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Mark Scheme Summer 2007IGCSEIGCSE Mathematics (4400)Edexcel Limited. Registered in England and Wales No. 4496750Registered Office: One90 High Holborn, London WC1V 7BH

Edexcel is one of the leading examining and awarding bodies in the UK and throughout the world. Weprovide a wide range of qualifications including academic, vocational, occupational and specificprogrammes for employers.Through a network of UK and overseas offices, Edexcel’s centres receive the support they need tohelp them deliver their education and training programmes to learners.For further information please call our Customer Services on 44 1204 770 696, or visit our website atwww.edexcel-international.org.Summer 2007All the material in this publication is copyright Edexcel Ltd 20072

Contents1.4400/1F5 – 122.4400/2F13 – 203.4400/3H21 – 324.4400/4H33 – 403

4

4400 IGCSE MathematicsSummer 2007Paper 1FQ1.Working(ai)(ii)(b)(c)AnswerMark8 forA1cao40100,2050etcTotal 5 marks2.(ai)(ii)(b)(c)(d)(ei)(ii)(1,5)(5,0)648(0) 2 “64”204-212 incisosceles77acute21212B1B1B1M1A1B1B1B1Allow 2mmAlso award for 20.4-21.2ft from “64”Allow 2Total 8 marks5

ocaoTotal 7 marks4.5.(a)(b)(c)(d)(e)31eg “Add 6”61289eg “Sum of two odd numbers is always B1B1B1B11caocaoft from (b)Accept if ‘odd’ used correctlyTotal 5 markscaocaocaocaocaoTotal 5 marks6

li100 bar 150300 : 12511112B1B1B1B1M12A1M112 : 5(f)70 330100231(g)caofor 300:125, 60:25also for 125 : 300, 25 : 60, 5 : 12A12143 100332Notes43.1M1A1143or 0.430722 332for 43.1 or betterforTotal 10 marks7.(a)2x 1 9(b)5y 2y 7 42 4 oe211,3233 oe7M1A1M1A1Also accept 2 or more d.p. roundedor truncated e.g. 3.66, 3.67Total 4 marks

Q8.Working(ai)(ii)(b)(c)(di)(ii)AnswerMark1 pm10 pm 6Rio de tAcceptAccept13002200“Rio” 7 5Total 6 marks9.(a)(b)(c)(d)207 4 (5 2)54.8722.61111B1B1B1B1caocaocaoTotal 4 marks10.(i)(ii)(iii)y 3x 53y xB1B1B1Total 3 marks11.(a)68.899.17.5703 7.57(b)82M1for 8.3, 68.89, 9.1 or 30.90 1A1B1Accept if first 5 figures correctft from (a) if non-trivialTotal 3 marks

Q12.WorkingAnswerMark(a)1535(b)(c)1B1Accept 0.2, 20%2M1for fraction with denominator 5A1for235150 “ ”9013.(a)228 15420rectangle 5.6 cm long and 3 cm wide(b)Notes235Accept 0.6, 60%M13590150Total 5 marksA1ft from “ ” Do not acceptM1A1B2caoB1 for each Allow 2mmTotal 4 marks14.(a)( 3)2 5 3224(b)x( x 5)29M1A1B2for substn or 9 or 15 seecaoB1 for factors which, when expandedand simplified, give two terms, one ofwhich is correctSC B1 for x(5 x), x(x 5x)Total 4 marks

Q15.Working(a)(b)AnswerMark4751 46125(c)346 3 47 6 48 3 49 5 50 2 51 1 or138 282 144 245 100 51or 960“960” 2048NotesB1M1A1M1caofor 51 46, 46-51 etccaofor finding at least 4 products andaddingM1A1(dep) for division by 20caoTotal 6 marks16.(a)translation 3 squares to the right and 1 square down2B2B1 for translationAccept translate,translated etcAccept ‘across’instead of ‘to theright’B1 for 3 right and1 down or(b)rotation of 90 clockwise about (2, 1)3B3These marks areindependent butaward no marksif answer is nota singletransformation 3 1 but not (3, 1)B1 for rotationAccept rotate,rotated etcB1 for 90 clockwiseor 90 or 270 B1 for (2, 1)Total 5 marks10

