plumiShortest paths: OCR MEI A‑Level Further Maths questions
OCR MEI 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.
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All 14 questions on Shortest paths, as a list
- June 2025, Modelling with Algorithms, Q5 (13 marks): The diagram shows a network. The weights on the arcs are distances. B A 15 19 C 37 29 29 48 8 F 2 6 20 G E D 11 37 30 H 3x 60 x I The weight of arc HI is x and
- June 2025, AS Modelling with Algorithms, Q3 (7 marks): The diagram shows a network of roads. The number on each arc represents the length, in miles, of the corresponding road. E F 77 24 14 10 11 12 65 29 34 A G D 50
- June 2024, Modelling with Algorithms, Q2 (12 marks): The table shows the distance, in kilometres, along the direct roads between eight towns, A to H. A dash (-) indicates that there is no direct road linking the t
- June 2024, AS Modelling with Algorithms, Q5 (15 marks): The objective function for a LP formulation to find the shortest path from A to G in a network with seven vertices, A, B,…, G is given below. Minimise 5AB + 13A
- June 2023, AS Modelling with Algorithms, Q2 (10 marks): The journey times (in minutes) between eight towns, A, B, …, H, for which there is a direct route are given in the table in Fig. 2. Fig. 2 A B C D E F G H A – 2
- June 2022, Modelling with Algorithms, Q6 (11 marks): Fig. 6.1 shows a weighted graph. The weights represent arc lengths. A 15 32 B 16 11 29 C 10 20 D 12 37 17 8 6 F E 16 7 G Fig. 6.1 (a) Apply Dijkstra’s algorithm
- June 2022, AS Modelling with Algorithms, Q3 (10 marks): In Fig. 3 the weights of the arcs represent distances. A 10 H 50 9 20 G B 85 31 7 23 42 5 37 14 C D F 29 6 E Fig. 3 Dijkstra’s algorithm is to be used once to f
- November 2021, Modelling with Algorithms, Q3 (13 marks): A vertex of a graph for which the order is an odd number is called an odd vertex. (a) (i) By considering the number of arc endings for a general graph, explain
- November 2021, AS Modelling with Algorithms, Q5 (16 marks): An LP formulation to find the shortest path from A to G in a directed network with seven vertices, A, B, …, G is given below. Minimise 15AB + 28AC + 31AD + 17BE
- November 2020, Modelling with Algorithms, Q2 (10 marks): The table in Fig. 2 shows the distances, in miles, along the direct roads between ten villages, A to J. A dash (–) indicates that there is no direct road linkin
- November 2020, AS Modelling with Algorithms, Q6 (8 marks): Fig. 6 shows a network. 6 54 3 24 56 54 24 B D G 8 70 77 70 5 42 A 1 0 52 50 47 42 E 7 63 H 70 63 C F 2 15 4 32 15 32 Fig. 6 Dijkstra’s algorithm has been appli
- June 2019, Modelling with Algorithms, Q1 (11 marks): Fig. 1 shows a network. The weights on the arcs are distances. 35 D 25 A 4 6 17 9 E 11 G 6 8 13 13 7 B F 12 14 10 C 18 H Fig. 1 (a) Apply Dijkstra’s algorithm t
- June 2019, AS Modelling with Algorithms, Q3 (10 marks): A network has 9 vertices, A to I. The table in Fig. 3 shows the distance between each pair of vertices for which there is a connecting arc. A B C D E F G H I A
- June 2018, AS Modelling with Algorithms, Q1 (11 marks): Fig. 1 shows a network. The weights on the arcs are distances. B F 14 2 I 7 10 11 21 G 13 C 4 15 8 17 E 2 A 12 19 10 D H Fig. 1 (i) Apply Dijkstra’s algorithm t
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