0607 CAMBRIDGE INTERNATIONAL MATHEMATICS
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1 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 011 question paper for the guidance of teachers 007 CAMBRIDGE INTERNATIONAL MATHEMATICS 007/41 Paper 4 (Extended), maximum raw mark 10 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 011 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 (a) 11.1(1.) B3 If B0, M for (8 5.) 5. ( 100) oe 8 for 8 5. or soi 5. (b) 1 B3 If B0, M for oe for 10% = 5. (c) (i) 34.7 (34.7 to 34.7) final answer B3 If B0, M for oe for n, n > 1 o.e. SC for 4.7 or 4.7 to 4.7 or 34.7 or 34.7 to 34.7 seen (ii) 5.8 to 5.9 or www B If B0, for multiplying 30 by 1.05 more than 3 times or dividing 40 by 1.05 more than 3 times or n = 40 oe SC1 for 5 [11] (a) B3 for cubic with max then min for x-intercept 3, (between and 4) for max at origin, mm accuracy (b) 0, 3 (c) (0, 0) or (, 4) B for one correct and one incorrect [] 3 (a) (i) Rotation, (0, 0) 90 clockwise oe All independent (ii) Reflection, y = x oe Independent (b) (i) Triangle vertices ( 5, 3), (, 3), (, 5) B SC1 translation k or k (ii) Triangle vertices (1.5, 1), (, 1), (, 3) B mm accuracy for 1.5 SC1 for stretch of P wth s.f 1.5 and invariant line x = k or stretch of P s.f. 1.5 with x-axis invariant. [9] 4 (a) (i) 0 (ii) 135 B If B0, for (5 ) 180 (10 + their ) soi by 195 their (i) oe (iii) 110 (b) (i) 75 (ii) 105 ft ft ft 180 their (b)(i) only if +ve. Can recover to correct answer [] University of Cambridge International Examinations 011
3 Page 3 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June (a) 4 B Condone ( 4, 9) for 3 = h 8 oe (with + or ) or for y = 3 x + implied by answer 4 oe (b) 4 7 y = x or other simplified equation B4 isw if equation seen and spoiled If B0, for gradient =, for (4, 3) 3 (a) (i) 9. (0.) A1 (ii) cos (13.15 to 13.1) A 4 seen and for correct use of any linear equation form with their 3 4 or their (4, 3) [] for sin110 SC1 for 9. ww If A0, A1 for 173 or or SC for 13. (13.15 to 13.1) ww (iii) 10 B for 0 or 130 or 50 and 70 (with BA extended) seen at A in correct positions (b) sin 75 (sin R) = their ( ) cao www 5 7 (a) Points at (70, 14), (0, 70), (44, 4) and (50, 50) M M A1 (b) Negative (c) 1.14c ( 1.14 and 9.8 to 9.83) soi by 5 or 8.0 or 8.0. ( for soi by 5) sin R sin 75 ( for = ) their 5 11 P Points touching correct corners. P1 for 3 points B [1] 1.14c + k or mc ( 1.14 and 9.8 to 9.83) If B0, SC1 if 1.1 and 97 Allow x for c (d) 0 or 1 ft ft ft their equation only if answer is positive integer [] 8 (a) 9 B If B0, for 1 8 oe (b) 3.(0..) B3 If B0, M for 550 ( 8) 3 oe 8 ( for ( ) ( ) oe or oe ) (c) 0.55 [] University of Cambridge International Examinations 011
4 Page 4 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June (a) (i) B for shape for approaching y-axis in 4 th quadrant (ii) (1, 0) (iii) x = 0 (iv) (f(x)) 1 B If k to 1, allow. Allow in words. Allow y or x f(x) (b).4(0) (.399 ) B If B0, for line added to sketch (negative gradient, positive y-intercept, may be freehand) must cross curve. Pen 1 if y-coord given (c) 0 g ( x) 1 Allow in words. Allow y or f(x) or x for g(x). SC1 for 0 < g(x) < 1 (d) ft Shape correct translated to left of their original curve ft for passing through origin Condone if stops at origin 10 (a) (i) 00 (08 to 3) B If B0, for π (17584 to ) Allow 700π (ii) 5.43 (5.45 to 5.49 ) ft B3 ft If B0, for 100 and for.40 (M s independent) ft their (i) (b) (i) to B If B0, for π Allow 11000π (ii) h 1 or 13 min cao final answer www 4 A1 [1] ( to ) (73.5 to ) (1.0 to 1. ) or 1 remainder 1.48 to (8 0 0 = 8800) [11] University of Cambridge International Examinations 011
5 Page 5 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June Throughout question 11, do not allow ratios or words. If decimals or percentages used, usual accuracy applies except penalise two sf by 1 only once. isw any cancelling/converting to decimal or % 11 (a) (i) oe 0.8 (0.857.) 7 (ii) 7 Ignore embellishments (b) (i) (ii) 1 5, 7 1 5,,, 4 oe B for 3 or 4 correct (iii) oe B ( to 0.047) 4 1 If B0, for their their 7 (iv) 0 oe B (0.471 to 0.47) 4 If B0, M for 5 5 their their + their their 7 7 for one of the products (c) 40 oe B 0.19(0) ( to ) If B0, for 7 5 [1] 1 (a) 10, 90, 180 (b) ft B ft Accept 58.7 or 58.8 ft their frequencies with correct mid-values If B0, for at least two correct midvalues seen (c) 180, 90, 380 ft B ft for correct ft their (a) (d) (30, 0), (50, 180), (0, 90), (70, 380), (100, 50) ft P ft C1 Points touching lines P1 for 3 or 4 correct ft Smooth curve through these 5 points (0.5 square accuracy) and correct shape (e) (i) 58 med < 0 ft ft In all parts of (e) ft their graph but only if it is cumulative (ii) 43 to 4 ft ft (iii) 9 to 3 ft ft ft is upper quartile their (ii) (iv) 440 to 40 ft B ft If B0, SC1ft for 100 to 10 (may be on graph) If use 00 in all 4 parts mark on ft basis but deduct marks [15] University of Cambridge International Examinations 011
6 Page Mark Scheme: Teachers version Syllabus Paper IGCSE May/June (a) 0.5( x + )( x + 1) = x or ( x + )( x + 1) = x x + x + x + oe seen x 3x = 0 E1 Must be one of these two forms Independent oe includes 1 1 x + x + x + 1 At least one intermediate line after the and no errors or omissions (b) for sketch of parabola with a zero either side of origin or formula correctly used ( 3) ± ( 3) (1) 4(1)( ) or better 0.5, 3.5 A1A1 If M0 or other GDC applications, SC for 0.5 and 3.5 If M0 or, SC1 for 0. and 3. or 0.51 to 0.5 and 3.51 to 3.5 (c) to ft B ft ft a positive root. If B0, for tan = ((their root + 1) / (their root + )) [8] University of Cambridge International Examinations 011
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