A2 June 2025 Q4
4.
[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. The number on each edge represents the length, in metres, of the corresponding corridor.
On Monday morning, Turvi needs to walk from J to K via A. She wishes to minimise the distance she travels along the corridors.
On Monday afternoon, Turvi needs a route that traverses each corridor at least once. She plans to start at J and finish at A and wants to minimise the distance travelled.
Turvi discovers that she cannot walk along corridors AB, CD and JK because they are being decorated. Turvi walks from J to A travelling along all the other corridors at least once. She does this in the minimum distance possible.
| Scheme | Marks | AO |
|---|---|---|
 | M1 A1 (ACBGD) A1 (FKE) A1ft (HJ) | 1.1b 1.1b 1.1b 1.1b |
| (i) Route from J to K via A: JEBCACGFK | A1 | 2.2a |
| (ii) Length of shortest route from J to K via A is 76 (m) | A1ft | 2.2a |
| (6) |
Notes
In (a) it is important that all values at each node are checked very carefully – the order of the working values must be correct for the corresponding A mark to be awarded e.g. at F the working values must be 22 21 18 in that order (so 22 18 21 is incorrect)
It is also important that the order of labelling is checked carefully – some candidates start with a label of 0 at A (rather than 1) – which is fine. Also the order of labelling must be a strictly increasing sequence – so 1, 2, 3, 3, 4,… will be penalised once (see notes below) but 1, 2, 3, 5, 6,… is fine. Errors in the final values and working values are penalised before errors in the order of labelling
If starting at J or K instead of A M0
a1M1: A larger value replaced by a smaller value in at least two of the working value boxes at either B or D or F or H or J or K
a1A1: All values at A, C, B, G and D correct and working values in the correct order. Condone lack of 0 in As working value
a2A1: All values at F, K and E correct and the working values in the correct order. Penalise order of labelling only once per question (F, K and E must be labelled in that order and F must be labelled after A, C, B, G and D)
a3A1ft: All values at H and J correct on the follow through and the working values in the correct order. Penalise order of labelling only once per question. To follow through H check that the working values at H follow from the candidate’s final values from the feeds into H (which will come from nodes D and K (in the order in which the candidate has labelled them)) and that the final value, and order of labelling, follows through correctly. Repeat this process for J (which will possibly have working values from B, E and K with the order of labelling determined by the candidate’s order of labelled at B, E and K)
a4A1: CAO (correct path from J to K via A – JEBCACGFK) (accept in terms of arcs)
a5A1ft: ft their final value at J + their final value at K only (if 76 stated and 76 is not the sum of these final values then A0)
If route and length are written on the wrong lines this can still score both marks
| Scheme | Marks | AO |
|---|---|---|
| (i) BC + D(GF)K = 6 + 18 = 24 | M1 | 3.1b |
| B(FG)D + C(GF)K = 15 + 26 = 41 | A1 | 1.1b |
| B(F)K + C(G)D = 23 + 10 = 33 | A1 | 1.1b |
| Edges to traverse twice are BC, DG, FG, FK | A1 | 2.2a |
| (ii) Length of route = 268 + 24 = 292 (m) | A1ft | 2.2a |
| (5) |
Notes
bi1M1: The correct three pairings of the correct four nodes (B, C, D and K)
bi1A1: Two rows correct including pairings and totals
bi2A1: All three rows correct including pairings and totals
bi3A1: Correct repeats (BC, DG, FG, FK)
bii4A1ft: Length of route correct on the follow through (268 + smallest repeat) but must be from a choice of 3 totals
| Scheme | Marks | AO |
|---|---|---|
| E.g. [ 24 – ] (“45” – 13 – 11 – 16) Or [292 – ] (268 + “45” – (13 + 11 + 16)) | M1 | 3.1b |
| = 19 (m) | A1 | 2.2a |
| (2) | ||
| (13 marks) |
Notes
c1M1: For using their final value at J and the blocked lengths in attempt to work out the length or change in length of the new route (sight of “45” 13 11 and 16) (follow through their final value at J for this mark) (condone use of 40 for 13 + 11 + 16)
c1A1: CAO (19)