MARK SCHEME for the October/November 2014 series 0580 MATHEMATICS. 0580/11 Paper 1 (Core), maximum raw mark 56

Transcription

1 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 04 series 0580 MATHEMATICS 0580/ Paper (Ce), maximum raw mark 56 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 October/November 04 series f 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.

2 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied Qu. Answers Mark Part Marks 7 4 (a) (a) 5. cao 0 cao E B A cao Z cao 4 M f 60 ( ) better 5 7 M f attempt at dering to at least 7 th term and 4 indicated 6.4 π.4 7 and 5 cao 8 4w( wx y) Final answer 7 B f.4[5...] to.46 and.48 to.49.4 seen SC f 4 in crect der M A Equivalent denominats can be used, wking must be shown. B f 4( w x wy) w( 8wx y) w( 4wx 6y) 9 65 to 65 M f π.6 6 better 0 (a) 4 FT FT their numerical mode 4x 7 Final answer B f answer 4x + k answer jx 7 where j 0 crect answer seen then spoilt Cambridge International Examinations 04

3 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) (a) 9, 7 and B f crect products of primes method crect fact tree ladder crect and 0 wrong crect and extra B f oe 6 B f answer k 0 k (a) 4 [days] [C=] 5 + 6d Final answer M f ( 9 5) [sides] M f 60 ( 80 40) M f (a) 66 4 FT FT their (a) 4, only if their (a) > 4 B f either of these, may be on diagram, angle OAC = 4 angle BAC = their (a) 7 [$] 94.4 M f oe M f oe SC f answer of interest only cao M f M f Crect ruled net drawn B f rectangles, even if increct not joined, drawn one on each side of the given one and two triangles opposite sides and B f crect ruled rectangles and B f crect ruled equilateral triangles 0 [x =], [y =] 0.5 M f crect method to eliminate one variable A f [x =] A f [y =] 0.5 If zero sced, SC f crect substitution and evaluation to find the other variable Cambridge International Examinations 04

4 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) 80 M f 5 ( 4) 5 4 better y y [ ± ] 5 5 Final answer M f crect first step i.e. x 5 y = 5 x crect nd step after increct st step seen (a) 8.4 M f [PQ =] better [0]60.4 to [0] tan = better M f [... ] 9 6 sin = better their(a) [... ] 9 cos = better their(a) [... ] If zero sced, SC f answer [0]9. to [0]9.4 Cambridge International Examinations 04

5 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 04 series 0580 MATHEMATICS 0580/ Paper (Ce), maximum raw mark 56 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 October/November 04 series f 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.

6 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied Qu. Answer Mark Part marks (0 8) = 6 One pair of brackets only (a) 5 and 5 and and 5 and B f 8 9 seen in the wking 0... B f 6 in the wking on the answer line , If zero, SC f both crect but reversed [mm] and [mm] in crect place 7 (a) cao 8 (a) [0] x 8 oe 5 B f 5y = x 8 5y = 8 x If B0 SC f x x (a) FT FT f their (a) 40.4% B f in crect der f , and Cambridge International Examinations 04

7 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) k B f seen in the wking. (a) 700 M f oe their oe cao must see wking B M A 56 4 Or M f equivalent division with fractions with common denominats cancelled 5 [x =] [y =] 5 M f crect method to eliminate one variable A f x A f y If zero sced SC f crect substitution and evaluation to find the other variable. 6 (a) 6 oe 60 9 cao B f 76 their76 M f (a) 4 points crectly plotted B f crect Crect ruled line of best fit (c) Positive 8 (a) 9 cao 5 and 5, (c) Any multiple of 8 (d) 6 9 (a) (c) [x =] 66 B f angle BED = 90 soi [y =] 4 [z =] 48 FT MFT f angle ABC = 90 their y Cambridge International Examinations 04

8 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) 0 to 06 B f 5. to 5. seen Crect position of F with crect arcs f angle bisect 5 B f Crect ruled angle bisect of A with crect arcs B f crect bisect with no/wrong arcs and B f Arc centre C, radius 8 cm B f arc centre C with increct radius crect conversion to 8 cm and B f marking position of F on their bisect and 8 cm from C their arc centre C Cambridge International Examinations 04

9 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 04 series 0580 MATHEMATICS 0580/ Paper (Ce), maximum raw mark 56 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 October/November 04 series f 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.

