Lesson DC4-DC7

DC4-DC7 Supersources, augmenting flows and capacities Quiz: AQA Further Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson DC4-DC7, Supersources, augmenting flows and capacities: 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 capacity is assigned to arcs connecting a supersource to original sources?

    • Zero capacity
    • Unit capacity
    • Very large capacity
    • Minimum node capacity

  2. What capacity is given to arcs joining original sinks to a supersink?

    • Minimum sink capacity
    • Zero capacity
    • Very large capacity
    • Unit capacity

  3. On an augmenting path, what condition must a backward arc satisfy?

    • Zero capacity
    • Zero flow
    • Full capacity
    • Positive flow

  4. How is a node with a restricted capacity represented in a flow network?

    • Removed from network
    • Merged with source
    • Kept as single
    • Split into two

  5. What does a lower capacity on an arc in a flow network represent?

    • Minimum required flow
    • Net arc capacity
    • Maximum permitted flow
    • Average flow value

  6. A directed network has source S and sink T, with arcs SA (capacity 4), SB (capacity 3), AB (capacity 2), AT (capacity 3) and BT (capacity 4). A flow of 3 currently passes along the route S-A-T only. How much can the flow be augmented along the route S-B-T?

    • 7
    • 3
    • 2
    • 4

  7. A directed network has source S and sink T, with arcs SA (capacity 4), SB (capacity 3), AB (capacity 2), AT (capacity 3) and BT (capacity 4). A flow of 3 along S-A-T is augmented by 3 along S-B-T. What is the value of the resulting flow?

    • 6
    • 7
    • 9
    • 3

  8. A directed network has source S and sink T, with arcs SA (capacity 4), SB (capacity 3), AB (capacity 2), AT (capacity 3) and BT (capacity 4). After the flow has value 6, what is the largest amount the flow can be augmented along the route S-A-B-T?

    • 2
    • 3
    • 4
    • 1

  9. What is the maximum flow value in a network with a minimum cut capacity of 7?

    • 12
    • 7
    • 3
    • 4

  10. What represents the residual capacity of a forward arc carrying flow below its maximum?

    • Total capacity
    • Upper minus flow
    • Flow minus lower
    • Lower plus upper

  11. What single node is added to unify multiple sinks in a flow network?

    • Supersource
    • Central node
    • Supersink
    • Terminal vertex

  12. A node X has capacity 5, while its incoming arcs have total capacity 8. After X is split into X_in and X_out joined by an arc of capacity 5, what is the maximum flow through X?

    • 3
    • 5
    • 8
    • 13

  13. An arc has a lower capacity of 2 and upper capacity of 6. What is the valid flow range?

    • 2 to 6
    • 4 to 6
    • 0 to 6
    • 2 to 8

  14. An arc with capacities 2 to 6 currently carries flow 4. By how much can flow decrease?

    • 4
    • 0
    • 6
    • 2

  15. An augmenting path uses forward arcs with spare capacities 5 and 2 and 7, and a backward arc currently carrying flow 4. What is the largest amount by which the flow can be augmented along this path?

    • 7
    • 2
    • 4
    • 5

  16. Why are arcs connecting a supersource given very large capacities?

    • To increase costs
    • To reduce nodes
    • To balance supplies
    • To avoid bottlenecks

  17. A node has capacity 6. Two incoming arcs each have capacity 4, and one outgoing arc has capacity 10. What is the maximum flow through the node?

    • 4
    • 8
    • 10
    • 6

  18. What action on a backward arc allows overall network flow to increase?

    • Removing the arc
    • Reducing flow
    • Doubling capacity
    • Increasing flow

  19. A supersource S has arcs SS1 of capacity 5 and SS2 of capacity 7, and the sink can receive at most 9 units in total. What is the maximum flow from S to the sink?

    • 12
    • 7
    • 5
    • 9

  20. At what point does an augmenting-flow algorithm for maximum flow terminate?

    • All capacities reached
    • No augmenting path
    • Network gets disconnected
    • Flow reaches zero

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