MATHEMATICS 0580/43 May/June 2017 - Eigsr

Cambridge International ExaminationsCambridge International General Certificate of Secondary EducationMATHEMATICS0580/43Paper 4 (Extended)May/June 2017MARK SCHEMEMaximum Mark: 130PublishedThis mark scheme is published as an aid to teachers and candidates, to indicate the requirements of theexamination. It shows the basis on which Examiners were instructed to award marks. It does not indicate thedetails of the discussions that took place at an Examiners’ meeting before marking began, which would haveconsidered the acceptability of alternative answers.Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report forTeachers.Cambridge will not enter into discussions about these mark schemes.Cambridge is publishing the mark schemes for the May/June 2017 series for most Cambridge IGCSE ,Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Levelcomponents. IGCSE is a registered trademark.This document consists of 7 printed pages. UCLES 2017www.egyptigstudentroom.com[Turn over

0580/43May/June 2017Cambridge IGCSE – Mark SchemePUBLISHEDAbbreviationscaocorrect answer onlydepdependentFTfollow through after erroriswignore subsequent workingoeor equivalentSCSpecial Casenfwwnot from wrong workingsoiseen or impliedQuestionAnswerMarksPart marks1(a)(i)95501(a)(ii)23 158 7502FT FT their (a)(i) 2425 correctly evaluatedM1 for their lower bound 24251(a)(iii)23 160 0001FT FT their (a)(ii) rounded to 4 sf1(a)(iv)2.316 1071FT FT their (a)(iii)or their (a)(ii) rounded to 3sf or more andin standard form1(b)520 nfww31(c)3380 or 3376 to 337722(a)3811181162100oe(100 5)or M1 for 105[%] associated with 546 oeM2 for 546 43 M1 for 3 000 1 oe 100 1FT FT 180 – their y2(b)693 B2 for ACB 42or B1 for ADB 42If zero scored, SC1 for ACB their ADB2(c)1072 B1 for QPS 73 or [reflex] QOS 2143(a)03(b)Fully correct smooth curve2.2521.254 B1 for each4 B3 FT for 7 or 8 pointsor B2 FT for 5 or 6 pointsor B1 FT for 3 or 4 points UCLES 2017www.egyptigstudentroom.comPage 2 of 7

0580/43Question3(c)May/June 2017Cambridge IGCSE – Mark SchemePUBLISHEDAnswerMarksPart marks113(d)(i)[y ] x 113(d)(ii) 2.2 to 2.11 0.45 to 0.410.51 to 0.61 If zero scored, SC1 for their line in (d)(i)drawn.It must be of the form y mx c (m 0)and drawn ‘fit for purpose’3(e)4(a)(i) 1.33 k 0 to 0.12FT FT Strict ft of their max point and minpoint dep on cubic graph or accept correctanswer from calculusB1 for eachIf zero scored, SC1 for two correct valuesreversed17.5 or 17.46.nfww6 B3 for triangle height 3.46[4.] or 12 oeor M2 for 42 22or M1 for h2 22 42and M2 for 2 7 or M1 for4(a)(ii)140 or 139.6 to 139.7.4(b)(i)2.62 or 2.618 1212 2 their h oe 2 their h1FT FT their (a) 83M2 for [r2 ]28013πoeor M1 for 280 π r2 134(b)(ii)10.2 or 10.20 or 1031049M2 for280[ 100] oe143or B1 for 2 744 or 143 seen5(a)(i)80335(a)(ii)17.3 nfww201, 1, 14 M1 for 5, 15, 22.5, 27.5, 40 soiM1 for fx with their f’s and x in correctinterval including both boundariesM1 (dep on 2nd M1) for fx 200 UCLES 2017www.egyptigstudentroom.comPage 3 of 7