10 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied Qu. Answers Mark Part Marks oe 00 (a) FT (a) B f 9.609[ ] f their answer seen rounded to d.p. 5 (a) 6 (a) 7 (a) 8 (a) oe oe M oe A 5 Answer must be a fraction Cambridge International Examinations 04

11 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November y + 6 oe y B f y + = 6x = x 6 y y If B0 SC f M f decimal conversion: 0.7[7 ] 0.8 f 0. 6 and 0.6 f 0.6 and 0.4 f 0.7 B f three in the crect der B f oe 8 B f k M f x + x + 4x + 90 = 60 oe 4 48 M f 5 65 [ 60] oe implied by 0.8 k 5 (a) 440 M f (a) 6 j k B f 6 j ± ak bj k (a and b 0) 5 ( p + ) 7 (a) 60 (c) Irrational number between and M f = ( 8 ) 5 x better oe M f x + 5 = 8 better 9 (a) (c) (i) 6 [kg] Positive Ruled line of best fit Crect reading from ruled line FT Cambridge International Examinations 04

12 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) Complete circle centre E radius cm Crect ruled bisect with two pairs of crect arcs B f crect bisect with no/wrong arcs (c) dep on attempt at bisect of C and enclosed region (a) 58 B f ACB = 90 o soi as angle at C 8 M f tan to 9.44 M f [ ] AB = sin = cos = oe AB AB (a) Trapezium 55 o (c) to.7 nfww B f [AB =] 7., [DC =] 4.7, and [height =].6 seen and 0.5 their.6 their M f ( ) Cambridge International Examinations 04

13 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 04 series 0580 MATHEMATICS 0580/ Paper (Extended), maximum raw mark 70 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 October/November 04 series f 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.

14 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied Qu. Answers Mark Part Marks 8.7 cao B f π.4 7 B f.4[5...] to.46 and.48 to.49.4 seen SC f 4 in crect der (a) E B A cao Z cao 4 (a) 4 FT FT their numerical mode 5 and 5 cao M A Equivalent denominats can be used, wking must be shown. 6 (a) 5. cao 0 cao 7.5[0].50 nfww 6 M f ( ). + oe 00 6 M f. ( + ) n oe where n 00 + oe 6 f figs ( ) cao M f 0 ( 4.78) ( 4.78) 0 00 M f (a) B f oe 6 B f answer k 0 k 5 0 Cambridge International Examinations 04

15 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November oe M f 5 = 7x x oe 7 M f ( x + 5) = 7x x + 5 = x x = better (a) x 6 x 5 5 B f answer kx k x nfww M f crectly eliminating one variable A f x = 5 A f y = 5 If zero sced SC f crect substitution and evaluation to find the other variable [±] 8 nfww M f y = k x + 5 A f k = [±] 4 M f = + 5 y + 5 oe M f 8 and M f f (a) (i) B f crect ruled bisect with crect arcs B f crect bisect with no/increct arcs B f crect ruled bisect with crect arcs B f crect bisect with no/increct arcs crect shading B f CBD = 0 6 sin theirb M f [ sin D = ] oe M f sin D = sin( their0) A f [D =].0.0 BFT f 90 + (their0 + their) evaluated crectly f their final answer f theirbcd evaluated crectly f their final answer Cambridge International Examinations 04

16 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE October/November to M4 f 4 π 5 + π M f π 5 and π M f π 5 π M f π 5 8 (a) in crect places B f 0.6 in crect place B f 0. and 0.8 in crect places 0.5 oe nfww MFT f (their 0.6 their 0.8) oe MFT f a crect product from their tree in (a) 9 (a) CBA and BDA are equilateral oe 67[.0] 67.0 to 67.0 M f 0 60 π 8 oe (c) (i) to 9. MFT f ( b) 8 sin0 their oe M f 8 sin0 oe to FT FT their(c)(i) crectly evaluated 0 (a) B f [f() =] 4 M f ( x ) + better M f 0( + ) = x better (c) x ( ) 6 x nfww M f ( x ) ( ( x + ) ) M f [ f ( x ) = ] ( x) [ f ( x + ) ] = ( x + ) Cambridge International Examinations 04

17 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 04 series 0580 MATHEMATICS 0580/ Paper (Extended), maximum raw mark 70 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 October/November 04 series f 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.

