plumiGraphs and networks: OCR MEI A‑Level Further Maths questions
Every OCR MEI A-Level Further Maths exam question on D.2 Graphs and networks, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 AS Modelling with Algorithms, question 4: (a) Determine the number of nodes in the complete graph with 1431 arcs. [2] (b) In this question you must show detailed reasoning. A simply connected graph G ha](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y41301-jun25-04-qp.webp?v=3)
![June 2024 AS Modelling with Algorithms, question 1: Fig. 1 shows a graph. Fig. 1 A B E C D (a) (i) State the order of node B. [1] (ii) State the order of node D. [1] (b) Complete the incidence matrix for the grap](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y41301-jun24-01-qp.webp?v=3)
![June 2022 AS Modelling with Algorithms, question 1: (a) (i) State the number of arcs in the complete graph with 6 nodes. [1] (ii) State the minimum number of arcs in a simply connected graph with 6 nodes. [1] (b)](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y41301-jun22-01-qp.webp?v=3)
![November 2020 AS Modelling with Algorithms, question 4: (a) Draw an example of a simply connected graph with five nodes of orders 1, 1, 2, 2 and 4. [1] (b) A simply connected graph G has seven nodes. (i) Write down t](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y41301-nov20-04-qp.webp?v=3)
All 20 questions on Graphs and networks, 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, Q1 (4 marks): A network has ten vertices, A to J. The table shows the distances between each pair of vertices for which there is a connecting arc. A B C D E F G H I J A 12 6
- 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 2025, AS Modelling with Algorithms, Q4 (8 marks): (a) Determine the number of nodes in the complete graph with 1431 arcs. [2] (b) In this question you must show detailed reasoning. A simply connected graph G ha
- 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, Q1 (5 marks): Fig. 1 shows a graph. Fig. 1 A B E C D (a) (i) State the order of node B. [1] (ii) State the order of node D. [1] (b) Complete the incidence matrix for the grap
- 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, Modelling with Algorithms, Q3 (11 marks): A directed network consists of eight nodes, A–H, and fifteen arcs. A shortest path from A to H needs to be found for this network. The objective for an LP formu
- 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, Q1 (4 marks): (a) (i) State the number of arcs in the complete graph with 6 nodes. [1] (ii) State the minimum number of arcs in a simply connected graph with 6 nodes. [1] (b)
- 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, Q4 (7 marks): (a) Draw an example of a simply connected graph with five nodes of orders 1, 1, 2, 2 and 4. [1] (b) A simply connected graph G has seven nodes. (i) Write down t
- 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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