Lesson 3D.1.2-3D.1.4

3D.1.2-3D.1.4 Bin packing, sorting, Eulerian graphs and planarity Quiz: Pearson Edexcel Further Maths, Unit 35

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 3D.1.2-3D.1.4, Bin packing, sorting, Eulerian graphs and planarity: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 35: Algorithms and graph theory, written with Revision Ninja.

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The 20 questions

  1. What is the aim of bin packing?

    • to pack items into the fewest bins
    • to sort items by weight only
    • to make each bin hold exactly one item
    • to maximise the number of bins used

  2. In the quick sort algorithm as specified here, which item is chosen as the pivot?

    • the first item always
    • the largest item
    • a randomly chosen item only
    • the middle item of the list

  3. A graph is Eulerian when every vertex has

    • even degree
    • odd degree
    • degree exactly 3
    • degree at most 4

  4. A semi-Eulerian graph has exactly

    • no vertices of odd degree
    • four vertices of odd degree
    • exactly one vertex of odd degree
    • two vertices of odd degree

  5. An Eulerian cycle is a cycle that includes

    • every vertex at least once
    • the shortest possible route
    • every edge of the graph exactly once
    • every vertex exactly once

  6. A Hamiltonian cycle passes through

    • only the vertices of odd degree
    • every edge exactly once
    • every vertex exactly once and returns to its start
    • every edge at least once

  7. A planar graph is one that can be drawn in a plane so that

    • all edges have equal weight
    • every vertex has degree 2
    • no vertex has degree more than 3
    • no two edges meet except at a vertex to which they are both incident

  8. Items of sizes 6, 5, 4, 3 and 2 are packed into bins of capacity 10. What is the minimum number of bins?

    • 4
    • 2
    • 5
    • 3

  9. Items of sizes 8, 5, 4 and 3 are packed into bins of capacity 10. What is the minimum number of bins?

    • 5
    • 4
    • 2
    • 3

  10. A connected graph has vertex degrees 4, 4, 2, 2 and 4. Which statement is true?

    • It is semi-Eulerian, with exactly two odd vertices
    • It is Eulerian, so it has an Eulerian cycle
    • It has no Eulerian cycle because it has an odd number of vertices
    • It cannot be Eulerian since its degrees differ

  11. A connected graph has exactly two odd vertices A and B. Where must an Eulerian trail start and end?

    • both at A
    • anywhere, as long as the start has even degree
    • it must be a cycle returning to its start
    • at A and at B

  12. How many edges does the complete graph K6 have?

    • 30
    • 15
    • 6
    • 12

  13. Using quick sort with the middle item as the pivot, what is the pivot for the list 5, 2, 9, 1, 7?

    • 7
    • 9
    • 1
    • 5

  14. A graph has 4 vertices, each of degree 3. How many edges does it have?

    • 12
    • 4
    • 6
    • 3

  15. Which graph has an Eulerian cycle?

    • a star with three leaves
    • a square with a pendant edge
    • a path on three vertices
    • a triangle

  16. Which complete graph is planar?

    • K4
    • K7
    • K5
    • K6

  17. Items of sizes 5, 5, 4, 4, 3 and 3 are packed into bins of capacity 10. What is the minimum number of bins?

    • 5
    • 3
    • 2
    • 4

  18. A connected graph has six vertices, four of which have odd degree. Does it have an Eulerian trail?

    • Yes, it is semi-Eulerian
    • No: with more than two odd vertices there is no Eulerian trail
    • Yes, since it is connected
    • No, because its vertices have even degree

  19. Why can a greedy packing method fail to find the minimum number of bins?

    • it always wastes exactly half of each bin
    • a locally best choice may leave gaps that another arrangement would fill
    • it ignores the capacity of the bins
    • it requires items sorted by weight

  20. A graph has seven vertices with degrees 3, 3, 3, 3, 3, 3 and 2. How many edges does it have?

    • 9
    • 10
    • 12
    • 20

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