18 PagP ge MarM k Schemee Cambridgee IGCSEE October/ /November 0 4 Syllabus 0580 Paper Abbreviations caoo crectt answer only depp dependent FTT followw through afterr errr isww igne subsequent wkw king oe equivalent SCC Special Case nfwww not from wrong wking soii seenn r implied Qu. Answers Mark Part Marks (0 8) = 6 One pair of brackets only ξ A B ξ A B 5 v p M f v = p + r in crect placess cao B f in crectt place f answers reversedd 7 (a) 700 M f oe 6 7 their 4 must 8 oee 6 7 caoo seee wking B M A 56 Orr M f 6 4 equivalent divisionn with fractionss withw common dend ominat Cambridgee International Examinationss 044

19 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November to 9.7 M f [.] oe [0.76] oe Or M f [.7] oe [0.44] oe 000 figs440 figs000 figs000 figs [0] M f C = kr² A f k = c M f = oe (a) 8 8 M f a by matrix with two crect elements 6 4 SC f R 0 SC f [..] M f sin0 M f ½ a sin 0 = oe [80.9..] sin0 4 (a) to.4744 M f π.5 oe to 0.74 FT FT their (a) 0.[0] crectly evaluated. Cambridge International Examinations 04

20 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) 5 B f,, [] and 5 identified as only prime facts M f partial prime factisation M f 5 7 oe f listing multiples of 90 and 05 at least up to 60 6 (a) 08 Angle at centre is twice angle at circumference oe (i) 4 oe 7 [0.]08 4 M f oe M f and M f [+00] 00 8 (a) 56 B f 6 soi M f 7 their 6 (i) 6 6 to to nfww B f 49.8 to 50. seen 7.8 to (a) (i) c a a + c M f a + (c + a) oe e.g. a + c + a (c + a) Or M f a crect route from A to X AC is a multiple of AX and they share a common point [A] oe oe Cambridge International Examinations 04

21 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) 0 to 06 B f 5. to 5. seen (a) Crect position of F with crect arcs f angle bisect x + 7 (x )( x + ) Final answer x x + 7 Final answer 5 B f Crect ruled angle bisect of A with crect arcs B f crect bisect with no/wrong arcs and B f Arc centre C, radius 8 cm B f arc centre C with increct radius crect conversion to 8cm and B f marking position of F on their bisect and 8cm from C on their arc centre C B f ( x + ) ( x ) seen better B f denominat (x )(x + ) oe seen x + 5 SC f final answer (x )( x + ) 4 M f 4x(x 4) partial factisation of numerat and M f [](x + 7)(x 4) oe M f [](x + x 8) [](x + a)(x + b) where ab = 8 a + b = 4x SC f answer oe x + 4 Cambridge International Examinations 04

22 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 04 series 0580 MATHEMATICS 0580/ Paper (Extended), maximum raw mark 70 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 October/November 04 series f 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.

23 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied Qu. Answers Mark Part Marks 870 M f M f decimal conversion: 0.7 [7 ] 0.8 f 0. 6 and 0.6 f 0.6 and 0.4 f 0.7 B f three in the crect der B f oe 8 B f k k 4 0 M f x + x + 4x + 90 = 60 oe 5 48 M f 5 65 [ 60] oe implied by M f x = (8 ) 5 better oe M f x + 5 = 8 better ( ) M f M f 80 (8 ) (y ) oe final answer M f y = (x 8) M f squaring both sides completed crectly M f adding their 8 completed crectly on answer line 9 4 M f 6( + 5) = y(7 + 5) oe k M f y = oe x + 5 A f k = [0] M f oe 00 oe M f oe n > 00 n Cambridge International Examinations 04