Q17.Working(ai)(ii)(b)AnswerMark78569 4 n 8 or 13 n 822518.(a)(b)12 x 15 8 x 44 x 192y 3y 8y 245p 3 4 p11M1A1M1caocaoAlso award for 2n 5, 2n 32or 25 on answer linecaoTotal 4 marksfor at least 3 terms correctfor 3 terms correct or y2 11y seenA1y 2 11 y 24(c)B1B1M1A122Notes2B2cao B1 for either 5p 3 or for 4pTotal 6 marks

WorkingQ19.(a)AnswerMark338.538.521 60 or 0.35 ;0.356021NotesM1M1110(b)2π 4.19 385002 120 0003A1M2A138.5or 1.8333 2138.521oror 183.33 oror 0.350.216038.5for ‘1.8333 ’ 60 or'0.35'caoM1 for π (no with digits 419)2 no with digits 385for 2 120 000 or for answer whichrounds to 2 120 000(π 2123433.4193.14 2122356.9293.142 2123708.749)Total 6 marksforPAPER TOTAL 100 MARKS12

4400 IGCSE MathematicsSummer 2007Paper 2FQ1.Working(ai)(ii)(iii)(bi)(ii)AnswerMark199, 999, 1009, 1999, 90009000999 or 90004321124311112NotesB1B1B1B1B23B1 for begin with 1 or end with 1 orTotal 6 marksA at 0.5 2mmB at 1C at 2 d 25mm from 02.111B1B1B1ie between 0 & 0.25 exclusiveTotal 3 smisspellingsmisspellingsTotal 4 marks13

Q4WorkingAnswerMark213(a)(b)(c)397040006315.83289 15.8(d)(e)(fi)(ii)1111111NotesB1B1B1B1B1B1B1or 3000 or 3 thousandor 1000 or thousandsftTotal 7 marks5(a)4 5 222(b)228 / 472M1A1M1A1Allow 30/4 or ans 7.25 oeTotal 4 marks612(a)(b)(c)3/36/1011B1B1M1Attempt convert all to dec or % or c. d.All correctly converted9/253M1A1Total 5 marks14

QWorking7Answer2 1.10 3 1.2510.00 – “5.95”Markor 5.954.053NotesM1M1A1depTotal 3 marks8(a)(b)(c)(di)(ii)Σx attempted/8Arrange in order735.5 oeSameMiddle unchanged211B1M1eg 48.125M1 depA1M1 or answer 5 or 6A1B1indepB1or still 5.5oe2B1 num6cm2Triangle correct 2 mm32or 56(e)9(a)(b)2/815B1 denomRatio subtr B1Total 3 marksB2 B1 for 5 to 7 inclB1B2 B1 for a vertex correct 2 mmor correct size & orientation 2 mmTotal 5 marks

Q10Working(a)(6 3) 5(b)70/5(-3)(c)-85/5 – 3AnsweroeM1 Bracket essential unless ans correctA1M1 Allow 67/5 or 13.22112-205(x 3) or (x 3) 5or 5x 15 oe2A1M1A12B213040 sum of triangle111B1B1B1or -17 – 3(a)(bi)(ii)Notes45or 14(d)11MarkB1 for answer x 3 5.B0 for answer 5x 3 or x 15‘x ’ subtract B1Total 8 marksNot 180 – (90 50)Total 3 marks12(a)2(b)0.85 x “1920” oe/5x48001920216322Allow 0.85 x 4800 oeTotal 4 marks13(i)(ii)26x 21 or 6x – 21 0 etcx 2x 1 3x - 5 171x 3.5 oe eg 21/6216B1 oe eg 6x – 4 17 ISW not ‘ p’M1 ft (i) if 6x cA1Total 3 marks

QWorking14Answer9 seen7/9 27or 7 27/9Markoe211535x – 20 355x 55113NotesB1M1 dep B1A121 seen, & ans 3 B1M1A0Total 3 marksM1M1depA1or M2 for x – 4 7Total 3 marks16(a)(b)7 502175200 or 1002B1 for 7 and 2B1 for 50M1 (6or7) (48or50) correctly eval’d2 or 3eg 168A1fIf no wking: ft (a)Num incr or 6.8 & 47.6 incrdenom decr or 2.09 decr(b) rnded up (not rnd to 1 sf)or ‘175’ rnded to 2002B2 any two of theseB1 any one of theseor 7, 50, 22(c)Ignore otherTotal 6 marks17(a)(b)(2 3)/2 6 or 2 6 1/2 6 1 oe15/20 10001000 / 20 1515275031000 15/ 20M1A1M1 or 0.75M1A1ft ‘15’ for M1M1 onlyTotal 5 marks17

