MARK SCHEME for the May/June 2011 question paper for the guidance of teachers 0580 MATHEMATICS

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1 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 0 question paper for the guidance of teachers 0580 MATHEMATICS 0580/4 Paper 4 (Extended), maximum raw mark 0 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 0 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

2 Page Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 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 art anything rounding to soi seen or implied Qu. Answers Mark Part Marks (a) (i) 5 (ii) 5.5 (5.46 to 5.47) (iii) 0.05 oe B for /00 or 0.0 seen (b) final answer www Condone 88.5 M for oe (implied by final answers 880, 88, 88 or 88.5(0) seen) or B for.5 as final answer or M for oe (implied by final answers 0,, ) (c) (i) 5 (ii) (iii) 40 Allow 5 M for any correct product of factors = 60 seen or correct factor ladder or correct tree (condone s on tree/ladder) M for or oe M for 4 5 or 5 oe SC only for both correct answers (ii) (iii) reversed (a).0 (.0 ) www 4 4 M for oe may be in two steps or 9. to (.08 to.06..) or M for oe implied by 9. to 9.5. or M for any correct Pythag in of the faces e.g. +.5 (b) 4. to 4. cao www M for sin =.7/their EC or cos = their EG/their EC or tan =.7/their EG or complete long method (M for CEG as required angle accept on diagram if clear) (c) (i).95 cao (ii) Yes and because their (c)(i) < their (a) ft ft their (a) and their (c)(i), must say yes or no oe and compare the two distances numerically or by labels University of Cambridge International Examinations 0

3 Page Mark Scheme: Teachers version Syllabus Paper IGCSE May/June (a) (i) 4 to 50 (ii) (0)59 to (0)6 (iii) 48 o to 5 o drawn Distance 6.8 to 7. cm drawn (iv) 8 to o (v) 60 www B for 7. to 7.5 seen Both marks available from the position of B as lines don t need to be drawn. M for 0 or better seen (b) 667 (666.6 to 666.7) www B for.5 (h), 5 (mins), 800 (sec) and M for 500 their time in hours (time must be in range.09 to.5) (could be implied by 697 to 698) (c) (cos =) (96.87 to 96.88) www 4 4 (a) or 5.75 or 5.7 M A M for 450 = cosQ A for (cos =) 0.97 (which implies M) (b) 0 correct plots ft Correct shape curve through 0 points (condone points slightly missed) Two separate branches not crossing y-axis Pft Cft B ft from their values in (a) generous with ( 0.5,.) P for 8 or 9 correct plots ft or P for 6 or 7 correct plots ft ft their points if shape correct ignore anything between 0.5 and 0.5 C and B are independent (c).5 to. 0.5 to to.9 (d) Correct tangent drawn at x = 4 to.5 T Allow slight daylight Dep on T M Rise/Tread attempt Dep on T or SC for answer in range.5 to 4 after T University of Cambridge International Examinations 0

4 Page 4 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June (a),, 4, 5 M for < n 5 seen (M for < n or n 5) Allow n < 6 in M or M case If 0, B for correct with no extras or 4 correct with extra. (b) (i) x(x + 5y) (ii) (a b)(a + b) (c) (i) ½ x(x + 7) = 84 or x ( x + 7) = 84 Correct proof of x + 7x 68 = 0 (ii) (x 7)(x + 4) (iii) 7 and 4 ft M E ft B for x(x +0y) or (x + 5xy) B for (a 6b)(a + b) or (a b)(a + 6b) or correct answer seen in working or B for (a 4b ) If B0, SC for a b = ( a b)( a + b) Condone ½ x x + 7 = 84 but only for M mark No errors or omission of brackets anywhere SC for (x + a)(x + b) where a and b are integers and a + b = 7 or ab = 68 Correct or ft from their factors if quadratic (d) www B for 5 6 = x 4x oe or better M for 5 x = ( x) or better or 7½ x/ = x (e) ( 5) 4 6 p = 5 and r = B B ( 7 ) p + Dependent on r 5 x B or ( ) B.9, 0.89 final answers BB SC for.4 or.86 or.9 seen and 0.9 or or 0.89 seen 4 q or p r q University of Cambridge International Examinations 0

5 Page 5 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June (a) (i) 45 < t Y 55 (ii) 5.6 (5.6.. ) www (b) (i) 40, 77, 0, 50 (ii) Correct scales 6 correct plots ft Curve or ruled lines through the 6 points S Pft Cft Allow any indication e.g. 4 th interval M for (= 7895) Allow error/omission and M dep for 50 B for or correct values ft from (i) if increasing values. (5, ) must be inside square 0 but (55, 77) may be inside or edge of square P for 4 or 5 correct plots ft P for or correct plots ft ft their points if increasing condone graph starting at (0, 6) (c) (i) 54 to 55 (ii) (iii) Their reading at 60 their reading at their reading at 50 ( ± ) (iv) 50 B for UQ = 6.5 to 65 or LQ = 4.5 to 44 seen their reading at 50( ± ) oe SC for oe 50 k (v) If their (iv) is, then ft their ft In (iv) and (v), condone answers as decimals to 50 k k sf Penalise first occurence only of sf decimals isw cancelling/conversion M for k k University of Cambridge International Examinations 0

6 Page 6 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June (a) 87.5 (87.45 to 87.5) www 4 4 M for ½ soi by.875 or 7.5 and M for ½.5 sin60 6 oe (6. to 6.4) or M for ½.5 sin60 (.706..) or trapezium (8.89..) (b) to www Must see at least 4 figures 55 M for π 5 55 or M for seen (c) (i).9 (.9 to.9) www M for 08 = 5πr oe allow 07.9 to 08.0 for their 08 (ii) 4.8 (4.8 to 4.8) cao www M for 5 their.9 (M for h + their.9 = 5 ) (d) 70.9 to 7.5 cao www M for π (their.9 their 4.8 their.45 their 7.4) (not 5 or 7.5) or 8 7 π their.9 their or M for /8 oe e.g. 5 and ½ their h) seen or 7/8 or (½ their R 8 (a) Correct enlargement B for any enlargement of in correct orientation (b) (i) Stretch only y- axis oe invariant (factor) 4 (ii) ft Ft their factor 4 k 0 SC for 0 factor 4 k 0, or 0 0 ft their 4 (c) Shear only x-axis oe invariant (factor) University of Cambridge International Examinations 0

7 Page 7 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June (a) (i), 8, 5 in correct positions (ii) (b) (i) + n oe (ii) n oe B for correct values in correct positions M for ( + ) (= 68) or, ( + ) or M for n + n = 68 then M for (n + a)(n + b) where a and b are integers and ab = 68 or a + b = oe Allow unsimplified e.g. 5 + (n ) B for n oe seen B for k seen (c) a =, b = cao 6 B for or 0 seen but if 0 clearly only from Diagram 4 then B0. M for any of a + b + = oe 8a + 4b + = oe 7a + 9b + = 0 oe M for a nd of the above equations M (indep) for correctly eliminating a or b from pair of linear equations B for one correct value University of Cambridge International Examinations 0

MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 0580 MATHEMATICS

MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 0580 MATHEMATICS UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 0 question paper for the guidance of teachers 0580 MATHEMATICS 0580/4