24 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) cao 4 M f 9 ( 9 + ) n (n + ) oe (a) Complete circle centre E radius cm Crect ruled bisect with two pairs of crect arcs B f crect bisect with no/wrong arcs (c) dep on attempt at bisect of C and enclosed region 6x + 8x + 9 6x final answer 4 M f 9 [+] 4x [+] 8x [+] x better M f of these and MFT f adding their four numerats together crectly and B f denominat 6x to a maximum of marks 4 (a) b a oe M f ( AO + OB ) oe crect unsimplified route e.g. AO + OB + BP a + b + BA = a + b + (a b) a + b oe 4 4 M f OA + AQ oe crect unsimplified route 5 (a) 9 8 B f any two crect 8 9 FT BFT f a crect ft from (a) BFT f any two crect f any crect two ft from (a) 6 (a) 64 B f [f() =] 4 M f ((x ) ) better 4x + oe M f x = y 4y = x 4 (c) x 4 oe final answer (d) nfww Cambridge International Examinations 04

25 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a).08 to. nfww B f 50.5 to to oe 00 B f 6 soi their6 M f 00 (c) B f 8.5 and 6 B f 8 (a) 4 B f.56 to.54 as an answer M f 000 π 6 5 M f π 6 5 and SC f truncating their.54 to a whole number 0 to 04 M f 000 their their volume M f their their volume 9 (a) rotation 90 clockwise [about] igin oe B f each 0 0 M f any one column row crect (c) Triangle at (, ), (6, ) and (, 5) M f any two vertices crect crect answer translated hizontally Cambridge International Examinations 04

26 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 04 series 0580 MATHEMATICS 0580/ Paper Ce, maximum raw mark 04 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 October/November 04 series f 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.

27 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied Qu. Answers Mark Part Marks (a) (i) their 60 ( ) M MFT A Alternative method M MFT their A 0.06 ( ) If 0 sced SC f M f 5 ( ) 500 (540/9) (iii) 0 FT M f their (a) oe (i).5 5.6[0] B f 4 (7/8) 6.4[0] (iii) 46. FT M f (their 6) 6 00 M f their 6 M f their M f their 6 [ 00] (a) (i) Trapezium 6 cm M f ½( + 6) 4 oe Rotation B Independent marks 90 [anti-clockwise] oe B [centre] (, 8) B (c) (i) Crect reflection in y = 0 SC f crect reflection in x = 0 Translation 5 left and 7 up SC f one of 5 left 7 up Cambridge International Examinations 04

28 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November (iii) (d) Crect Enlargement Obtuse angle marked SC f enlargement, SF ½, but increctly placed. (a) (i) 4 points crectly plotted. B f crect Crect continuous ruled line of best fit. Dependent on at least 8 points on graph (iii) (iv) Distance on their line of best fit. Negative FT FT their single straight line in part. (v) Faster the time, the longer the distance oe (i) NFWW M f Attempt at f to 4.67 B f 5 seen (iii).45 4 (a) x + x + 80 = 480 x = 00 M M 060 [cm] M f (0 + 0) oe (c) (i) M f oe FT FT their (c)(i) 70 (iii) FT FT their (c) 00³ 6 M f their (c) 6 Cambridge International Examinations 04

29 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) (i) (iii) > FT FT their answers to (i) and (c) 945, 955, SC f both crect but reversed (d).667 cao B f better (e) (i) 5 (iii) 4x 9 B f 4x k kx 9 6 (a) (i) 4, 7, 4 B f crect 7 points crectly plotted Crect curve through the points FT B f 5 6 crect B f 4 crect (iii) x = 0 (iv).7 to.9,.7 to.9, (i) Points crectly plotted and a ruled line through points and beyond them. B f crect plot. (even if line is not drawn) [y =] x + 4 B f x + j B f kx + 4 k 0 rise [gradient =] run crect values (iii) (. to.4, 6.4 to 6.6) 7 (a) 06 to 0 (i) Crect bisect of AB constructed with pairs of arcs. B f crect bisect Crect bisect of angle ABC with arcs B f crect bisect without arcs (iii) T marked at intersection of their bisects FT Cambridge International Examinations 04

