w w w. Xt r e m e P a p e r s. c o m Example Candidate Responses (Standards Booklet) Cambridge IGCSE® Mathematics 0580 Cambridge Secondary 2 University of Cambridge International Examinations retains the copyright on all its publications. Registered Centres are permitted to copy material from this booklet for their own internal use. However, we cannot give permission to Centres to photocopy any material that is acknowledged to a third party even for internal use within a Centre. ® IGCSE is the registered trademark of University of Cambridge International Examinations. © University of Cambridge International Examinations 2012 Contents Introduction ..........................................................................................................................2 Assessment at a glance .......................................................................................................3 Paper 1 (Core) .......................................................................................................................4 Paper 2 (Extended) .............................................................................................................34 Paper 3 (Core) .....................................................................................................................73 Paper 4 (Extended) ...........................................................................................................109 Introduction Introduction The main aim of this booklet is to exemplify standards for those teaching Cambridge IGCSE Mathematics (0580), and to show how different levels of candidates’ performance relate to the subject’s curriculum and assessment objectives. In this booklet candidate responses have been chosen to exemplify grades C and E for Papers 1 and 3, and grades A, C and E for Papers 2 and 4. Each response is accompanied by a commentary explaining the strengths and weaknesses of the answers. For ease of reference the following format for Papers 1, 2 and 3 has been adopted: General comment Mark scheme Example candidate response (whole script) Examiner comment The mark scheme for each paper is followed by examples of marked candidate scripts, each with an examiner comment on performance. Comments are given to indicate where marks were awarded, and how additional marks could have been obtained. In this way, it is possible to understand what candidates have done to gain their marks and what they still have to do to improve their grades. For Paper 4, the mark scheme is followed by examples of marked candidate responses for questions 4, 6, 8 and 9 with an examiner comment on performance for each. These questions are then followed by three whole scripts. Past papers, Principal Examiner Reports for Teachers and other teacher support materials are available on our Teacher Support website at http://teachers.cie.org.uk 2 Cambridge IGCSE Mathematics 0580 v0.2 Assessment at a glance Assessment at a glance Teachers are reminded that a full syllabus and other teacher support materials are available on www.cie.org.uk v0.2 Cambridge IGCSE Mathematics 0580 3 Paper 1 (Core) Paper 1 (Core) General comment For Paper 1, two scripts have been chosen to exemplify a typical grade C and E script. Each script is accompanied by a brief commentary on each question. These two scripts were originally chosen as they had almost all questions attempted. It is difficult to say what defines a typical script at a particular level as they vary so much. For a grade E script it is common to find quite a number of questions are either not attempted or simply have a small amount of working, suggesting no real knowledge of the topic. Such candidates then tend to have some topics that they clearly know very well and gain their marks on those topics, not all of which are recognised as the easiest ones. The script commented on at grade E suggests a candidate who has been quite well prepared for the examination as far as syllabus coverage is concerned. However, a combination of weakness in understanding and carelessness in interpreting the questions has resulted in this lower grade. A general observation on grade C candidates is that they have covered the syllabus well and attempted all, or nearly all, the questions. All candidates are prone to errors, particularly those who have not been considered for extended level, and overall it is this factor that mainly reduces the mark from extremely high. Of course, even when a candidate is competent on a particular topic, they still need to interpret the particular question on that topic. Thorough practice on past papers and examination style questions can minimise this. The script selected was felt to be quite typical of a grade C candidate, with only a very few cases observed of lack of understanding, but mainly marks were lost through carelessness in reading and incorrectly interpreting what was required in certain questions. Mark scheme Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working Qu. Answers Mark Part Marks 1 134 1 2 512(.00) 1 3 (a) –7 1 (b) (+)6 1ft ft –1 – their (a) 4 1.43 × 109 final answer 2 B1 for answers of 1.43 × 10n (n ≠ 0) or figs 143 or 1.429(….) × 109 SC1 for answer of 1.42 × 109 or 1.4 × 109 4 Cambridge IGCSE Mathematics 0580 v0.2 Paper 1 (Core) Qu. Answers Mark Part Marks 5 899.5 ≤ w < 900.5 2 B1 for 1 correct or SC1 for correct but reversed. 6 10 www 2 M1 for 15 ÷ 6 soi 6 15 or B1 for = oe or better 4 EF 7 662.794 to 663.304…. 3 M2 for 600 × 1.0343 or final answer M1 for (600 + 0.034 × 600) × 0.034 or (600 × 1.034) × 0.034 and M1 dep correct method for the remaining time. 8 (a) 4p(2q + 3r) 2 B1 for p(8q + 12r) or 2p(4q + 6r) or 4p(aq + br) a, b integers or 4(2pq + s 3pr) (b) (p =) oe 1ft 4(2q+3r) ft if p is a common factor in (a) or in working in (b) 9 (a) 245 1 3 M1 for × 840 or 7 (b) 360 2 SC1 for answer 480 10 15 If zero in (a) and (b) then (a) 43 cao final 1 SC1 if both (a) and (b) are correct answer decimals or percentages as answers. (Mark as 0 for (a) and SC1 for (b)) 1 42 (b) cao final 43 answer 1 0 (c) 0 or 43 11 (a) (x=) 35 2 B1 for angle BDC = 90 soi May be marked on the diagram (b) (y=) 55 1 ft ft 90 – their x 12 (a) (i) (x=) 6 1 (ii) (x=) –2 1 (b) 3 1 v0.2 Cambridge IGCSE Mathematics 0580 5 Paper 1 (Core) Qu. Answers Mark Part Marks 13 (a) Two stage proof 2 1×7+2×5 1×7 2×5 M1 for or + 5×7 5×7 5×7 4 2 5 1 or alt – or – 5 7 7 5 17 18 17 35 M1dep for 1– their or + = 35 35 35 35 28(cid:16)10 25(cid:16)7 or alt oe or oe 35 35 1 18 M1 for × oe 6 3 35 (b) final answer 2 35 12 If zero SC1 for answer of 35 14 10(cid:117)8(cid:16)0.5(cid:117)90 1 (a) (i) 5 2 B1 for 80 (from 10 × 8) or 45 (from 0.5 × (ii) 7(.0) cao 90) or 1 5 (denominator) seen (b) 5.92 or 5.919(…..) 15 (a) (i) 175 1 (ii) 70 1 (b) 2 points plotted 1 correctly (±1mm). (c) Positive 1 16 (a) Rotation or 1 Two transformations named, zero for (a) enlargement 1 Independent 180° (SF) –1 1 Independent (about or centre) origin oe B1 for 5 right or 3 down applied 2 (b) Correct translation 5 right and 3 down 17 (cid:167)(cid:16)12(cid:183) 2 B1 for 1 component correct. (a) (cid:168) (cid:184) (cid:169) (cid:16)3(cid:185) −3 (b)  3 1 (c) (i) Vector AB drawn 1 Diagonal line, ignore working lines (ii) 134° to 136° 1 18 (a) (i) 12.7 to 12.73 2 x x M1 for = sin45 or = cos45 or 18 18 (ii) 161 to 162.1 2ft better M1 for method for squaring their (a)(i). (b) 254 to 255 2 M1 for π × 92 6 Cambridge IGCSE Mathematics 0580 v0.2 Paper 1 (Core) Example candidate response – grade C (whole script) v0.2 Cambridge IGCSE Mathematics 0580 7 Paper 1 (Core) 8 Cambridge IGCSE Mathematics 0580 v0.2