D1 June 2016 Q4

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 50 49 48 in that order (50 48 49 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

a1M1: A larger value replaced by smaller value at least once in the working values at either D or F or G

a1A1: All values at A, B, E, C and K correct. Condone lack of 0 in A’s working value – please check carefully for a 5 in the working values at B

a2A1: All values at D, J and H correct and the working values in the correct order. Penalise order of labelling only once per question (D, J and H must be labelled in that order and D must be labelled after A, B, E, C and K)

a3A1ft: All values in G and F correct on the follow through and the working values in the correct order. Penalise order of labelling only once per question (G and F must be labelled in that order and G labelled after all other nodes (excluding F)). Note that an additional working value of 54 at G inbetween the 47 and 46 is not an error (it is the working value from J into G) so 49 48 47 54 46 is fine, however, any other number or the 54 not in this position is incorrect and scores A0 in this part

To follow through G check that all the working values at G follow from the candidate’s final values from nodes E, K, D, J and H (in the order that the candidate has labelled these five nodes) and that the final value, and order of labelling, follows through correctly. Repeat this process for F (which will have working values from D, J and G)

a4A1: CAO for the path (from either A to F or F to A)

a5A1ft: If their answer is not 48 follow through their final value at F (condone lack of units)

Notes

b1B1: CAO (shortest path via J)

b2B1: CAO (length of shortest path)

Notes

c1M1: First four arcs correctly chosen in order (GF, GH, FJ, DG) or first five nodes correctly chosen in order (G, F, H, J, D). If any explicit rejections seen at any point then M1 (max) only. Do not accept only a list of weights for this mark. Candidates may apply Prim in matrix form so the order of the nodes may be seen at the top of a matrix – accept {-, -, -, 5, -, 2, 1, 3, 4, -} for the M mark

c1A1: First seven arcs correctly chosen in order (GF, GH, FJ, DG, JK, EK, BE or GF, GH, FJ, DG, CD, JK, EK) or all ten nodes correctly chosen in order (G, F, H, J, D, K, E, B, A, C or G, F, H, J, D, C, K, E, B, A) Candidates may apply Prim in matrix form so the order of the nodes may be seen at the top of a matrix – accept {9, 8, 10, 5, 7, 2, 1, 3, 4, 6} or {10, 9, 6, 5, 8, 2, 1, 3, 4, 7} – do not condone any missing numbers e.g. the number 10 must be above either the C or the A

c2A1: CSO – all arcs correctly stated and chosen in the correct order. Candidates must be considering arcs for this final mark (do not accept a list of nodes or numbers across the top of the matrix unless the correct list of arcs (in the correct order) is also seen)

Notes

d1B1: CAO (condone lack of units)