Cambridge International Examinations Cambridge International General Certificate of Secondary Education. Published

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1 Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/4 Paper 4 (Extended) May/June 06 MARK SCHEME Maximum Mark: 0 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 ds 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 May/June 06 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. This document consists of 6 printed pages. UCLES 06 [Turn over

2 Page Mark Scheme Syllabus Paper Cambridge IGCSE May/June Abbreviations awrt answers which round to cao correct answer only dep dependent FT follow through after error isw ignore subsequent working or equivalent SC Special Case nfww not from wrong working soi seen or implied (a) (i) 05. (ii) 00 (iii) 0 (iv) 05.7 (b) 0 (a) (x+ )( x 4) SC for ( x+ a)( x+ b) where ab = 8 or a + b = 0 (b) < x < 4 FT B for either correct (c).8 or.8 8. or 8.8 to 8.9 B for either correct or M for sin x = their where < their < or M for sketch or M for 4.8 or 4.8 seen (a) 6.5 B for y = k( x + ) B for k = 0.5 OR M for y (4 + ) = ( + ) (b) BFT for x+ = their 7 (c) x= y final answer M for division by their k M for cube root M for subtracting, must be final step Cambridge International Examinations 06

3 Page Mark Scheme Syllabus Paper Cambridge IGCSE May/June (a) (i) A = 4r πr final answer M for ar bπ r (ii) 0.9 or 0.88 to 0.90[ ] (b) 8r+ π r final answer B for 8r B for π r If B0 scored then M for r+ r+ π r 4 5 (a) x sin0 [ = 4.] (b) 6. or 6.05 to 6.06 B for 8.50 to 8.5 or M for cos0 (c) 6. or 6.4 or 6. to 6.4 sin0 M for sin A = their ( their ( b)) or cos A =.4 their( b) or M for 6. = their sin A sin 0 (d) 6. M for.4 sin0 6 (a) 66 or 65.6 to 65.7 M for correct use of mid-pts at least 4 of (50, 57.5, 6.5, 67.5, 7.5,8.5) (b) (i).6,., 6.4,.6, 6.4,.7 B for 4 or 5 correct (ii) Suitable vertical scale Correct column widths Correct heights FT dep B for 4 or 5 correct dep on at least B in (b)(i) 7 (a) M for.05. a = 0950 or better M for or. M for = 05% or M for.05. (b) M for.05 = where n > 0950 or M for n where n > If 0 scored SC for.4 or.4 seen Cambridge International Examinations 06

4 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE May/June (a) 6p q B for XD = q or M for AD = AX + XD (b) p + q M for AC = 9p or XC = p or correct route (c) p q M for BD = their (a) M for CB = CD + DB 9 (a) [QR =] P [PQR =] Q [ST =] Q [SQ =] T [PTP =] T [TPP =] S 6 B for each (b) (i) Points (, ) (, ) (5, ) B for (, ) or (5, ) correct (ii) Points (, ) (, ) (5, ) FT FT their B reflected in x-axis (iii) Rotation 90 [anticlockwise] [Centre] (0, 0) 0 (a) (i) Points correctly plotted B for 4 or 5 correct points B for or correct points (ii) Positive (b) (i).7 (ii).6 (c) (i) [ y = ] x B for kx, or B for a x, If 0 scored SC for x (ii). or.9 FT FT their (c)(i) using x = 0 (iii) Outside range Cambridge International Examinations 06

5 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE May/June (a) Correct sketch 4 B Correct graph for x > B Correct graph for x < B Correct graph for < x < B Approximately correct intercepts (b) x = x = y = (c) (, ) (d).8,,.6 B for each (a) 8 M for 4x + 6x = 80 (b) 8 M for 80 6x x (c) 90 M for 80 x x x or B for CED = x or DCE = 4x (a) (i) 4.7 or.5π or 4.7 to 4.7 M for 60 π 60 (ii).5 or.5π+ 4.5 or.50 to.5 (iii).4 or 7.5π+ 4.5 or.5 to.6 (b) 6 or.5π or 6.6 to 6.7 M for 0.5 sin 60 + their(a) cos60 or M for cos60 B for hyp = 6 60 M for π ( 6) 60 their 4 M for.5π + 6π + 4π or M for.5π + 6π + 4π and M for or M for correct new triangle in diagram 4 or M for correct new sector in diagram 5 or M for correct new triangle in diagram 6 Cambridge International Examinations 06

6 Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE May/June (a) (i) x x + y final answer B for x x + y xy (ii) ( ) x+ y x y final answer M for ( x+ y ) ( x + y ) or B for y x+ y seen (b) (i) xx ( ) ( x+ y)( x+ y ) final answer x B for x + y or B for x+ y seen xy (ii) ( x+ y )( x+ y ) final answer x y M for ( x+ y ) ( x+ y ) y or B for seen x + y Cambridge International Examinations 06