D1 June 2014 Q5
5.
Sharon is planning a road trip from Preston to York. Figure 2 shows the network of roads that she could take on her trip. The number on each arc is the length of the corresponding road in miles.
Sharon has a friend, John, who lives in Manchester (M). Sharon decides to travel from Preston to York via Manchester so she can visit John. She wishes to minimise the length of her route.
| Scheme | Marks |
|---|---|
 | M1 A1 (PBCAW) A1 (HMS) A1ft (LY) |
| Shortest route: P – B – A – S – L – Y Length: 89 (miles) | B1 B1ft |
| (6) |
Notes
In part (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 L the working values must be 70 69 68 – in that order (70 68 69 is incorrect).
The values in brackets in the working values at P, A, H and L can be ignored but if a candidate does have additional values at these nodes then they must be these ones only. Penalise any other/incorrect working values with the corresponding A mark. It is also important that the order of labelling is checked carefully – some candidates start with a working value of 0 at P (rather than 1) – this 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.
a1M1 A larger value replaced by smaller value at least once in the working values at either A or M or L or S or Y.
a1A1 All values in P, B, C, A and W correct. The working values at A must be in the correct order. Condone lack of 0 in P’s working value. Ignore additional working value of 30 at the end of A (may read 20 16 30 – rather than 20 16 - at A).
a2A1 All values in H, M and S correct and the working values in the correct order. Penalise order of labelling only once per question (H, M and S labelled in that order and H must be labelled after P, B, C, A and W). Ignore additional working value of 33 at the end of H (may read 27 33).
a3A1ft All values in L and Y correct on the follow through and the working values in the correct order. Penalise order of labelling only once per question (L and Y labelled in that order and L labelled after all other nodes). Ignore additional working value of 81 at L - may read 70 69 81 68 – rather than 70 69 68 – which is fine – however, 70 69 68 81 is incorrect and loses this mark.
To follow through check that all the working values at L follow from the candidate’s final values from nodes A, H, M and S in whatever order the candidate has labelled these four nodes and that the final value and order of labelling follows through correctly. Repeat for Y (which will have working values from S and L).
a1B1 CAO for the route
a2B1ft Follow through on their final value at Y – if answer is not 89 ft their final value at Y (condone lack of units)
| Scheme | Marks |
|---|---|
| Shortest route: P – C – H – M – L – Y | B1 |
| Difference in routes: (41 + 40 + 21) – 89 = 13 (miles) | M1 A1 |
| (3) | |
| (9 marks) |
Notes
b1B1 CAO for the route
b1M1 Their final value at M + 40 + 21 - accept a value of 102 (with no other working) for this mark.
b1A1 CAO (condone lack of units) – accept, as a minimum,102 followed by 13 for both marks. If 13 with no working then award the previous M mark but withhold the final A mark