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w w ap eP m e tr .X w CAMBRIDGE INTERNATIONAL EXAMINATIONS om .c s er Cambridge International General Certificate of Secondary Education MARK SCHEME for the October/November 2014 series 0580 MATHEMATICS 0580/23 Paper 2 (Extended), maximum raw mark 70 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 before 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 Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2014 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components. ® IGCSE is the registered trademark of Cambridge International Examinations. Page 2 Mark Scheme Cambridge IGCSE – October/November 2014 Syllabus 0580 Paper 23 Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Qu. Answers Mark Part Marks 2 M1 for 350 × 8.2 2 M1 for decimal conversion: 0.7 [7…] or 0.8 for and 0.36 for 0.62 and 0.343 for 0.73 or B1 for three in the correct order 2.4 × 108 2 B1 for 240 000 000 oe or B1 for k × 108 or 2.4 × 10 k 4 30 2 M1 for 2x + 3x + 4x + 90 = 360 oe 5 48 2 M1 for 52 ÷ 65 [× 60] oe implied by 0.8 6 9.5 or 3 M2 for 2x = (8 × 3) – 5 or better oe or M1 for 2x + 5 = 8 × 3 or better 7 160 3 8 8 + (y – 2)2 oe final answer 3 M1 for y – 2 = √(x – 8) M1 for squaring both sides completed correctly M1 for adding their 8 completed correctly on answer line 9 4 3 M2 for 6(3 + 5) = y(7 + 5) oe or k M1 for y = oe x+5 A1 for k = 48 10 13891.5[0] 3 1 2870 2 0.34 0.7 3 3 0 .6 2 0 .6 19 2 0.6 360 180 × (18 − 2 ) or oe 18 18 360 or M1 for 180 × (18 – 2) or 18 M2 for 180 − 5 M2 for 12000 × 1 + 100 3 oe n 5 or M1 for 12000 × 1 + oe n > 2 100 © Cambridge International Examinations 2014 Page 3 11 (a) Mark Scheme Cambridge IGCSE – October/November 2014 608 400 cao 2 (b) 2n2(n + 1)2 oe M1 for Syllabus 0580 Paper 23 1 2 × 39 2 × (39 + 1) 4 1 Complete circle centre E radius 3cm 1 (b) Correct ruled bisector with two pairs of correct arcs 2 B1 for correct bisector with no/wrong arcs (c) 1 dep on attempt at bisector of C and enclosed region 12 (a) 13 16 x 2 + 18 x + 9 final answer 6x 4 M2 for 9 [+] 4x2 [+] 18x [+] 12x2 or better or M1 for 2 of these and M1FT for adding their four ‘numerators’ together correctly and B1 for denominator 6x to a maximum of 3 marks 14 (a) 1 1 b − a oe 2 2 2 M1 for 1 2 ( AO + OB ) oe or correct unsimplified route e.g. AO + OB + BP or –a + b + 1 2 BA = –a + b + 1 2 (a – b) (b) 1 3 a + b oe 4 4 2 M1 for OA + AQ oe or correct unsimplified route 15 (a) 19 2 1 8 2 B1 for any two correct (b) 1 8 19 2 2FT 16 (a) 64 (b) 4x + 1 oe (c) x3 − 1 oe final answer 4 (d) 3 nfww B2FT for a correct ft from (a) or B1FT for any two correct or for any correct two ft from (a) 2 B1 for [f(1) =] 4 or M1 for ((x – 3)2)3 or better 2 M1 for x = y −1 or 4y = x – 1 4 1 1 © Cambridge International Examinations 2014 Page 4 Mark Scheme Cambridge IGCSE – October/November 2014 Syllabus 0580 Paper 23 3.08 to 3.22 nfww 2 B1 for 502.5 to 502.62 or 505.7 to 505.8 (b) 16 oe 200 2 B1 for 16 soi their 16 or M1 for 200 (c) 18.5 2 B1 for 18.5 and 26 B1 for 3 4 B3 for 3.536 to 3.54 as an answer or 1 M2 for 2000 ÷ π × 6 2 × 15 3 1 or M1 for π × 6 2 × 15 3 and SC1 for truncating their 3.54 to a whole number 3 M2 for 2000 – their 3 × their volume or M1 for their 3 × their volume 3 B1 for each 17 (a) 18 (a) 26 3 3 (b) 303 to 304 19 (a) rotation 90 clockwise [about] origin oe (b) 0 1 1 0 2 M1 for any one column or row correct (c) Triangle at (3, 3), (6, 3) and (3, 5) 2 M1 for any two vertices correct or correct answer translated horizontally © Cambridge International Examinations 2014