D1 June 2013 (R) Q5
5.
[The total weight of the network is 181 miles]
Figure 4 represents a network of power cables that have to be inspected. The number on each arc represents the length, in km, of that cable.
A route of minimum length that traverses each cable at least once and starts and finishes at A needs to be found.
It is now decided to start and finish the inspection route at two distinct vertices. The route must still traverse each cable at least once.
| Scheme | Marks |
|---|---|
| AF + GH = 15 + 31 = 46* | M1 |
| AG + FH = 32 + 15 = 47 AH + FG = 30 + 17 = 47 | A3,2,1.0 |
| so repeat arcs AB, BF and GH | A1 |
| (5) |
Notes
a1M1 Three distinct pairings of their four odd nodes
a1A1 Any one row correct including pairing and total
a2A1 Any two rows correct including pairing and total
a3A1 All three rows correct including pairing and total
a4A1 CAO correct arcs identified AB, BF and GH. Accept ABF or AF via B (check to see if via B appears in working) but do not accept AF for this mark
| Scheme | Marks |
|---|---|
| E.g. ABCDBFDEHGFHGAFBA (17 nodes) | B1 |
| length = 181 + 46 = 227 | B1 ft |
| (2) |
Notes
b1B1 Any correct route (checks: 17 nodes, the route starts and ends at A, pairings AB, BF and GH appear twice in the route and every letter from A to H (inclusive) appears at least once).
b2B1ft correct answer of 227 or 181 + their least out of a choice of at least two totals given in part (a)
| Scheme | Marks |
|---|---|
| One path will have to be repeated. The shortest is 15 | M1 |
| So repeat AF, use G and H as the start and finish. or repeat FH, use A and G as the start and finish. | A1A1 |
| (3) | |
| (10 marks) |
Notes
c1M1 Identifies need to repeat one pairing (maybe implicit) and 15 (or either AF or FH) specifically identified as the least
c1A1 Repeat (either AF or FH) identified clearly
c2A1 G and either A or H identified as start and finish.