Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education MATHEMATICS 0580/32 Paper 32 (Ce) MARK SCHEME Maximum Mark: 04 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 details of the discussions that took place at an Examiners meeting befe marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Rept f Teachers. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes f the series f most Cambridge IGCSE, Cambridge International A and AS Level components and some Cambridge O Level components. IGCSE is a registered trademark. This document consists of 7 printed pages. UCLES 208 [Turn over
Generic Marking Principles These 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 generic level descripts f a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE : Marks must be awarded in line with: the specific content of the mark scheme the generic level descripts f the question the specific skills defined in the mark scheme in the generic level descripts f the question the 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, other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively: marks are awarded f crect/valid answers, as defined in the mark scheme. However, credit is given f valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate marks are awarded when candidates clearly demonstrate what they know and can do marks are not deducted f errs marks are not deducted f omissions answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous. GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently e.g. in situations where candidates have not followed instructions in the application of generic level descripts. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme f the question (however; the use of the full mark range may be limited accding to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds grade descripts in mind. UCLES 208 Page 2 of 7
Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied (a)(i) One rectangle is an enlargement of the other oe (a)(ii) 9 2 M f 3 2 2 3 SF is 3 3.5 2.5 and 4.5 7.5 7.5 4.5 2.5.5 (b)(i) T in crect square B T (b)(ii) A different crect net drawn (c)(i) 08 3 M2 f [ 2 ]( 3 4 + 3 6 + 4 6) oe (c)(ii) 72 2 M f 3 4 6 M f one of 3 4, 3 6, 4 6 evaluated (c)(iii) 3 positive numbers (other than 3,4,6) with product 72 FT their (c)(ii) 2(a)(i) 3043 306 2 B f each 2(a)(ii) [Column] 7 [Row] 5 2 B f each 2(a)(iii) 20n + 298 oe 2 B f 20n + k 2(b) 2 [h] 5 [min] 2 2 M f 00.25 oe 3 25.25 oe UCLES 208 Page 3 of 7
2(c)(i) 3 2(c)(ii) 7 2(c)(iii) 6.84 6.836 to 6.837 4 3 M f 6 49 5 27 + 6 42 + 7 63 + 8 64 M dep f their340 96 2(c)(iv) 32 96 oe 2 64 M f 27+42+63 32 [ ] 3(a)(i) 5, 8, 4, 2, 6 2 B f one err, f two errs and total still 25 If 0 sced, SC f all crect tallies if frequency column blank increct 3(a)(ii) Surfing 3(a)(iii) 24 FT their frequency f snkelling 4 3(b)(i) 3.37pm cao 3(b)(ii) 2[h]26[min] 3(b)(iii) 2 52[pm] 96 4(a)(i) 4 7 36 3 B2 f two of 4, 7 36 in crect place M f 20 72 5 9 soi by [ ] 8 20 + 72 + 32 + x = 360 oe 4(a)(ii) 32 sect drawn 4(b) 36 5(a)(i) Six hundred (and) four thousand, nine hundred (and) twenty five Condone Six lakh (and) four thousand, nine hundred (and) twenty five 5(a)(ii) 53 59 5(a)(iii) UCLES 208 Page 4 of 7
5(b)(i) 05 5(b)(ii) 64 5(b)(iii), 3, 5, 9, 5, 45 2 B f 4 5 crect facts 5(b)(iv) Any irrational number between 6 and 7 e.g. 37 2π 6(a)(i) 20 2 4 M f [ 60 ] 2 6(a)(ii) 28 6(a)(iii) 5 28 3.28pm FT 5 00 + their 28 mins 6(b)(i) 3 : 0 2 M f 6 and 20 seen If 0 sced, SC f 0 : 3 6(b)(ii)(a) Straight lines drawn (5 00, 0) to (5 20, 2) and (5 20, 2) to (5 28, 4) 2 B f line from (5 00, 0) to (5 20, 2) BFT f line from (their 5 20, 2) to (their 5 20 + 8, 4) 6(b)(ii)(b) 4 FT their graph 6(b)(ii)(c).25 to.5 FT their graph 7(a) 4 7(b)(i) 7(b)(ii) 7(b)(iii) Rotation 90 clockwise oe [centre] (0, 2) Translation 4 2 Enlargement [scale fact] 2 [centre] ( 2, 7) 3 B f each 2 B f each 3 B f each 7(c) Crect reflection 2 B f a crect reflection in x = f 6 me vertices plotted crectly If 0 sced, SC f crect reflection in y = k UCLES 208 Page 5 of 7
8(a)(i) [:] 500 000 2 M f 5000 m seen [5 ]000 00 8(a)(ii) 96 2 B f 6.4 seen M f their 6.4 5 8(a)(iii) 7 8(a)(iv) Crect region shaded 5 B2 f 2 crect arcs drawn, centre Y with radius 3 cm and 4 cm B f 3 cm and 4 cm seen implied by calculation f one crect arc drawn B2 f 2 crect lines drawn B f crect line drawn B depbb f crect region 8(b) 253 2 M f 80 + 73 360 07 sketch with alternate angles marked sketch with 73 and crect bearing marked 9(a) 450 9(b) 0 p+ 3n = 525 2 M f 0 p + 3n 9(c) f crectly eliminating one variable M FT [p] = 30 A [n] = 75 A If 0 sced, SC f 2 values satisfying one of the iginal equations SC f both crect but no wking 0(a) Cala, Elu 2 B f one crect and no extras B f two crect and one extra 0(b)(i) 4 2 M f [ s = ] 9.6 0 0(b)(ii) [ h ] 2 = s 9.6 2 2 M f s = 9.6[ ] h (a)(i)(a) C (a)(i)(b) A (a)(i)(c) D (a)(ii) 0 2 M f 26 = 3x + 4 better UCLES 208 Page 6 of 7
(b)(i) 39, 0, 9 3 B f each (b)(ii) Crect smooth curve 4 B3FT f 8 7 crect plots B2FT f 5 6 crect plots BFT f 3 4 crect plots (b)(iii) (j, k) where 4.4 < j < 6 and 28 < k < 24 UCLES 208 Page 7 of 7