MATHEMATICS 0580/42 March 2019 - Eigsr

Cambridge Assessment International EducationCambridge International General Certificate of Secondary EducationMATHEMATICS0580/42Paper 4 (Extended)March 2019MARK 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 International will not enter into discussions about these mark schemes.Cambridge International is publishing the mark schemes for the March 2019 series for most CambridgeIGCSE , Cambridge International A and AS Level components and some Cambridge O Level components.This document consists of 8 printed pages. UCLES 2019www.egyptigstudentroom.com[Turn over

0580/42Cambridge IGCSE – Mark SchemePUBLISHEDMarch 2019Generic Marking PrinciplesThese general marking principles must be applied by all examiners when marking candidate answers.They should be applied alongside the specific content of the mark scheme or generic level descriptorsfor a question. Each question paper and mark scheme will also comply with these marking principles.GENERIC MARKING PRINCIPLE 1:Marks must be awarded in line with: the specific content of the mark scheme or the generic level descriptors for the questionthe specific skills defined in the mark scheme or in the generic level descriptors for the questionthe standard of response required by a candidate as exemplified by the standardisation scripts.GENERIC MARKING PRINCIPLE 2:Marks awarded are always whole marks (not half marks, or other fractions).GENERIC MARKING PRINCIPLE 3:Marks must be awarded positively: marks are awarded for correct/valid answers, as defined in the mark scheme. However, creditis given for valid answers which go beyond the scope of the syllabus and mark scheme,referring to your Team Leader as appropriatemarks are awarded when candidates clearly demonstrate what they know and can domarks are not deducted for errorsmarks are not deducted for omissionsanswers should only be judged on the quality of spelling, punctuation and grammar when thesefeatures are specifically assessed by the question as indicated by the mark scheme. Themeaning, however, should be unambiguous.GENERIC MARKING PRINCIPLE 4:Rules must be applied consistently e.g. in situations where candidates have not followedinstructions or in the application of generic level descriptors.GENERIC MARKING PRINCIPLE 5:Marks should be awarded using the full range of marks defined in the mark scheme for the question(however; the use of the full mark range may be limited according to the quality of the candidateresponses seen).GENERIC MARKING PRINCIPLE 6:Marks awarded are based solely on the requirements as defined in the mark scheme. Marks shouldnot be awarded with grade thresholds or grade descriptors in mind. UCLES 2019www.egyptigstudentroom.comPage 2 of 8

0580/42Cambridge IGCSE – Mark SchemePUBLISHEDMarch 2019Abbreviationscaocorrect answer onlydepdependentFTfollow through after erroriswignore subsequent workingoeor equivalentSCSpecial Casenfwwnot from wrong workingsoiseen or impliedQuestionAnswerMarksPartial Marks1(a)4732 M1 for 645 (11 4)1(b)212.52 M1 for 50 4.251(c)31.5 or 31.45 to 31.4631(d)87511(e)10.4 or 10.38 to 10.3911(f)(i)30 [ ] 70 and 210011(f)(ii)both numbers rounded up oe12(a)(i)Reflection2 B1 for each43oe60or M1 for time 1h 43min or 103 [mins]or 54 their timeM2 for 54 1x 1.52(a)(ii)3 B1 for eachRotation(0, 1)90 [anticlockwise] oe2(b)(i)Image at (5, 1) (6, 1) (6, 3)2 B1 for correct size and orientation butwrong position1If 0 scored, SC1 for enlargement SF2with centre (3, 0)2(b)(ii)Image at ( 6, 3) ( 4, 3) ( 6, 7)22(b)(iii)Image at (2, 1) (2, 3) (6, 3)3 M2 for 3 correct coordinates soi 0 1 1 3 3 or M1 for 1 0 2 2 6 or B1 for stating reflection in y x UCLES 2019 3 k B1 for translation or k 1 www.egyptigstudentroom.comPage 3 of 8

0580/42Cambridge IGCSE – Mark SchemePUBLISHEDQuestionAnswerMarch 2019Marks3(a)5oe913(b)80oe1533Partial Marks10 8 oe18 1710 8oeor M1 for 18 17M2 for 2 If 0 scored, SC1 for3(c)411oe51M3 for160oe32410 9 8 8 7 6 oe18 17 16 18 17 16or M2 for10 9 88 7 6oe or 18 17 1618 17 16oeor M1 for10 9 88 7 6or, ,, ,18 17 1618 17 16If 0 scored, SC1 for1512oe58324(a)Correct ruled line with D marked2 B1 for correct ruled line or short line4(b)47.52 B1 for 9.5 or 95 mm seen or for answerfigs 465 to figs 4854(c)Correct arc radius 7 cm2 B1 for complete arc other radius, centre Aor correct but short arcCorrect ruled perpendicular bisector ofBC with correct pairs of arcs2 B1 for correct perpendicular bisectorwithout correct arcsor for correct arcs, no/incorrect lineCorrect ruled bisector of angle BCD withcorrect pairs of arcs2 B1 for correct angle bisector withoutcorrect arcsor for correct arcs, no/incorrect linecorrect region shaded1 Dep on at least B1B1B1 and fiveboundaries one of which is an arc[1 :] 50014(d) UCLES 2019www.egyptigstudentroom.comPage 4 of 8

