Lesson 3D.4.3

3D.4.3 Critical path algorithm Quiz: Pearson Edexcel Further Maths, Unit 38

20 questions

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Lesson 3D.4.3, Critical path algorithm: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 38: Critical path analysis, written with Revision Ninja.

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The 20 questions

  1. Critical activities are those with

    • no predecessors
    • maximum total float
    • zero total float
    • the longest duration

  2. The forward pass in the critical path algorithm computes

    • earliest event times
    • resource levels
    • latest event times
    • total float of each activity

  3. The backward pass computes

    • earliest event times
    • earliest start times of activities only
    • critical durations
    • latest event times

  4. The critical path is

    • a shortest path from start to finish
    • a longest path from start to finish made of critical activities
    • a path whose activities all have positive float
    • the path with the most activities regardless of duration

  5. The earliest time for an event is found by taking

    • the average of the incoming durations
    • the minimum over incoming activities of the same sum
    • the sum of all incoming durations
    • the maximum over incoming activities of the earliest start of the tail plus the duration

  6. The latest time for an event is found by taking

    • the sum of all outgoing durations
    • the minimum over outgoing activities of the latest time at their head minus the duration
    • the maximum over outgoing activities of the same difference
    • the earliest time plus the duration

  7. The project duration is equal to

    • the earliest time at the finish event
    • the latest time at the start event
    • the longest single activity duration
    • the sum of all activity durations

  8. Start node 0 has earliest time 0. Activity 0-1 takes 3, 0-2 takes 5, 1-3 takes 4, 2-3 takes 1 and 3-4 takes 6. What is the project duration?

    • 7
    • 13
    • 18
    • 12

  9. In the same network, the latest time at node 3 is 7. What is the latest time at node 2, where the activity 2-3 takes 1?

    • 6
    • 8
    • 7
    • 5

  10. In the same network (durations 0-1: 3, 0-2: 5, 1-3: 4, 2-3: 1, 3-4: 6), which activities form the critical path?

    • 0-1, 2-3 and 3-4
    • 0-1, 1-3 and 3-4
    • 0-2 and 2-3 only
    • 0-2, 2-3 and 3-4

  11. In the same network, what is the total float of activity 0-2, which takes 5, given earliest time 0 at node 0 and latest time 6 at node 2?

    • 1
    • 0
    • 5
    • 6

  12. An event has earliest time 4 and latest time 4. What can be said about it?

    • it is critical, with zero float
    • it cannot be reached
    • it has a float of 4
    • it is not critical

  13. An activity has earliest start 2, duration 4 and its head event has latest time 9. What is its total float?

    • 5
    • 1
    • 3
    • 0

  14. An event has two incoming activities: one from node 0 (earliest time 0, duration 4) and one from node 1 (earliest time 2, duration 7). What is the earliest time at this event?

    • 4
    • 9
    • 6
    • 11

  15. A node has outgoing activities to node 5 (duration 3, latest time 12) and to node 6 (duration 4, latest time 10). What is the latest time at this node?

    • 9
    • 6
    • 12
    • 7

  16. How many critical paths can a network have?

    • one or more
    • none
    • exactly two
    • exactly one

  17. Why does an activity with zero total float have to be critical?

    • it always has the longest duration
    • its earliest and latest times are always different
    • it has no predecessors
    • any delay to it delays the whole project, so it lies on a longest path

  18. An activity runs from node 2 to node 3 and takes 4. Node 2 has earliest time 8, and node 3 has latest time 12. What is the total float of this activity?

    • 4
    • 1
    • 2
    • 0

  19. Why compute latest times by working backwards from the finish?

    • because the forward pass is impossible
    • to find the latest each event can occur without delaying completion
    • to count the number of activities
    • to find the cheapest route through the network

  20. A network has edges 0-1 (2), 0-2 (6), 1-3 (5), 2-3 (1), 3-4 (4) and 1-2 (3). What is the project duration?

    • 11
    • 7
    • 12
    • 9

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