QWorking18Answerx 3 7x(6x 3 oe)MarkNotesM1 y 7(y-3) y 7y-217y 7x 21(6y 21)x 1/2, y 31/230 6x -3A1A1Total 3 marks19(a)tan usedtan x 5.1/4.2 or tanx 1.2 . oe(b)sin 29 AB/5AB 5sin 29or c/sin29 5/sin903x 50.5 AB 2.42. cm20(a)(b)(c)1 – (0.1 0.2 0.1)0.2 0.13M1 (sin or cos) & ( (4.22 5.12) or 6.6) usedM1 sinx 5.1/ (4.22 5.12) or cosx 4.2/ (4.22 5.12)A1M1BC 5cos29M1AB (52 (5cos29)2) or 5cos29 tan29A1Total 6 marks0.62M1 or 0.6 in tableA1 allow in table if not contrad on line0.32M1A1or 1 – 0.4 oeor 1 – (‘0.6’ 0.1)(Poss) overlap or mut exclor doesn’t wk for B or Y }No or poss or poss yes }B2218or 0.3 seenCan’t tell & (No or poss) B1Correct reason only: B1Incorrect reason: B0Unqualified Yes: B0Total 6 marks

Q21Working42 62 (42 62)AnswerMarkNotes3M1M1depA1( 52)or “52”or 2 13h 7.21 .Total 3 marksPAPER TOTAL 100 MARKS19

20

4400 IGCSE MathematicsSummer 2007Paper 3HQ1.Working(a)AnswerMark268.899.17.5703 NotesM1for 8.3, 68.89, 9.1 or 30.90 A1Accept if first 5 figures correctAlso accept 7(b)2.(a)7.57( 3)2 5 3x( x 5)3.46 3 47 6 48 3 49 5 50 2 51 1or 138 282 144 245 100 51or 960“960” 2048,68899101B1ft from (a) if non-trivial ie (a) musthave more than 2 d.p.Total 3 marks22M1A1B2for substn or 9 or 15 seencaoB1 for factors which, when expandedand simplified, give two terms, one ofwhich is correctSC B1 for x(5 x) and for x(x 5x)Total 4 marks3M1for finding at least 4 products andaddingM1A1(dep) for division by 20cao24(b)519910Total 3 marks21

Q4.Working(a)AnswerMarktranslation 3 squares to the right and 1 square down2NotesB2B1 for translationAccept translate,translated etcB1 for 3 right and1 down (accept‘across’ instead of‘to the right’) or 3 1 but not (3, 1)(b)rotation of 90 clockwise about (2, 1)3B3These marksareindependent butaward no marksif answeris not a singletransformationB1 for rotationAccept rotate,rotated etcB1 for 90 clockwiseor 90 or 270 B1 for (2, 1)Total 5 marks5.(ai)(ii)(b)78569 4 n 8 or 13 n 8225B1B1M1A1caocaoAlso award for 2n 25or 25 on answer linecaoTotal 4 marks22

Q6.Working(a)12 x 15 8 x 4(b)y 3 y 8 y 24AnswerMark2M1for at least 3 terms correct inc signs2A1M1caofor 3 terms correct or y2 11y seen4 x 192A1y 2 11y 24(c)7.(a)5p3 4 p2138.538.5 60 or 0.35 ;21600.35Notes2B23M1M1110(b)π 4.19 3850022 120 000233A1M2A1cao B1 for either 5p 3 or for 4 pTotal 6 marks38.5or 1.83 or better2138.5oror 183.3 or better0.2121oror 0.356038.5for ‘1.8333 ’ 60 or'0.35'caoM1 for π (no with digits 419)2 no with digits 385for 2 120 000 or for answer whichrounds to 2 120 000Total 6 marksfor

Q8.Working(a)AnswerMark2270 10045006(b)(c)117 1004 .5320024M1A12M13A1M226003328100or 3328 1.04104NotesA1for2704770or 0.06 oror 1.0645004500caoforcao117or 26 seen4 .53328100or 3328 1.041043328M1 for, 104% 3328 or 32 seen104caoTotal 7 marksfor

Q9.Working(a)AnswerMark5 x 2x 7 4211,3(b)233 oe47 2yor 7 2y4 4(2y 3)4 NotesM1for correct rearrangementA1Also accept 2 or more d.p. rounded ortruncated e.g. 3.66, 3.67for clear intention to multiply bothsides by 4 or a multiple of 4For example, award for7 2yor 7 2y4 4 4 2y 3 or 8y 3or 2y 3 4 or 2y 12M17 2y 8y 12 or simplerM110 y 5A1 12oefor correct expansion of brackets(usually 8y 12 ) or for correctrearrangement of correct termse.g. 8y 2y 7 12for reduction to correct equation ofform ay bA1Total 6 marks25

