A2 June 2019 Q2
2.
[The total weight of the network is 370]
Figure 1 represents a network of corridors in a building. The number on each arc represents the length, in metres, of the corresponding corridor.
On a particular day, Naasir needs to check the paintwork along each corridor. Naasir must find a route of minimum length. It must traverse each corridor at least once, starting at B and finishing at G.
On a different day, all the corridors that start or finish at B are closed for redecorating. Naasir needs to check all the remaining corridors and may now start at any vertex and finish at any vertex. A route is required that excludes all those corridors that start or finish at B.
| Scheme | Marks | AO |
|---|---|---|
 | M1 A1 A1 A1ft | 1.1b 1.1b 1.1b 1.1b |
| Path from A to D is AFGJD | A1 | 2.2a |
| Length of path from A to D is 78 metres | 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 H the working values must be 81 77 74 in that order (so 81 74 77 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
(a) M1: A larger value replaced by a smaller value in at least two of the working boxes at either C or D or E or G or J
A1: All values in A, B, F and E correct. Condone lack of 0 in A’s working value
A1: All values G, C and J correct and the working values in the correct order. Penalise order of labelling only once per question (G, C and J must be labelled in that order and G must be labelled after A, B, F and E). Note that an additional working value of 63 at G after the 54 is not an error so 54 63 is fine, however, any other number or 63 54 in this order is incorrect and scores A0 in this part
A1ft: All values in H and D 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 value at H follows from the candidate’s final values from their feeds into H (which will come from nodes F, G and/or J (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 D (which will possibly have working values from B and J with the order of these values determined by the candidate’s order of labelling at B and J)
A1: CAO - correct path from A to D (AFGJD)
A1ft: ft their final value at D only (if 78 stated and 78 is not the final value at D then A0)
| Scheme | Marks | AO |
|---|---|---|
| A(FG)C + E(J)H = 61 + 23 = 84 A(B)E + C(GJ)H = 53 + 27 = 80* A(FGJ)H + C(G)E = 74 + 17 = 91 | M1 A1ft A1 | 3.1b 1.1b 1.1b |
| Repeat arcs: AB, BE, CG, GJ and JH | A1 | 2.2a |
| (4) |
Notes
(b) M1: correct three pairings of the correct four odd nodes (A, C, E and H)
A1ft: any row correct including pairing and total (ft the final values from (a) for their shortest paths from A to the three other nodes C, E or H only (so the pairing that does not include A must be correct))
A1: all three rows correct including pairings and totals
A1: selecting the shortest pairing, and stating that these arcs (AB, BE, CG, GJ and JH) should be repeated. Must be these arcs and not e.g. ABE, CGJH or AE via B, etc.
| Scheme | Marks | AO |
|---|---|---|
| Length of the route is 370 + 80 = 450 metres | B1ft | 2.2a |
| (1) |
Notes
(c) B1ft: For 370 + their smallest repeat out of a choice of at least two totals seen in (b) – this mark is dependent on M1 in (b)
| Scheme | Marks | AO |
|---|---|---|
| (i) If node B is removed this makes D, C, G and H odd | M1 | 3.1b |
| The shortest path between any two odd nodes is CG (so repeat CG) so the route should start at D and finish at H (or vice-versa) | A1 | 2.2a |
| (ii) Length of new route is 370 – 38 – 42 – 15 + 7 = 282 metres | B1 | 2.2a |
| (3) | ||
| (14 marks) |
Notes
(d) M1: Mention of the fact that these four nodes D, C, G and H only are now odd or clear consideration of these four nodes only
A1: CAO D and H and must have clearly indicated that the shortest path is from C to G (or vice-versa) – but A0 if clearly selecting the shortest pairing first before selecting the shortest path (as the shortest path is embedded in the shortest pairing)
B1: CAO (282)