Treorchy (TR) Merthyr Tydfil (MT) Porth (PO) Abercynon (AB) 7 Pontypridd (PD) 33 Brynmawr (BY) 25 Pontypool (PP) Bridgend (BR) Cowbridge (CO) 31 Cardiff (CA) Llantwit Major (LM) Total of all these times is 318 minutes Gareth, a highways supervisor, lives in Cardiff and drives along all of the roads at least once, to decide on the state of the roads, before returning to his home. (i) (ii) Use the Chinese Postman algorithm to find the time of an optimal route for Gareth. Show all your working. [6 marks] State the roads that Gareth would have to drive along twice in this optimal route. Owen drives a snowplough to clear all the roads of snow in winter in the minimum amount of time. There are two bases for the snowploughs, Cowbridge (CO) and Merthyr Tydfil (MT). Owen starts at CO and drives along all of the roads at least once before finishing at MT. Find the time of an optimal route for Owen. (c) Given that Owen can start at any town and finish at any other town, find: (i) (ii) (05) the time for an optimal route for Owen; the start and finish towns to achieve this time. Turn over s

6 6 4 Huw, a salesperson, works in Cardiff (CA) and has five stores in five towns to visit. Huw wishes to arrange a tour of the five stores, starting from, and finally returning to, his base in Cardiff. The table shows the times, in minutes, that it takes to drive between the towns. The total minimum driving time of Huw s tour is x minutes. Abergavenny (AG) Cardiff (CA) Llantwit Major (LM) Merthyr Tydfil (MT) Penarth (PE) Treorchy (TR) Abergavenny (AG) Cardiff (CA) Llantwit Major (LM) Merthyr Tydfil (MT) Penarth (PE) Treorchy (TR) Starting from Treorchy, use the nearest neighbour algorithm to find an upper bound for x. Use your answer to part to write down a tour starting from Cardiff. (c) By deleting Abergavenny, find a lower bound for x. [5 marks] (d) Using your answers to parts and (c), what can be deduced about the smallest interval within which x must lie? (06)

7 7 5 A company requires a business document, currently written in English, to be translated into six other languages. The costs of translating the document vary as it is harder to find translators for some languages than for others. The costs, in tens of pounds, are shown in the table below. On the table below, showing the order in which you select the edges, use Prim s algorithm, starting from E, to find a minimum spanning tree for D, E, F, G, I, N and S. Draw your minimum spanning tree. (c) (d) (e) (f) Find the minimum total cost of translating the document into the six other languages and advise the company on how this minimum cost can be achieved. [3 marks] Prim s algorithm from different starting points produces the same minimum spanning tree. State the final edge that would be added to complete the minimum spanning tree if the starting point was N. Given that Kruskal s algorithm is used to find the same minimum spanning tree, state which edge will be the first to be chosen. Explain why the company might choose not to use the minimum cost method of part (c) to translate its document. Danish (D) English (E) French (F) German (G) Italian (I) Norwegian (N) Sicilian (S) Danish (D) English (E) French (F) German (G) Italian (I) Norwegian (N) Sicilian (S) Copyright ª 2015 AQA and its licensors. All rights reserved. (07)

PHA3/W PHYSICS (SPECIFICATION A) Unit 3 Current Electricity and Elastic Properties of Solids

PHA3/W PHYSICS (SPECIFICATION A) Unit 3 Current Electricity and Elastic Properties of Solids Surname Centre Number Other Names Candidate Number Leave blank Candidate Signature General Certificate of Education June 2005 Advanced Subsidiary Examination PHYSICS (SPECIFICATION A) PHA3/W Unit 3 Current