QWorkingAnswerMarkNotesAccept decimals in parts (a) and (b)10.(a)150 33590(bi)45 5341220(ii)25 1435 or35oe24820or25oe35B1forM1for 150 A1cao Do not acceptM1for45seen359015034 seenA1M1forM1(dep) foradding bothaboveproductsA1for2 1 5 43 2 5 4820oror25SC M1 for25 25or3 3 5 5SC M1 (dep) for addingboth above productsoeTotal 8 marks26

Q11.Working(a)(b)AnswerMarktangent at any point of a circle and the radius at that point areperpendicular1B1for mention of tangent andradius or line from centre5M1for squaring and subtracting6 . 9 2 5 .7 23.88844 M1(dep) for square rootA1for 3.89 or better2 5.7 2 "3.88844 ."M1A1for 2 5.7 2 “3.888 ” onlyfor 19.2 or answer which rounds to19.2 (19.176888 )Total 6 marks1B1cao ½ sq ft from sensible tableft if 4 or 5 points correct or if pointsare plotted consistently within eachinterval (inc end points) at the correctheightmay be shown on graph or implied by43, 44 or 45 statedIf M1 scored, ft from cumulativefrequency graphIf no method shown, ft only fromcorrect curveTotal 5 marks6.92 5.7 2 or 47.61 32.49or 15.1219.212.Notes(a)10, 26, 41, 50, 56, 60(b)Points correctCurve or line segments2B1B1(c)Use of w 430 on graph2M1Approx 1627A1

QWorkingAnswerMarklines13.4region14.(a)r2 2AπANotesB3B1B1 for each correct line (full or broken)Ignore additional linesfor correct region shaded in or out orfor correct region labelled RTotal 4 marksM1for r 2 A1Ignore M1A1for 13.5 seenfor answer which rounds to 2.073Aπor r2 A ππ(bi)13.5(ii)14.52.07296 ππ4M1or 2.14836 for14.5πor value which rounds to2.148 or 2.149 cao2.128A1dep on previous 3 marks in (b)Total 6 marks

Q15.Working(ai)f AnswerMarkkw4f (ii)NotesM1A1300000wB2fwk200kAlso award if answer is f butwk is evaluated as 300 000 in (a) or (b)B1 for graph with negative gradient(increasing or constant) even if ittouches or crosses one or both axese.g.May be implied by 1500 fO(b)300000f 12502240M1A1wfor substitution in f ft from kkwTotal 6 marks29

Q16.WorkingAnswer(ai)(ii)(iii)(b)Mark3b3b a2323or1(3b3 a) or 3b 232323231(3b3 a) bB2for23a or23PQ or k 23unless clearlyB1 for correct vector statement with atleast 3 terms which includes EF(or FE) in terms of capital lettersand/or a, bor (a)(iii) bor b a or b a or 2b 2or for expression in terms of aand/or b (need not be simplified) forEF either correct or ft from (a)a b bor 2b B1B1B1obtained by non-vector methodPQor a 3(3b a) oeaor k ora b or a Notes23231(3b a)31(a)(ii)3eg PQ PE EF FQPF PE EF(3b a)(a)(ii)a b EF FQIf an attempt is crossed out andreplaced, mark all attempts, includingcrossed out one, and award best mark.Total 5 marksoe30

QWorking17.AnswerMark416 dy 2x dx x2(2, 12)(a)312π 2.8 2 4π 2.8 273.9(b)B1for 2xB1for 16or 16x 22xM116"2 x 2 " 0x18.Notes125 or 5 seen25 73.89.cao For answer (2, 12) with nopreceding marks scored,award B0 B0 M1 A1Total 4 marksM2M1 for each termAlso award for values rounding to 24.6and to 49.2 or 49.3for 73.9 or for answer which rounds to73.9A133A1M1M1185031A1for 25 (a)or for π (2.8 5)2 2π (2.8 5)2or for substituting r 2.8 5 in theexpression used in (a)for 1850 or for any value in range1846.3 - 1847.5ft from 25 (a)Total 6 marks