30 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (c) 4.4[km] to 6.0[km] FT FT their AT B f their AT crectly measured. (d) Circle, radius 7.5(±0.)cm centre T. FT FT their intersection SC f circle centre T, increct radius. (e) No It is outside the circle. oe FT FT their circle. 8 (a) (i) Crect diagram with scale B scale crect. B f all widths the same B f all 6 heights crect 0 to cao (iii) [...] 5.8[...]% 0 Probability must be between 0 and oe (c) (i) % 0 0 oe 9 (a) (i) 8 8,, Allow one mark f each addition of 5 to the previous answer Add 5 oe (iii) 5n oe B f 5n + j kn k 0 (iv) 7 FT FT their (a)(iii) if linear. (i) 0 4, Allow mark f addition of 4 on their value f rd diagram. 4n oe B f 4n + j kn k 0 Cambridge International Examinations 04

31 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 04 series 0580 MATHEMATICS 0580/ Paper (Ce), maximum raw mark 04 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 October/November 04 series f 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.

32 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied Question. Answers Mark Part Marks (a) oe (c) (i) M f ( ) ( ) (iii) 5 70 FT MFT f their (d) (i) M M f k 40 40k final answer A If zero sced, 75 SC f ( ) = 0.75 = = 000 k [ ] 40 40k 75 SC f ( ) = 0.75 = 000 followed by increct fraction k SC f final answer 40 40k FT FT their (d)(i) (e) 8 6 cao M f oe M f oe If zero sced, SC f 6 Cambridge International Examinations 04

33 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) Octagon 5 M f 80 (60 8) M f ( 8 ) 80 8 M f (60 8) M f (8 ) 80 (c) (i) 9 6 B f two terms in crect places terms with a difference of 7. 7n + oe B f 7n + j kn + (k 0) (iii) 7 FT FT f their (c) if linear (iv) nfww MFT f their (c) = 9 M f (9 ) M f 7 + = 9 (a) Reflection [in] AB Rotation 80 o oe Midpoint of AB oe (i) Translation left and 7 up SC f one of 7 up left Crect Enlargement SC f enlargement scale fact but increctly placed (c) Crect line of symmetry FT FT is their 4 (a) (i) Line (0700, 0) to (08 40, 0) Hizontal line squares Line their (08 50, 0) to (09 40, 470) FT FT Lines need not be ruled and could be curves with positive gradients throughout. [h]40[min] (iii) 76.5 MFT f 470 their (a) (i) [h][min] M f soi Line from (07 45, 470) to (their 0 06, 0) FT B f (07 45, 470) crectly plotted BFT f (their 0 06, 0) crectly plotted (c) 90 to 00 FT (Crect follow through) FT from intersection on their graph. Cambridge International Examinations 04

34 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) (i) Trapezium Pentagon (i) [BC =] 5 0 [= 48] B B f 5 = BC + (70 50) 5 = BC + 0 BC = M f (70 + ) 48 oe (c) (i) M f 0.5( ) 48 oe (d) 08 B f [AE=] 4 M f 0.5 their AE 9 (e) 948 FT FT their (their (c) + their (d)) 6 (a) (i) B f crect 8 points crectly plotted Crect curve (iii) Ruled line y = 6 drawn. to.6 BFT BFT f 6 7 crect points BFT f 4 5 crect points Independent marks (i) 5 B f crect Ruled crect line (iii) oe (c) 7. to to 5.6 FT FT 7 (a) (i) 5.5 M Sum of the 0 items of data 0 6 M f dering at least first last 6 items f 4 and 8 indicated (iii) 6 (i) 6 crect bars B f 4 5 crect bars 6 crect heights Aug[ust] (iii) 4 oe Cambridge International Examinations 04

35 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) (i) [0]6 to [0]67 8 B f 6 ± 0. [cm] seen in wking QR on bearing o to 7 o B f bearing of o to 7 o 9. cm to 9.7 cm continuous ruled line FT MFT f 76 their (a) soi by calculation distance on diagram (c) (i) (60 97) 7.6 cao nfww PW PW M f cos7 = sin6 = better A f 7.57(...) Bind f crectly rounding their 7.57(...) to sig figs if their 7.57( ) is to sig figs me (d) Crect continuous perpendicular bisect of AB with two pairs of crect arcs B f crect continuous bisect without arc with increct arcs 9 (a) (i) 8.4[0] M f better M f better 89.6 FT MFT f.5 their (a)(i) oe (i) FT.8 their (i) (iii) FT FT their (a) + their their(iii) (c) nfww FT MFT f Cambridge International Examinations 04

36 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 04 series 0580 MATHEMATICS 0580/ Paper (Ce), maximum raw mark 04 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 October/November 04 series f 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.

