Lesson 3D.1.1

3D.1.1 Algorithms and the order of an algorithm Quiz: Pearson Edexcel Further Maths, Unit 35

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 3D.1.1, Algorithms and the order of an algorithm: 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 does the order of an algorithm describe?

    • how its running time grows with the size of the problem
    • the number of lines of code it contains
    • the amount of memory it uses only
    • the exact time it takes on one computer

  2. For algorithms on graphs, what is the size of a problem usually taken to be?

    • the total weight of all edges
    • the number of vertices
    • the number of edges only
    • the number of colours needed

  3. In a list of N items with N odd, the middle item is in position

    • N/2
    • (N-1)/2
    • N+1
    • (N+1)/2

  4. Bubble sort has order

    • n log n
    • 2^n
    • n
    • n^2

  5. How is the efficiency of an algorithm usually measured?

    • by the colour of the output
    • by the number of operations it must carry out
    • by the programming language used
    • by the number of inputs only

  6. The degree or valency of a vertex is

    • the number of paths through it
    • the number of edges incident to it
    • the number of vertices adjacent to all others
    • the sum of the weights of its edges

  7. A path in a graph is a finite sequence of edges in which

    • the start and end vertices coincide
    • every edge is used exactly once
    • every vertex is used
    • no vertex appears more than once

  8. An algorithm takes time proportional to n^2. If the problem size doubles, by roughly what factor does the running time increase?

    • 8 times
    • 16 times
    • 2 times
    • 4 times

  9. A graph has vertex degrees 4, 3, 3, 2 and 2. How many edges does it have?

    • 10
    • 6
    • 14
    • 7

  10. Which degree sequence cannot belong to any graph?

    • 4, 3, 3
    • 2, 2, 2
    • 1, 1, 2
    • 3, 3, 3

  11. How many edges does the complete graph K5 have?

    • 10
    • 5
    • 20
    • 25

  12. An algorithm needs T(n) = 3n^2 + 5n operations for input size n. What is its order?

    • O(n^2)
    • O(n)
    • O(n^3)
    • O(log n)

  13. A list has 6 items. In which position is the middle item, using the usual definition for an even-length list?

    • 6th
    • 4th
    • 3.5th
    • 3rd

  14. Bubble sort is applied to a list of 4 items. How many comparisons are made in the first pass?

    • 4
    • 6
    • 3
    • 2

  15. Algorithm A needs n^2 operations and algorithm B needs 100n operations. For n = 10, which takes fewer operations, and how many does it need?

    • B, with 1000 operations
    • B, with 100 operations
    • A, with 1000 operations
    • A, with 100 operations

  16. For which values of n does algorithm B (100n operations) need fewer operations than algorithm A (n^2 operations)?

    • n > 100
    • n < 100
    • n > 1000
    • n > 10

  17. A tree has 8 vertices. How many edges does it have?

    • 6
    • 8
    • 7
    • 16

  18. Which feature rules out two graphs being isomorphic?

    • one is drawn with crossing edges
    • they have different edge labels
    • they have different vertex names
    • their degree sequences differ

  19. Why is the order of an algorithm more useful than timing it on one computer?

    • It gives the exact time on every computer
    • It counts only comparisons
    • It measures only memory use
    • It describes how running time grows with problem size, independent of hardware

  20. A bubble sort of 20 items needs n(n - 1)/2 comparisons in the worst case. How many comparisons is that?

    • 200
    • 190
    • 380
    • 400

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