Q19.WorkingAnswerMarkNotesM1for correct substitutionx 2 9x 2 3x 3x 1 5or x 2 9x 2 6 x 1 5B1(indep) for correct expansion of(3x 1)2 even if unsimplified10 x 2 6 x 4 0(5x 2)(2 x 2) 0or (5x 2)( x 1) 0or (10 x 4)(x 1) 0B1for correct simplificationB1for correct factorisation6x 2 (3x 1)2 5or6 1963 49or2010or349 1010x 25or for correct substitution into thequadratic formula and correctevaluation of ‘b2 4ac’or x 125x , y 215A1or for using square completioncorrectly as far as indicatedfor both values of xA1for complete, correct solutionsx 1, y 2Total 6 marksPAPER TOTAL 100 MARKS32

4400 IGCSE MathematicsSummer 2007Paper 4HQ1.Working(i)(ii)Answer6x 21 or 6x – 21 0 etcMarkx 2x 1 3x - 5 171x 3.5 oe eg 21/62NotesB1M1A1B1 oe eg 6x – 4 17 ISW not ‘ p’ft (i) if 6x cTotal 3 marks2.9 seen7/9 27or 7 27/93M1M1A1oe213.3B1M1A15x – 20 355x 5511dep B121 seen, & ans 3 B1M1A0Total 3 marksor M2 for x – 4 7Total 3 marks33

Q4.Working(a)(b)7 502175AnswerMarkor 7, 50, 2200 or 100Notes2B1B1M12A1for 7 and 2for 50(6or7) (48or50) correctly eval’d2 or 3eg 168A1fIf no wking: ft (a)(c)Num incr or 6.8 & 47.6incrdenom decr or 2.09decr(b) rnded up (not rndto 1 sf)or ‘175’ rndedto 200B2B1B1any two of theseB2 any two of theseB1 any one of these2Ignore otherTotal 6 marks5.(a)(2 3)/2 6 or 2 6 1/2 6 1 oe15(b)15/20 10001000 / 20 1521000 15/ 207503M1A1M1M1or 0.75ft ‘15’ for M1M1 onlyA1Total 5 marks34

QWorkingAnswer7y 7x 21(6y 21)x 3 7x(6x 3 oe)6.MarkNotesM1x 1/2, y 31/23y 7(y-3) y 7y-210 6x -3A1A1Total 3 marks7.(a)tan usedtan x 5.1/4.2 or tanx 1.2 . oex 50.5 (b)sin 29 AB/53or c/sin29 5/sin90AB 5sin 29AB 2.42. cm3M1M1A1(sin or cos) & ( (4.22 5.12) or (6.61) usedM1BC 5cos29M1AB (52 (5cos29)2) or 5cos29 tan29sinx 5.1/ (4.22 5.12) or cosx 4.2/ (4.22 5.12)A1Total 6 marks8.(a)(b)(c)1 – (0.1 0.2 0.1) or 1 – 0.4 oe0.2 0.10.620.3(Poss) overlap or mutexclor doesn’t wk for Bor Y }No or poss or possyes }2or 1 – (‘0.6’ 0.1)352M1A1M1A1B2or 0.6 in tableallow in table if not contrad on lineor 0.3 seenCan’t tell & (No or poss) B1Correct reason only: B1Incorrect reason: B0Unqualified Yes: B0Total 6 marks

QWorking42 62 (42 62)9.AnswerMark( 52)or “52”or 2 13h 7.21 .3NotesM1M1A1M1 depTotal 3 marks10.(a)V/H in any correct triangle attemptedM1Grad 2, may be embedded or impliedA1M1y ‘2’x 14(b)y -2x c1B1(c)(0, -4)1B1eg 3 – 11–0not 31B2f B1f for grad.B1 for y-int (lineqn)or B1f for just ‘2’x 1No wking, ans 2x 1: M1A1 B1y -2x any no. (not 5) or letteror y -2xTotal 6 marks11.(a)(b)x/20 6/12 or 4/8oe56(c)y/10 4/6oe10or 8/12or 10.0 .6.6 to 6.7 incl oe36122B1M1A1M1A1or x/sin30 20/sin(180–30–56)or y (42 82–2 4 8 cos‘56’)or y/sin56 8/sin(180–30–56)(a)(b): ft (a) M-mks onlyTotal 5 marks