0580/42Cambridge IGCSE – Mark SchemePUBLISHEDQuestionAnswerMarch 2019MarksPartial Marks5(a) 2.1, 1.6, 1.7, 2.13 B2 for 3 corrector B1 for 2 correct5(b)Fully correct curve4 B3FT for 8 or 9 correct plotsor B2FT for 6 or 7 correct plotsor B1FT for 4 or 5 correct plots5(c)line y M21(1 x ) ruled2M1 for line with gradient 1211M1 for line through (0, ) but not y 22 2.15 to 2.01 0.45 to 0.22.25 to 2.45B2 B1 for two correct5(d)number of intersections of their curve andthe line y 11 strict FT for their curve6(a)5.83 or 5.832 to 5.8335 B2 for sector angle 210 soi0.25oeor M1 for [ cos DOE ]0.5M2 fortheir 210 2 π 0.5 2 1.5 2 0.5 oe360or M1 for6(b)1.21 or 1.208 3M2 fortheir 210 2 π 0.5 oe isw360their 210 π 0.5 0.5 1.5 0.5360oeor M1 for6(c)(i)4[.00.]3their 210 π 0.5 0.5 oe isw360M2 for 0.5 or M1 foror for6(c)(ii)77.44oetheir (b)77.44ortheir (b)their (b)77.44their (b) 0.52 2 oe77.44r3 M2 for 77.44 1.5 19 1000 oe2.20704or M1 for figs 2207[04] or figs 221 seenor [vol ] 77.44 1.5 UCLES 2019www.egyptigstudentroom.comPage 5 of 8

0580/42Cambridge IGCSE – Mark SchemePUBLISHEDQuestion7(a)(i)AnswerMarch 2019Marks111.25Partial Marks4 M1 for midpoints soi(25, 75, 112.5, 137.5, 175)M1 for fx with x in correct intervalincluding both boundariesM1 (dep on 2nd M1) for fx 207(a)(ii)2 7 11 172 B1 for three correct7(a)(iii)3oe2017(b)7(c)(i)20 625 nfwwB1 for one correct value or [SF ] 5 or1oe53 M2 for fx f 4.28 oeor M1 for 179 7x oe or4.28 (45 x ) oe seen7(c)(ii)317(c)(iii)418(a) 318(b)12oe1128(c)64 x 45 final answer2 M1 for 8 ( 8 x 5 ) 5 isw8(d)x 5oe final answer82 M1 for a correct first step y 5 8 x ,y5 x or x 8 y 5888(e)8 x 2 11x 13final answerx 23 M1 for ( 8 x 5 )( x 2 ) 3 oe isw UCLES 2019M1 for3soi3 2x 2B1 for common denominator ( x 2 )www.egyptigstudentroom.comPage 6 of 8

0580/42Cambridge IGCSE – Mark SchemePUBLISHEDQuestion8(f)(i)8(f)(ii)Answer( 8 x 5)2 6March 2019MarksPartial MarksM1 1964 x 2 40 x 40 x 25B164 x 2 40 x 40 x 25 6 19 oeleading to 16 x 2 20 x 3 0A1 with no errors and must show(8 x 5)2 6 19 with no omissions afterthis[ ]20 ([ ]20 )2 4 (16 )( 3)2 162oeB1 for([ ]20 )2 4 (16 )( 3)or B1 foror better[ ]20 qoe or2(16)[ ]20 q2(16)0.17 and 1.08 final ans2 B1 for eachIf 0 scored, SC1 for answer 0.2 and 1.1or answer 0.17 and 1.08or 0.174. and 1.075 to 1.076 seenor 0.17 and 1.08 seen in working9(a)(i)(a) 19(a)(i)(b)A B1B or A′19(a)(ii)9(b)9(c)(i)13x 7 19 oeM1 must see 19 and 73x 19 7 or better leading to x 4A1 with no errors seen2 B1 for 2 correct9(c)(ii)81859(c)(iii) or { }19(c)(iv)151 UCLES 2019www.egyptigstudentroom.comPage 7 of 8

0580/42Cambridge IGCSE – Mark SchemePUBLISHEDQuestion10(a)AnswerMarksPartial Markscorrectly equating one set of coefficientsM1 or making x or y the subject of oneequation correctlycorrect method to eliminate one variableM1 or substitution for x or y for theirrearranged formulax 7A2 A1 for one correct valueIf A0 scored, SC1 for 2 values satisfyingone of the original equationsor if no working shown, but 2 correctanswers giveny 310(b)March 201923koe( x 3) 2their koeM1 for y (7 3)2ORM1 for y M2 for 8 ( 2 3) y ( 7 3) oe210(c)23 M1 for 3x 6 7 x 14x 5 final answerM1 for their ( 6) their14 7 x 3x oe11(a)(i)11(a)(ii)(a)772 B1 for each2432 M1 for a quadratic expression as theanswer2n2 5 oeor B1 for common 2nd difference of 411(a)(ii)(b)3n 1 oe2 B1 for 3k oe where k is a linear functionof n11(b)(i)21111(b)(ii)113 B2 for ( 4n 45 )( n 11) seenor B1 for 4n2 n 3 498 oe UCLES 2019www.egyptigstudentroom.comPage 8 of 8

MATHEMATICS 0580/42 Paper 4 (Extended) March 2019 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 were instructed to award marks. It does not indicate the .