2 Nicky, reject Tom, reject 8-9

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1 umber Q cheme () (, ) (, ) () ft cso 4 st + 9 choice = 5 icky, reject - 5 nd choice 6+ 9 = [ 7.5] = 8 om, reject 8-9 rd choice 6+ 7 = [ 6.5] = 7 haron, reject 7 4 th choice 6 aul name found cso 4 otal 8 otes: : quick sort, pivots, p, chosen and two sublists one <p one >p. : first pass correct and next pivots chosen correctly/consistently. ft: second pass correct, next pivots correctly/consistently chosen. : all correct, cso. : binary search on what they think is a alphabetical list, choosing pivot, rejecting half list. : first pass correct, condone sticky pivot here, bod generous : second pass correct, pivot rejected. : cso. ote: If incorrect list in mark as a misread. earson Edexcel International earson Education imited 0 ample ssessment Materials dvanced evel in Mathematics 44

2 M ecision Mathematics Q lternative solutions Middle right Middle left () ( ) ( ) () First () () () () () 444 earson Edexcel International dvanced evel in Mathematics list sorted () ( ) ( ) () ft cso ft cso earson Education imited 0 ft cso ample ssessment Materials

3 umber Q DE GF DC not CE BD cheme EG (not EF not CF) C (not B) G B C D E F G B C D E F G B,, 0 (d) C CD DE BD GE GF G Weight: 74 otes: : Kruskal s algorithm first 4 arcs selected chosen correctly. : ll seven non-rejected arcs chosen correctly. : ll rejections correct and in correct order and at correct time. : condone two (double) errors : cao : rim s algorithm first four arcs chosen correctly, in order, or first five nodes chosen correctly, in order.{,c,d,e,b.} : First six arcs chosen correctly or all 8 nodes chosen correctly, in order. {,C,D,E,B,G,F,} : ll correct and arcs chosen in correct order. (d) : cao otal 9 tarting Minimum arcs required for odes order at C CD DE DB CDEB(GF) 54(768) B BD DE DC BDEC(GF) (7)4(658) C CD DE DB CDEB(GF) (7)4(658) D DE DC DB DECB(GF) (7)4(658) E ED DC DB EDCB(GF) (7)4(658) F FG GE ED DC DB FGEDCB() (7)654(8) G GF GE ED DC DB GFEDCB() (7)654(8) G GF GE GFE(DCB) (8765)4 earson Edexcel International earson Education imited 0 ample ssessment Materials dvanced evel in Mathematics 445

4 umber cheme Q e.g. total weight is 9, lower bound is 9 =.98 so 4 bins. 60 Bin : 4 Bin 4 : 6 Bin : 8 + Bin 5 : Bin : 4 Bin 6: 9 Full Bins : he other items (4, 4, 6) require separate bins (d) here are 5 items over 0. o two of these 5 can be paired in a bin, so at least 5 bins will be required. B,, 0 otal 9 otes: : ny correct statement, must involve calculation : cao (accept 4 for both marks) : Bins and correct and at least 6 values put in bins : Bins,, and 4 correct. : ll correct : ttempt to find two full bins and allocate at least 6 values : cao (d) : Correct argument may be imprecise or muddled (bod gets ) : good, clear, correct argument. (hey have answered the question why? ) Misread in First Fit Decreasing Bin : 4 Bin : 4 Bin : 6 Bin 4: 8 Bin 5: 9 (Remove up to two marks if earned so max in if first 4 bins correct.) 446 earson Edexcel International earson Education imited 0 ample ssessment Materials dvanced evel in Mathematics

5 umber Q4 BC + EG = = 0.5 smallest BE + CG = = 4.4 BG + CE = = 6.8 o repeat tunnels B, C and EG ny route e.g. CFGDCBDEGEB ength = 7. + their 0.5 = 9.8km 5 he new tunnel would make C and G even. o only BE would need to be repeated. Extra distance would be = 8. < 0.5 [9.6 < 9.8] o it would decrease the total distance. D otes: : hree pairings of their four odd nodes : one row correct : two rows correct : all correct 4: correct arcs identified : ny correct route (4 nodes) : 7. + ft their least, from a choice of at least two. : cao : correct explanation, referring to BE and relevant numbers (8.,.,., 8.,8., 9.6) maybe confused, incomplete or lack conclusion bod gets D: correct, clear explanation all there + conclusion (ft on their numbers.) otal 0 earson Edexcel International earson Education imited 0 ample ssessment Materials dvanced evel in Mathematics 447

