Shortest paths: Edexcel A‑Level Further Maths questions

Edexcel A-Level Further Maths past-paper questions on 2.3 Shortest paths, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 16 questions on Shortest paths, as a list

June 2025, Decision 1, Q3 (10 marks): A G F E D C B 17 40 9 11 12 14 11 31 25 8 24 47 35 35 Figure 1 Direct roads between seven villages, A, B, C, D, E, F and G, are represented in Figure 1. The wei
June 2025, Decision 1, Q4 (13 marks): Figure 2 [The total weight of the network is 268] Figure 2 represents a network of corridors between 10 offices, A, B, C, D, E, F, G, H, J and K, in a building.
June 2025, AS Decision 1, Q3 (14 marks): 3 10 3 8 12 6 9 8 4 6 9 2 4 10 15 14 30 3 E G H D B A C F J Figure 2 [The total weight of the network is 153] Figure 2 models a network of roads in a town, wher
June 2024, Decision 1, Q3 (13 marks): A B 25 47 24 5 17 18 20 34 26 4 12 37 41 25 27 15 21 9 6 E C D F G H J K Figure 1 [The total weight of the network is 413] Figure 1 represents a network of cycl
June 2023, Decision 1, Q1 (7 marks): A B D C E Figure 1 Figure 1 shows the graph G. (a) State whether G is Eulerian, semi-Eulerian, or neither, giving a reason for your answer. (1) (b) Write down a
June 2023, Decision 1, Q3 (8 marks): A D G B E H C F J 32 37 22 34 32 35 41 23 7 7 8 43 45 50 28 21 11 10 30 42 Figure 4 Figure 4 represents a network with nodes, A, B, C, D, E, F, G, H and J. The
June 2023, AS Decision 1, Q3 (11 marks): A D G J B E H C F 50 61 23 34 41 24 49 15 43 11 32 45 28 40 58 6 6 30 Figure 2 Figure 2 represents a network of train tracks. The number on each edge represents
June 2022, Decision 1, Q2 (13 marks): A B C D E F 10 10 10 31 17 6 G H J K 23 25 8 14 14 18 9 3 4 16 23 33 25 Figure 1 [The total weight of the network is 299] Figure 1 represents a network of cycle
June 2022, Decision 1, Q3 (10 marks): The initial distance matrix (Table 1) shows the lengths, in metres, of the corridors connecting six classrooms, A, B, C, D, E and F, in a school. For safety rea
June 2022, AS Decision 1, Q3 (14 marks): A C B D E F 4 G H 10 12 7 15 13 3 8 11 6 4 5 10 12 Figure 2 [The total weight of the network is 120] (a) Explain what is meant by the term “path”. (2) (b) State
November 2021, Decision 1, Q4 (8 marks): 150 191 230 63 57 95 72 289 84 D E A B C 160 F 125 132 Figure 3 [The total weight of the network is 1648] Direct roads between six cities, A, B, C, D, E and F,
November 2021, Decision 1, Q6 (10 marks): A B C D E F G H 32 33 75 16 50 17 15 95 30 41 25 10 50 70 105 113 Figure 4 In Figure 4 the weights on the arcs represent distances. (a) (i) Use Dijkstra’s algor
November 2020, Decision 1, Q3 (9 marks): A B C D E 1 7 8 3 6 4 10 1 Figure 2 Direct roads between five villages, A, B, C, D and E, are shown in Figure 2. The weight on each arc is the time, in minutes,
June 2019, Decision 1, Q2 (14 marks): H C G E J D B A F 38 75 42 15 10 42 20 12 10 17 14 23 6 39 7 Figure 1 [The total weight of the network is 370] Figure 1 represents a network of corridors in a b
June 2019, Decision 1, Q3 (14 marks): A B C D E 15 5 7 3 3 9 18 4 Figure 2 The network in Figure 2 shows the direct roads linking five villages, A, B, C, D and E. The number on each arc represents t
June 2019, AS Decision 1, Q4 (10 marks): B A C D E F G H 10 17 12 16 13 25 3x + y x + y 9 5 9 7 7 3 2 Figure 1 [The total weight of the network is 135 + 4x + 2y] The weights on the arcs in Figure 1 rep

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