0580/43Question5(b)(i)May/June 2017Cambridge IGCSE – Mark SchemePUBLISHEDAnswerMarks230oe210Part marksM1 for6 5 15 14If zero scored, SC1 for answer5(b)(ii)3108oe210M2 for6 9 9 6 oe15 14 15 14or 1 –9 8 6 5 15 14 15 14or M1 foror6 99 6 or15 1415 149 8 6 5 15 14 15 14If zero scored, SC1 for answer5(c)6(a)(i)6(a)(ii)1501Translation1 3 oe 13 1Enlargement1[sf ] 36oe225108oe22511oe2( 0, 4 )16(b)Image at( 0, 0 ) ( 0, 6 ) ( 4, 6 ) ( 4, 2 )2 B1 for rotation of 90º anticlockwise aboutthe wrong centreor 90º clockwise about (3, 1)or 4 points correct but not joined.6(c)Image at( 4, 0 ) ( 10, 0 ) ( 10, 4 ) ( 6, 4 )2 B1 for reflection in y k or in x 1or 4 points correct but not joined6(d)Enlargement1[sf ] 31Origin oe1 UCLES 2017www.egyptigstudentroom.comPage 4 of 7

0580/43Question7(a)May/June 2017Cambridge IGCSE – Mark SchemePUBLISHEDAnswerMarks[x ] 5Part marks4 M1 for correctly equating one set ofcoefficients[y ] 7with correct workingM1 for correct method to eliminate onevariableORM1 for correctly rearranging one equationM1 for correct method to eliminate onevariableA1 x 5A1 y 7both dep on M2If zero scored, SC1 for 2 values satisfyingone of the original equationsSC1 if no correct working shown, but 2correct answers given7(b)[a ] 36[b ] 63 B2 for either correctorM1 for a b 2 or for x 2 bx bx b 2 orbetter or for (x – 6)2 seenand M1 for 2b 12 soi7(c)7 x 2 12 x 10oe final answer nfww( 2 x 5)( x 1)4 B1 for common denom ( 2 x 5 )( x 1)seen oe iswM1 for x ( x 1) ( 3x 2 )( 2 x 5 ) soi iswB1 for 6 x 2 15 x 4 x 10 soi8(a)(i)4 points correctly plotted2 B1 for 2 or 3 points correctly plotted8(a)(ii)Positive18(b)mean 3.13M2 forsum of products30or M1 for at least 4 correct products soi8(c) UCLES 2017median 32 M1 for 15.5 oe indicatedmode 51range 5124 nfww3x 52 45 75 11 91[ 70.3]x 45 11M1 for clearing their fractionM1 forwww.egyptigstudentroom.comPage 5 of 7

0580/43May/June 2017Cambridge IGCSE – Mark SchemePUBLISHEDQuestionAnswerMarksPart marks9(a)1120 or 1121. .9(b)[QB or x ] 872 tan 1 seenM2tan their QB 525M11.7 or 1.660 to 1.661 nfwwA1 dep on M34 M2 for [ AC 2 ]5252 8722 2 525 872 cos 104or M1 for implicit versionA1 for 1 257 000 to 1 258 0009(c)(i)222 000 or 222 100. . or 222 1019(c)(ii)5.55 or 5.550 to 5.553 nfww10(a)A22M3 for 6 or 7 regions correctM2 for 4 or 5 regions correct2325M1 for 3 regions correctC10(b)(i) 110(b)(ii) 110(c)1 525 872 sin10424 All 8 regions correct292124M1 forQB8722FT FT their (c)(i) 1002 20 0002M1 for their (c)(i) 1002 20 0002or restartB273026282M1 for tan 1 21, 23, 24, 292FT Correct or FTSC1 for 1 omission or 4 correct and1 extra10(d)(i)51FT Correct or FT if less than 1010(d)(ii)91FT Correct or FT if less than 1010(e) UCLES 2017 or 1www.egyptigstudentroom.comPage 6 of 7

0580/43Question11 UCLES 2017May/June 2017Cambridge IGCSE – Mark SchemePUBLISHEDAnswer64( n 3)2173n 2 oe final answer47( n 3)2 (3n 2)76n 2oe final answern 1Marks1, 2 M1 for a quadratic expression seen orsecond differences 2oe final answeroe iswPart marks1, 2 B1 for 3n k (any k) or kn 2 (k 0)1, 2FT FT their difference expressions A – BM1 for expression an2 bn c seen orsecond differences 21, 2B1 forn k 1seenn kwww.egyptigstudentroom.comPage 7 of 7

MATHEMATICS 0580/43 Paper 4 (Extended) May/June 2017 MARK SCHEME Maximum Mark: 130 Published This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners