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w w ap eP m e tr .X w UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS for the guidance of teachers 0580 MATHEMATICS 0580/22 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 must be read in conjunction with the question papers and the report on the examination. • Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the May/June 2011 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses. om .c MARK SCHEME for the May/June 2011 question paper s er International General Certificate of Secondary Education Page 2 Mark Scheme: Teachers’ version IGCSE – May/June 2011 Syllabus 0580 Paper 22 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. 1 2 Answers 53.1 Mark 2 2 3+ 6,π Part Mark B1 C = 36.9 seen, must have C stated or marked on the diagram or M1 sinA = 54 or tanA = 43 but must have A stated –1 for each error or omission 3 Working must be shown 2 4 0.82 2 5 (6)€ or euros (with correct working) 2 6 3.322 cao 2 7 1.85 × 104 3 B2 18500 oe seen or M1 4x = 74000 or x = 2 × 104 – 1.5 × 103 8 16 3 9 1275, 1425 3 10 (a) (0)700 or 7 am 2 (b) 1700 or 5 pm 1 3 M1 p = k q A1 k = 1.6 or 8/5 B1 85 or 95 or 0.85 or 0.95 M1 their LB or UB × 1500 where 85 Y LB < 90 90 < UB Y 95 M1 100 – (5 × their(22 – 6) + their(13 – 8)) or better soi 11 4 + bc 4 or + b cao c c 12 x=1 y = 0.2 or 13 1 only 5 3 (a) 72 1 (b) 36 1 (c) 54 2ft 14 16 14 7 = and M1 oe 9 9 16 8 or visible cancelling M1 16 (= 0.5(9...)) and 27 0.82 (= 0.64) to decimals seen M1 one of 6 × 1.9037 or 11.5 ÷ 1.9037 or 11.5 ÷ 6 seen B1 3.3219(…) or 3.32(20) seen M1 conversion of M1 correct move completed M1 second correct move completed M1 third correct move completed M1 consistent mult and add/subtraction A1 one value correct after M awarded ft 90 – (b) M1 POQ = 108 © University of Cambridge International Examinations 2011 Page 3 14 Mark Scheme: Teachers’ version IGCSE – May/June 2011 (a) 84 1 (b) 15 1 (c) 6.28 2 4 c oe 2 M1 correct but unsimplified e.g. c oe 2 M1 correct but unsimplified 4 x 24 2 B1 4xn B1 2 B1 1 − 3x ( x + 1)( x + 5) 16 (a) 1 2 a– 1 2 (b) 3 4 a+ 3 4 (a) 4x–24 or www x2 16 (a) (6, 1½) (b) 18 (b) y = – 19 20 1 5 Paper 22 120 × 2 × π × 3 oe 360 M1 (x + 1)2 – x(x + 5) oe B1 x2 + x + x + 1 B1 denominator(s) (x + 1)(x + 5) or x2 + 6x + 5 15 17 Syllabus 0580 M1 1 2 a+– 1 2 c k or kx–24 for any numerical k, n x 24 xn x2 or B1 k 16 x SC1 ( )2 4 1 x + 4 oe 3 B1 correct numerical format B1 correct m B1 correct c (a) 8 1 (b) 4x – 9 2 M1 2(2x – 3) – 3 seen (c) 22(x + 1) or 22x + 2 or 4x + 1 (a) (i) 2 2 M1 (2x + 1)2 seen B1 correct line B1 2 sets of correct arcs 2 B1 correct line B1 two sets of correct arcs 1 2 correct region, shaded or shown by the letter R M1 6 × 2 + 3 × –4 or 12 + –12 2 M1 any 2 × 2 matrix with 2 elements correct 2 B1 (ii) R (b) 21 (a) (i) (0) brackets essential 12 18 (ii) − 8 − 12 (b) 1 2 1 − 1 −1 3 1 2 a c seen b d or 1 − 1 seen B1 k −1 3 © University of Cambridge International Examinations 2011