37 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied Qu. Answers Mark Part Marks (a) (i) 4, 5,, 6, B f crect f fully crect tally f in tally column Crect bar chart FT B f linear vertical scale to at least 6 B f all bars crect height and equal width bars Or B f unequal widths at least four bars crect height and equal width 4 oe 0.58[...] 58.[...]% 4 (c) No, 6 of each but different nos of boys and girls questioned oe (d) (i) M f th/th value used.8 M f [0 4] [5 0] + 6 M dep f their 57 5 (a) cao [= 864] Or (c) (i) 0.4[0] M f 864 ( ) 9 cao B f oe 5 5 (d) (i) M f 45 ( + 0.5) oe 9.5 FT M f their (d)(i) 0.5 [= 54.5] (e) (i) M f [= 97.9] Or M f seen Cambridge International Examinations 04

38 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) 0 Befe, steeper gradient oe (c) 0 8 (d) (i) hour 48 minutes M f [ 60] oe 0 Crect ruled lines drawn B line from ( 0, 8) to ( 0, 8) BFT f line (their 0, 8) to ( 58, 0) (e) (i) (f) Bearing 0 Length.5 cm 4 (a) (i) 85 0 FT FT 95 their (i) (iii) 0 FT FT 0 their (iv) 95 (v) 95 FT FT their (iv) (vi) 55 FT FT 50 their (iv) (vii) BCE and GCF BCD and GCH CED and CFH (i) 0 M f FT FT 80 their (i) Cambridge International Examinations 04

39 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) (i) M f change in y / change in x f two crect points x + FT FT their gradient (i) 6, 7, 6, 9 B f crect Or B f crect 8 points crectly plotted Crect smooth curve FT BFT f 6 7 points crectly plotted BFT f 4 5 points crectly plotted (iii).8 to.5 and.5 to.8 FT BFT f one crect (c) (.6 to,9, 0.7 to 0.) and (.9 to.6, 6. to 6.7) FT FT intersection of line with their curve B f one crect 6 (a) x 5x 4 MFT f x + x + + their (x ) oe (c) (i) 4x + 4 M f [(x 4) + 4 x] oe 8 FT FT crect solution of their equation MFT f their (5x 4) = their (4x + 4) (d), 6 FT BFT f each (e) 7 FT FT their length width 7 (a) B4 f 5 crect B f 4 crect B f crect B f crect (i) n + 4 oe final answer B f n + k jn + 4 j 0 4n + oe final answer B f 4n + k jn + j 0 (c) B [by] 5 [tables] MFT f their (n + 4) = 66 their (4n + ) = 66 and AFT f n = n = 6 Cambridge International Examinations 04

40 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) (i) [Triangular] prism Crect net B f rectangles and two triangles, one on each side, even if increct sizes B f three crect ruled rectangles B f two crect ruled equilateral triangles (iii) cao (iv) 5 cao (i) to M f π.5 0 Or B f.5 seen Or SC f answer to to M f π 4 Or M f π 9 (a) (i) Line x = drawn Crect reflection FT FT reflection in their drawn line (iii) Crect rotation B f clockwise rotation 90 about igin crect ientation increct position (i) Translation 4 Enlargement [scale fact] [centre] (6, 0) B B B B B Accept left 4 down Cambridge International Examinations 04

41 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 04 series 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 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 October/November 04 series f 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.

