D1 January 2013 Q4
4.
Figure 4 represents a network of canals. The number on each arc represents the length, in miles, of the corresponding canal.
Next week the canal represented by arc AB will be closed for dredging.
| Scheme | Marks |
|---|---|
| A path is a (i) finite sequence of edges, such that (ii) the end vertex of one edge in the sequence is the start vertex of the next, and in which (iii) no vertex appears more than once. | B2, 1, 0 |
| (2) |
Notes
a1B1 One of the three points made clearly or two suggested. Arcs (edges)/ vertices (nodes) must be referred to correctly. Do not condone incorrect technical language e.g. point for vertex.
a2B1 All three points made clearly.
| Scheme | Marks |
|---|---|
 | M1 A1 (S,A, B, C) A1ft (D, F) A1 (E, T) |
| Shortest path: SBADET Length: 40 (miles) | B1 B1ft |
| (6) |
Notes
b1M1 A larger value replaced by a smaller value at least once at A or D or E or F or T.
b1A1 All values in S, A, B and C correct. The working values at A must be in the correct order. Condone lack of 0 in S’s working value.
b2A1ft All values in D and F ft correctly and working values in the correct order. F must be labelled before E but penalise order of labelling only once per question.
b3A1 All values in E and T correct and working values in the correct order. Penalise order of labelling only once per question.
b1B1 Route CAO
b2B1ft Their final value ft (if answer is not 40 ft their final value at T)
| Scheme | Marks |
|---|---|
| Shortest distance S to F = 29 (miles) | B1ft |
| (1) |
Notes
c1B1ft Their final value ft (if answer is not 29 ft their final value at F)
| Scheme | Marks |
|---|---|
| SADET or SCDET; of length 41 (miles) | B1 B1 |
| (2) | |
| (11 marks) |
Notes
d1B1 Either route CAO
d2B1 Length CAO (condone lack of (or incorrect) units throughout)