Lesson DE1-DE3

DE1-DE3 Activity networks and critical paths Quiz: AQA Further Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson DE1-DE3, Activity networks and critical paths: 20 multiple choice questions for the AQA Further Maths (7367), Unit 5: Optional application 3: discrete mathematics, written with Revision Ninja.

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The 20 questions

  1. What does an activity-on-node precedence network show?

    • Each node is an activity with its duration, and arcs show which activities must finish before others can start
    • All activities are listed in a single chain with no branching
    • Each arc is an activity and nodes are the events marking the start and end of activities
    • Only the arcs carry weights, representing travel times between locations

  2. What is the earliest start time of an activity in a critical path analysis?

    • The earliest time it can begin, once all its immediate predecessors have finished
    • The latest time it can start without delaying the whole project
    • The total duration of the longest path from the start to that activity
    • The time by which it must finish to keep the project on schedule

  3. What is a critical activity in a project network?

    • An activity with the greatest duration in the project
    • An activity with zero float, so any delay to it delays the completion of the whole project
    • An activity that has no predecessors in the network
    • An activity whose float is equal to its own duration

  4. What is the critical path of a project network?

    • A path from start to finish with the longest total duration, made up entirely of critical activities
    • The path that passes through the largest number of activities
    • The shortest path through the network from start to finish
    • The path whose activities have the largest total float

  5. What is the float of an activity in a project network?

    • The total time spent on the activity including any waiting time
    • The time an activity can be brought forward without affecting any earlier activities
    • The amount of time the activity can be delayed without delaying the completion of the project
    • The difference between the project duration and the duration of the activity

  6. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). What is the minimum duration of the project?

    • 9
    • 11
    • 14
    • 12

  7. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). What is the earliest start time of activity E?

    • 8
    • 9
    • 5
    • 12

  8. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). Which activities form the critical path?

    • B, D and E
    • A, C and E
    • B, C and E
    • A, D and E

  9. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). What is the total float of activity A?

    • 4
    • 0
    • 7
    • 3

  10. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). What is the total float of activity C?

    • 4
    • 5
    • 0
    • 2

  11. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). If activity C is delayed by 3 time units, what happens to the project duration?

    • It is unchanged, since C has float 4 and the delay of 3 does not exceed it
    • It increases by 1
    • It increases by 3
    • It decreases by 3

  12. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). If activity D is delayed by 1 time unit, what happens to the project duration?

    • It is unchanged, since D is not on the critical path
    • It increases by 1 to 13, since D is critical
    • It increases by 4, since that is the float of activity B
    • It decreases by 1, since the delay shortens the path

  13. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). What is the latest start time of activity D?

    • 4
    • 5
    • 0
    • 9

  14. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). What is the latest start time of activity B?

    • 0
    • 2
    • 1
    • 4

  15. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). What is the total float of activity E?

    • 9
    • 12
    • 3
    • 0

  16. In a critical path analysis, what does the forward pass find, and what does the backward pass find?

    • The forward pass finds earliest start and finish times, and the backward pass finds latest start and finish times
    • The forward pass uses floats, and the backward pass uses durations only
    • Both passes start at the same node and use the shortest path
    • The forward pass finds latest times from the finish, and the backward pass finds earliest times

  17. Why is the minimum project duration equal to the length of the longest path in the network?

    • Each activity must wait for all its predecessors, so the finish is governed by the longest chain of dependent activities
    • Because only the first activity in the network determines the finish time
    • Because the shortest path determines when the last activity finishes
    • Because the total of all activity durations is always the project time

  18. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). If the duration of A is increased from 3 to 8, what are the new project duration and critical path?

    • 17, with critical path A, C and E
    • 13, with critical path B, D and E
    • 12, with critical path B, D and E
    • 13, with critical path A, C and E

  19. Which statement about critical paths is correct?

    • A network always has exactly one critical path, from the first activity to the last
    • Non-critical activities always have zero float
    • A network may have more than one critical path, and every activity on a critical path has zero float
    • The critical path always contains the activity with the longest duration

  20. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). If the duration of D is increased from 5 to 6, what is the new minimum project duration?

    • 14
    • 13
    • 11
    • 12

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