42 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied Qu Answers Mark Part Marks (a) (i) M f 7 (7 + + ) M f.5 (7 + + ) oe (iii) M f 8.4[0]. oe M f [%] associated with [$]8.4[0] oe (i) sin60 oe M M f a crect relevant area inside the hexagon e.g. 0.5 sin60 oe 0.8 to 0.9[ ] [= 0.4] A Must see 0.8 to 0.9[ ] 4.67 to 4.68 M f 0.4 figs 45 [figs 467 to 468] (iii) 7 4 M f their A FT f their evaluated to at least sf Mdep on previous M f their mass in tonnes (rounded up) 45.5[0] if between 6 and 0 f their mass in tonnes (rounded up) 47[.00] if between and 5 f their mass in tonnes (rounded up) 44[.00] if over 0 Cambridge International Examinations 04

43 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Qu Answers Mark Part Marks (a) [±] v + as final answer M f crect first step, i.e. u = v + as (i) 60 x 45 + x + 4 = 6 oe M B f either seen x x (x + 4) + 45x = 6x(x + 4) better M Dep on M 60x x = 6x + 4x oe 0 = x 7x 80 A [6x 8x 40 = 0] Dep on M and brackets expanded and with no errs omissions throughout 6 final answer M f (x 6)(x + 5) [= 0] M f partial factisation e.g. x(x + 5) 6 (x + 5) SC f (x + a)(x + b)[ = 0] where ab = 80 a + b = 7 B f [ ] ( 7) B f x q. ( 7) (c) (i) [=5] 50 cao 4 M f 90 + T = oe T 0 = (800 (90 5) (0 5 )) 5 oe t = (800 (90 5) (0 5 )) 5 oe [t = 40] M f ½ (90 + T) 5 = 800 oe ½ (T 0) ½ (0 5) = 800 oe 800 ½ oe [00 f area of end triangle] M f method f area of triangle rectangle trapezium soi Cambridge International Examinations 04

44 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE October/November Qu Answers Mark Part Marks (d) 0 cao nfww M f.5.5 M f.5 to.5.5 to.75 B f.5.5 seen (a) Crect reflection (0, ) (, ) (, ) Crect rotation ( 5, ) ( 7, ) ( 5, 4) SC f rotation of 90º anticlockwise about the wrong centre 90º clockwise about ( 4, 0) f crect points plotted but not joined (c) (i) Enlargement [scale fact] [centre] ( 7, 7) B f each : 4 : ¼ : M f : oe, e.g. ( )/ : (6 4)/ SC f 4 : : : ¼ (d) k 0 B f, k may be algebraic numeric 0 but 0 0 SC f 0 4 (e) (i) Crect shear drawn (0, ) (, 5) (, ) B f two crect points plotted if not plotted crectly shown in wking 0 B f better Shear y-axis x = 0 invariant [fact] B f each (iii) 0 oe B f [determinant =] shown stated 0 k soi, k 0 Cambridge International Examinations 04

45 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE October/November Qu Answers Mark Part Marks 4 (a) (i) x final answer M f 8x 4 9x + 5 B f final answer kx k x 6x xy y final answer M f 6x + 8xy 9xy y [= 0] f final answer with one err in a coefficient (includes sign) but otherwise crect M f any two of 6x, 8xy, 9xy, y x(x 5) final answer Condone x(x 5 ) (x + 5 ) as final answer (c) x [ 4 4 Y x final answer nfww B f 4 with no/increct inequality equals sign as answer M f 8x + 4 Y 5x 4 better M f 4(x + ) Y (5x 8) (d) (i) p = 4.5 oe q = 8.5 oe B f one crect answer f (x 4.5) 8.5 oe seen M f (x 4.5) oe seen x px px + p seen and M f p q = p = oe FT FT their q (iii) x = 4.5 oe FT FT x = their p 5 (a), 5.5 B f each value Crect curve 5 B5 f crect curve over full domain 0 y BFT f 9 0 points BFT f 7 8 points BFT f 5 6 points 5 Point must touch line if exact be in crect square if not exact (including boundaries) and x B independent f one branch on each side of the y-axis and not touching crossing the y-axis 5 SC4 f crect curve with branches joined (c).6 Y x Y Y x Y Y x Y.9 B f each value If B0 then SC f y = 5 used Cambridge International Examinations 04

