0580 MATHEMATICS. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.
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1 CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME f the May/June 3 series 58 MATHEMATICS 58/ Paper (Extended), maximum raw mark 3 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 befe 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 Rept f Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes f the May/June 3 series f most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.
2 Page Mark Scheme Syllabus Paper IGCSE May/June 3 58 Abbreviations cao crect answer only cso crect solution only dep dependent ft follow through after err isw igne subsequent wking oe equivalent SC Special Case www without wrong wking art anything rounding to soi seen implied (a) (i) []8 5 (ii) [= ] oe M M f 7 oe [.667 better] (b) (i) 75 3 M f 5 5 oe M f oe. 8 (ii) 73.3[3 ] 3 M f 5 6 [=7. min] and 7 their 7. 7 oe. 8 M f 5 6 [=7. min] final answer of 6.6[6 ] 6.7 (iii) 5 M f 9 figs36 oe Cambridge International Examinations 3
3 Page 3 Mark Scheme Syllabus Paper IGCSE May/June 3 58 (a) 3,.33[3 ], 3 B f each crect value (b) Crect quadratic curve 3 BFT f 7 crect points BFT f 5 6 crect points Crect exponential curve 3 BFT f 7 crect points BFT f 5 6 crect points (c) (i) Answer in range. < x <. (ii) Answer in range. < x <.35 Not from a line other than y = (±mm) (iii) Answer in range.55 < x <.7 (d) Crect tangent drawn And answer in range.5 < m <.5 3 B f crect tangent at x =.5 B f answer in range dep on close attempt at tangent rise M f [ ] used with values soi run from tangent, dep on close attempt at tangent answer in range.5 < m <.5 SC f close attempt at tangent to exponential curve and answer in the range.6 < m <. 3 (a) (i) 3. (ii). (iii).6 (iv) 96 (b) (i), 6, B f crect (ii) M f frequency of 6 seen in wkspace Cambridge International Examinations 3
4 Page Mark Scheme Syllabus Paper IGCSE May/June 3 58 Qu. Answer Marks Part marks (a) Enlargement [centre] ( 3, ) [scale fact] 3 Do not allow column vect f codinates (b) (i) Image at ( 5), (, 5), (, 6), (, 7) 5 SC f translation by k (ii) Image at (5, ), (8, ), (8, 3), (5, ) SC f reflection in y = k (iii) Image at (, 3), (, 3), (, 6), (, 9) SC f three crect vertices shape with vertices at (, ) and (, ), (, ) and (, 7) (iv) 3 SC f 3, k ± k (c) Reflection B B independent y = x oe 5 (a) 7.5 ( ) www 3 M f [= 79.5] and M (dep on M) f their Σfx (b) 6 < x 65 oe (c) Blocks with heights of.8,.,, with crect interval widths and no gaps B3 f crect blocks B f crect block B f 3 crect frequency densities heights 3 crect widths Cambridge International Examinations 3
5 Page 5 Mark Scheme Syllabus Paper IGCSE May/June 3 58 Qu. Answer Marks Part marks 6 (a) M f sin 3 M f crect implicit statement 5.7 sin 5 (b) [sine =] (c) (i) [ ACE = ] M A M M f crect implicit statement [= 79.3] [ ECD = ].57 A (ii) to 5.8 www M f [(DE) =] cos(.6.57) M f full crect implicit statement A f 33 to 3 (d) to 66.5 M f their 3. sin(9 3) oe M f sin(8 their ) oe M f sin (.6.57) oe Cambridge International Examinations 3
6 Page 6 Mark Scheme Syllabus Paper IGCSE May/June 3 58 x (a) 6.6 (6.6 ) www 6 B f = oe x M f 6(x + ) = 9(x + 3) better A f [x =].5 M f {( their x + 3) (their x + ) } M f ( their x + 3) (their x + ) SC f final answer of better SC f final answer of 5 7 better (b) (i) White = 8.5, red = 5 B3 f 7w + 5(w +.5) =.5 f 7 ( r.5) + 5r =. 5 oe B f 8.5 SC f 7w + 5 w +.5 =.5 leading to 9.33[3 ] SC f 7w + 5 w +.5 =.5 OR B f r = w +.5 oe B f 7w + 5r =.5 oe M f elimination of a variable A f 8.5 (ii) (a) (ii) (b) ( to.38) (.53[].533 ) 7 M f M f their (a) 7 M f SC f oe from replacement Cambridge International Examinations 3
7 Page 7 Mark Scheme Syllabus Paper IGCSE May/June (a) (i) 8 M f (3 8 8) [ ] better (ii) 3 FT FT (8 their (i)) (iii) FT FT 8 their (ii) their (ii), only if positive answer and less than 8 (b) 3 B f 36 3y = (y + ) oe and B f y = 35 oe M f angle at centre = angle at circumference soi (c) (i) Opposite angles [cyclic quad] add to 8 (ii) 68 3 M f [angle PRS =] 3 and M f angle PQS = angle PRS angle PRQ = angle PSQ (d) M f oe M f evidence of ratio of areas = (ratio of sides) sf =. 9 (a) ± ( 3).3,.3 final answer B f ( 3) better p + q p q and if in the fm r r then B f p = and r = () better B B SC f.3 and.3 seen.3.33 to.3 and.3.3 to.33 final answer.3 and.3 (b), 3, 53 3 M f (x + 7) + (x + 7) 3 and B f (x + 7) = x + x + x + 9 oe Cambridge International Examinations 3
8 Page 8 Mark Scheme Syllabus Paper IGCSE May/June 3 58 (c) x 7 M f y 7 = x x = y then clearly seen in crect der y 7 with arrow better (d) (e) B3 f B f 56 seen B f 8 seen 56 (a) 5, 7 n oe 5, 7 n + oe (b) (i) (ii) n + (iii) n + 5 (c) (i) = 63 and = = = 63 (ii) 56 (d) Complete solution with no errs seen and a conclusion e.g. 5n + 6n + (n + ) + = 5n + 6n + n + + = 5n + n n + 6 = 5n + n n + 6 = 5(n + ) + 6(n + ) B f 5n + 6n + n + + better B f use of 5(n + ) = 5n + n + 5 oe at any stage B f use of 6n + 6 = 6(n + ) oe at any stage Cambridge International Examinations 3
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