Q12.Working(a)AnswerMarka7 / a2 or a a4 or a3 a25(b)(c)ax321Correctly cancel numbers or (x 1)NotesM1A1B1M1eg 1/2 or 0.5 or denom 2or1/2(x 1) or 0.5(x 1)x 1x 1oror 22 2or equiv2A13( x 1)3x 3oror k(x 1) (k 1)66Not ISWTotal 5 marks13.(a)Attempt arrange one set in orderState or indicate correct 15 & 4 or14 & 6M1M1NB: IQR for B 8, check wkingA: 11(b)B: 84A more spreador gter dispersionor less consistent thanB137A1A1B1B1f Consistent with (a). Ignoreother.Not: gter “range” or “difference”or“more constant” or “gter IQR”or “gter variance”Total 5 marks

Q14.Working5x – 7 x2 – 1x2 – 5x 6 0AnswerMarkor 5x – 7 (x – 1)(x 1)(x – 2)(x – 3) ( 0)orNotesM1M1M15 ( 5) 2 4 62x 2 or 34condone 5x – 7 x – 1 x 1allow different order with 0(x – 2.5)2 6 – 6.25A1T & I or no wking: 4 mks or 0 mksTotal 4 marks15.2 overlapping circles, 12 in overlap6 in H only2 in T only1416.92 52 – 2 5 9 cosx 6290cosx 70 or -90cosx -70(cosx 70/90)4M1M1M1A1M1M1x 38.9 or better3or 6 play H only M2or 20–6, 6 12 x 20, 20-18, 35-33: M3ans 2: M3A0Total 4 marksor cosx 92 52– 622 5 9M2A1Total 3 marks38

Q17.Working(ai)(ii)(b)(c)AnswerMark-2x 1or (10 – 1)1her\/9 2\ /9(a)(b)B1B2M1M11/5or 0.2or x -2 or x -2B1 for x 1 or 0, -1, -2, -3 . . .or1x 1 2y \/ (x – 1)y2 x -1- 1, \/Reverse orderA1M1M1ignore ans -1M1y \/(x – 1)M1dep x \/(y – 1)x y2 1squ, 1M1M1(g –1(x) ) x2 1 oe18.12Notes1/6 1/6 1/6 alone1/216 or 0.0046 3421,1,4 or 1,2,6 or 2,1,6 seen or implied1, 1, 4 and 1, 2, 6 (or 2, 1, 6) seen orimplied(1/6)3 31/72 or 3/216 or 0.014 orbetter394A1M1A1M1M1M1A1condone x-1 ifnext step correctx2 y -1y2 1M32y x 1 M3x x2 1 M3SC (g-1(x) ) (x 1)2: B1Total 10 marks0.173 or 0.163 or better. Not kie one routeie two routes incl 1, 1, 4ie three routes and correct exp’n(1/6)3 2 or 1/108, no wking: M0A0Total 6 marks

Q19.Working(a)(b)1AnswerMark/2 5 5 sin6010.8 or 13.1sect 1/6 π x 5212“10.8” 2( /6 π 5 –“10.8”) or “10.8” 2 2.26or 2 1/6 π 52 – “10.8”2NotesM1A1M1M115.4 cm23A11/2 5 (52 –(5/2)2) or 1/2 5 4.33(25 3)/4 M1A0 2(sect - )or 2 sect - Allow eg 1/2 5 5Total 5 marks2021.(i)201(ii)302(a)(4x – 1)(4x 1)1(bi)(ii)16 102 – 1 seen or implied(4 10 – 1)(4 10 1)or 39 411599 103or 1599 10003 13 41‘3 13 41’ 23 53 oe32M1A1B1B2or 1 sq reps freq of 5seen anywhere: B1Total 3 marksB1M1M1A113 or 39 or 41 or 123 as factorfactors 3, 13, 41 or 39, 41 or 13, 123Ans 3 533 M0A0M1or tree including 1000 or 10 and 100A1fft her (i) 23 53Total 3 marks40

Further copies of this publication are available fromEdexcel Regional Offices at /For more information on Edexcel qualifications, please visit www.edexcel-international.org/qualsAlternatively, you can contact Customer Services at www.edexcel.org.uk/ask or on 44 1204 770 696Edexcel Limited. Registered in England and Wales no.4496750Registered Office: One90 High Holborn, London, WC1V 7BH

(b) π 4.192 38500 M2 M1 for π (no with digits 419) 2 no with digits 385 2 120 000 A1 for 2 120 000 or for answer which rounds to 2 120 000 (π 2123433.419 3.14 2122356.929 3.142 2123708.749) Total 6 marks PAPER TOTAL 100 MARKS

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