6 umber Q5 e.g. G = E = 4 = 6 Change status G = E = = 4 = 6 Improved matching = 4 (C unmatched) E = G = = 5 = 6 e.g. Both C and can only be matched to 5 Both and 6 can only be done by B,, 0 C 5 = 4 = = E 6 = Change status C = 5 = 4 = E = 6 = Complete matching = C = 5 E = 6 G = = 4 = otes: : ath from G to 6 or : CO including change status ( stated or shown), chosen path clear. : CO must ft from stated path, diagram ok : Correct answer, may be imprecise or muddled (bod gets ) all relevant nodes should be referred to and must be correct, but condone one (genuine) slip. : Good, clear, correct answer. : ath from C to or 6 [whichever they didn t use before.] : CO including change status ( stated or shown), chosen path clear. (Don t penalise change status twice.) : CO must ft from stated path, diagram ok otal 8 lt G = E = 4 = c.s. G = E = = 4 = = 4, (C unmatched), E =, G =, = 5, = C 5 = 4 = = E 6 c.s. C = 5 = 4 = E = 6 =, C = 5, E = 6, G =, = 4, = 448 earson Edexcel International earson Education imited 0 ample ssessment Materials dvanced evel in Mathematics

7 umber Q6 cheme ft Route: BEF ime: 87 minutes ft 6 ccept demonstration of relevant subtractions, or general explanation. Bft,ft, 0 Route: EF otal 9 otes: : maller number replacing larger number in the working values at C or D or G or or. (generous give bod) : ll values in boxes,, B, E and F correct ft: ll values in boxes C and D (ft) correct. enalise order of labelling errors just once. : ll values in boxes G, and correct : CO (not ft) ft: Follow through from their value, condone lack of units here. ft: artially complete account, maybe muddled, bod gets ft: Complete, clear account. : CO earson Edexcel International earson Education imited 0 ample ssessment Materials dvanced evel in Mathematics 449

8 umber Q7 o indicate the strict inequality cheme x = and 5x + 4 = 80 added to the diagram. R correctly labelled., (d) [Minimise C =] 500x oint testing or rofit line eeking integer solutions (, 7) at a cost of 00.,, 5 otal 450 earson Edexcel International earson Education imited 0 ample ssessment Materials dvanced evel in Mathematics

9 otes: : CO : x = passing through small square of (0,0) and (, 8), but must reach x = 5 : 5x+ 4 = 80 passing through small square of (0, 0) and (6, 0) (extended if necessary) but must reach y = 6 : R CO (condoning slight line inaccuracy as above.) : ccept expression and swapped coefficients. ccept 5x + 8y for mark : CO (expression still ok here) (d) : rofit line [gradient accept reciprocal, minimum length line passes through (0,.5) (4, 0)] OR testing points in their FR near two different vertices. : Correct profit line OR points correctly tested in correct FR (my points) e.g (7,0 ) = 6 or (7,) = (8,0) = 000 (8,) = 800 (, 6) = or (,6) = 0 00 (5, 6) = 00 or (5, 7) = 00 (5, ) = or (5, ) = 5 00 (, 7) = 00 : eeking integer solution in correct FR (so therefore no y = 6 points) : (,7) CO : 00 CO earson Edexcel International earson Education imited 0 ample ssessment Materials dvanced evel in Mathematics 45

10 umber Q8 cheme 4 () Critical activities: C E 4 (d) 4 workers needed e.g. at time 8 ½ (noon on day 9) activities E, D, F and G must be happening. B,, 0 otal 45 earson Edexcel International earson Education imited 0 ample ssessment Materials dvanced evel in Mathematics

11 otes for Q8 : op boxes completed generally increasing left to right. : CO. : Bottom boxes completed generally decreasing right to left. : CO. : Critical activities cao. : t least 0 activities placed, at least five floats. cheduling diagram gets M0. : my critical activities correct. : condone one error on my non-critical activities. : my non-critical activities correct. (d) : correct statement, details of either time (7<time<9, 8<day<0), or activities, bod gets. llow B mark (only) on ft from their activity, 7 float diagram. : correct, complete full statement details of time and activities. earson Edexcel International earson Education imited 0 ample ssessment Materials dvanced evel in Mathematics 45

Mark Scheme (Final) January 2009

Mark Scheme (Final) January 2009 Mark (Final) January 2009 GCE GCE Decision Mathematics D1 (6689/01) Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH General Marking Guidance