Graph Theory and Critical Path Analysis · CAPE Applied Mathematics Unit 2

28 past-paper questions on Graph Theory and Critical Path Analysis, part of Module 1: Discrete Mathematics, from every CAPE Applied Mathematics Unit 2 paper on Quelpr.

1. 1(c)3 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2For the diagram provided, list any THREE paths which start and finish at A.
2. 2(d)(i)9 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Copy and complete the table for the earliest start time, latest start time, and float time for activities A through G.
3. 2(d)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Hence, determine the critical path.
4. 2(b)(i)5 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Construct an activity network for the project.
5. 2(b)(ii)10 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Copy and complete the table of Earliest Start Time, Latest Start Time, and Float for activities A to E.
6. 2(b)(iii)a)2 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Hence, determine the critical path.
7. 2(b)(iii)b)1 mark· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Hence, determine the MINIMUM completion time of the project.
8. 2(a)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine the EARLIEST start times of the activities S and X.
9. 2(a)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine the MINIMUM completion time of the project.
10. 2(a)(iii)3 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine the LATEST start times of the activities X and Q.
11. 2(a)(iv)2 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine a critical path of the activity network.
12. 2(a)(v)3 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine the float time for activity T.
13. 2(b)2 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2State the degree of the vertices A and C.
14. 2(a)(i)12 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Using the algorithm method, or otherwise, construct the activity network for these activities.
15. 2(a)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Copy and complete the table, giving the earliest start time, latest start time and float time for EACH activity.
16. 2(a)(iii)2 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Hence, obtain the critical path(s).
17. 1(b)2 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Determine the SHORTEST and LONGEST path from Town S to Town G.
18. 1(c)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2List the vertices that have a degree greater than 2.
19. 1(c)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2List all the paths from C to E.
20. 2(a)(i)6 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Construct the activity network for the project.
21. 2(a)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Complete the table of earliest start time, latest start time, and float for each activity.
22. 2(a)(iii)2 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2State the critical path of the activity network.
23. 2(a)(iv)2 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Determine the minimum time needed to complete the project.
24. 1(a)(i)6 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Determine the earliest and latest start times for EACH activity, in order for the project to be completed in the minimum time. Write your answers in the relevant spaces in the table.
25. 1(a)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Identify the critical path.
26. 1(a)(iii)1 mark· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Determine the minimum time for completion of the project.
27. 1(a)(iv)4 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Draw a fully labelled activity network to represent these activities and their precedence.
28. 1(a)(v)4 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Assume that the duration of Activity C is increased to 6 days. Determine which activities are now critical, and the new minimum time for completion of the project.