0580 MATHEMATICS. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Transcription

1 CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 03 series 0580 MATHEMATICS 0580/43 Paper 4 (Extended), maximum raw mark 30 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 May/June 03 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

2 Page Mark Scheme 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 (a) 84 final answer M for soi by 469 or ans = 80 (b) final answer M for oe or ans = 58 (c) (i) 80.5[0] final answer M for 330 ( 0.5) oe or ans = 8 (ii) M for 330 ( 0.) oe Or M for 330 = (00 )% oe (d) or 605.9[0] 3 M for 500 ( ) 3 oe soi by or (05 ) Or M for 500 ( ) oe (e) 3. or 3.07 to M for 00 oe Or M for soi by sf or or 00 soi by Cambridge International Examinations 03

3 Page 3 Mark Scheme Syllabus Paper IGCSE May/June (a) (i) Perpendicular bisector of QR ruled with correct sets of arcs centred Q and R Bisector of angle SPQ ruled with correct arcs. (Marks on PS and PQ and correct pair of arcs) Compass drawn arc centre R with radius 6 cm (± mm) Correct region shaded cao B dep B for correct bisector ruled B for correct angle bisector ruled B for any compass drawn arc centre R not used in any construction with no feathering Dependent on all B4 marks for the correct loci (ii) 7 to (b) (i) 6360 or 636 to 6363 M for π 45 0 (ii) 65 or 64.9 to 65 M for π (a) (i) x 5 once for strict inequalities in (i) to (iii) (ii) y (iii) x + y 0 (b) 4x + 8y 60 and divide by 4 If there is a final inequality it must be the given one (c) (i) x = 5 ruled Must be on correct grid line y = ruled Must be on correct grid line x + y = 0 ruled B for one axis intercept correct when extended if necessary but not parallel to an axis x + y = 40 ruled B for one axis intercept correct when extended if necessary but not parallel to an axis Correct shading of unwanted region dep Dependent on 6 marks earned for the boundaries (ii) 9 M for x + y evaluated where (x, y) is a point in their quadrilateral and x and y are integers Cambridge International Examinations 03

4 Page 4 Mark Scheme Syllabus Paper IGCSE May/June (a) 3080 M for ½ 7 40 (b) 46. or 46.8 to 46. www 4 M3 for or M for soi by 33 or M for correct Pythagoras on one face 7 (c) 8.7 or 8.7 to 8.7 www 3 M for sin their(b) oe 7 or M for sin = their(b) oe (d) 7 3 M for 3 4 π.5 3 soi by 4. to 4.4 and M dep for their (a) their 4.4 soi by 8. Dependent on M earned (e) (i) final answer B for 4.55 and.05 seen or seen and then spoiled (ii) 5.4 FT Strict FT their (e)(i) correct to 4s.f. if rounding is possible 5 (a) 5.04,.75, 0 3 B for each correct value (b) Fully correct curve 5 B3FT for 0 correct plots from their (a) BFT for 8 or 9 correct plots or BFT for 6 or 7 correct plots and SC for two branches not joined (c).6 to to to.9 (d).6 to.5 www 0.4 to 0.3 After 0 scored, M for y = x drawn (e) 3.5 to 4.5 with correct tangent 3 B for correct tangent B for answer in range dep on close attempt at tangent rise Mdep for [ ] used with values soi from run tangent, dep on correct or close attempt at tangent Cambridge International Examinations 03

5 Page 5 Mark Scheme Syllabus Paper IGCSE May/June (a) 3 correctly placed 0 Accept and correctly placed 9 9 Accept or and or 7 and correctly placed 9 9 Accept or and 0. or (b) or or or M for + soi by or or M for or soi by 0.33 or (a) (i) Triangle at (, 3) (, 9) (3, 3) SC for correct vertices not joined or triangle(, ) (3, ) (, 7) (ii) SC for, k ± or 0 k 3 0 or (b) (i) Shear x-axis oe invariant [factor] (ii) FT FT from their in (b)(i) k SC for, k 0 0 or FT 8 (a) (i) 7 (ii) 54 (iii) 53 (b) (i) 59.6 or www 4 M for cos00 or M for implicit cos rule and A for (ii).[0] or.99 www 3 M for 34 (½ 3 sin67) or M for [34 =] ½ 3 x sin67 (iii) 8[.0] B for or (½) oe seen or ½ 6 ½ their(b)(ii) sin67 Cambridge International Examinations 03

6 Page 6 Mark Scheme Syllabus Paper IGCSE May/June (a) (i) 4 (ii) 8 (iii) 30 their (ii) FT (b) SC for 80 (c) 6, 4 B for each correct value (d) rot to 3sf or or 8. www 3 M for Σmf for m as mid values of 5,.5,.5, 35 and 45 (= 445) and M dep for Σmf 80, dep on M earned (e) Correct widths with no gaps nd block w = 5, fd =.4 3 rd block w = 5 fd =. 4 th block w = 0 and fd =.6 5 th block w = 0 and fd = 0.4 FT FT Strict FT from their (c) Strict FT from their (c) After 0 scored for blocks, SC for 4 correct fds soi by correct heights 0 (a) (i) 4.5 or 4½ 3 M for a complete correct method or M for one correct step at any stage. (ii) (x 6)(x ), 6 M AFT M for (x +a)(x +b) where ab = 6 or a + b = - 7 FT their brackets dep on M earned After M0 scored SC for, 6 as answer (iii) 6 4 B for (3x ) + x + = 4 0 oe and B for correct multiplication of a bracket and M for correct rearrangement of their linear equation without brackets to ax = b + c + d or (b) a = /3 oe, b = / oe 6 B for any one of = a + b + /6 oe 5 = 8a + 4b + /6 oe 4 = 7a + 9b + 3/6 oe 30 = 64a + 6b + 4/6 oe Or any other correct equation and B for another of the above equations and M for equating one coefficient or correct rearrangement to give a or b as subject and M for subtracting to eliminate a or b or correct substitution for their a or their b A for a = /3 oe or b = / oe Cambridge International Examinations 03