46 Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE October/November Qu Answers Mark Part Marks (d) y = x + 5 ruled crectly and. Y x Y Y x Y Y x Y.6 4 B f y = x + 5 ruled crectly Bindep f each value 6 (a) nfww 4 M f midpoints soi (condone err omission) (500, 50, 750, 50, 000) and M f use of fx with x in crect interval including both boundaries (condone further err omission) (5000, 7500, 9650, 6000, 99000) and M (dep on nd M) f fx 00 (i) 0, 40, 95, 67, 00 B f crect Crect curve ruled polygon BFT their (i) f 5 crect heights within mm vertically and B f 5 points at upper ends of intervals on crect vertical line and BFT (dep on at least B) f increasing curve polygon through 5 points After 0 sced, SCFT f 4 crect points plotted (iii) 68 to 80 M f 0 to seen (c) 9 oe 4 M f + oe better M f oe oe M f sight of and 0 5 Cambridge International Examinations 04

47 Page 7 Mark Scheme Syllabus Paper Cambridge IGCSE October/November Qu Answers Mark Part Marks 7 (a) (i) Any two of with conclusion Angle ACD = angle ABD Angle CAB = angle CDB Angle AXC = angle DXB AND triangles have equal angles oe OR All three of without conclusion Angle ACD = angle ABD Angle CAB = angle CDB Angle AXC = angle DXB B f two pairs without a conclusion e.g. similar and AA AAA (a) 0 M f DX. =.5 4 oe cos0 4.9 to to 5.96 M A B M f implicit version Implied by answer to 5.96 after M (c) [ ] FT FT f ½.5 their 0 sin0 oe crectly evaluated to me sig figs M f ½.5 their 0 sin0 oe ½ 4. sin0 (.5/4) After 0 sced and in (a)(a), allow SC f ½ 4. sin0 (.5/.) to B4 f 7.6[ ] M f [AB =] tan 0 tan59 oe 0 AB M f tan = tan59 = oe AB 0 And M f [BD =] their AB tan7 oe BD M f tan7 = oe their AB Cambridge International Examinations 04

48 Page 8 Mark Scheme Syllabus Paper Cambridge IGCSE October/November Qu Answers Mark Part Marks 8 (a) c + b M f OQ recognised as pos vect. (i) c 6a (c a) c 4a (c a) M f any valid route from P to Q e.g. ( b a) 6a + theiroq PQ = PA + AO + OQ PQ = PB + BQ (c) PQ = AC oe and PQ is parallel to AC FT STRICT FT dep on PQ = k AC from (i) and BFT f each statement After 0 sced and PQ = k AC in (i) and, allow SCFT f crect statement, e.g. PQ is not parallel to AC 9 (a) 6, 9, 45 8n + 4 oe (n ) oe B f two crect values M f 8n + k, f any k M f a quadratic expression of fm n [+ an + b ] oe 9 M f (n + )(n + 5) = 480 better 0 4 seen (c) (i) + p + q = and no errs seen Accept p + q = after [ ] p [ ] + q[] + shown (iii) 8 + 4p + q = + M f + seen seen 7 [p =] oe M f crect multiplication and subtraction substitution using the crect given equations 49 [q =] oe B f [p =] [q =] 6 After 0 sced, SC f values satisfying one of the iginal crect given equations Cambridge International Examinations 04

49 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 04 series 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 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 October/November 04 series f 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.

50 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied Qu. Answer Mark Part marks (a) (i) 49.5[0] M f 6.5[0] 5 ( ) M f 6.5[0] 5 66 FT FT their (a)(i) to sf better hours 9 mins 45 secs B f oe, e.g..665 [h] 9585 [s] M f hrs mins oe / ( ) oe (c) 8.75 final answer M f 6.5[0] 0.88 oe M f 6.5[0] associated with 88[%] (a) x > 0.5 oe final answer nfww B nfww f 0.5 with no/increct inequality equals sign as answer M f 7x + 5x > better 6 5 > 7x 5x better M f 6 5x seen (i) (p )(q + 4) final answer M f q(p ) + 4(p ) p(q + 4) (q + 4) (p 5)(p + 5) final answer (c) (5x 9) (x + ) 9 oe and final answer 5 M B M partial factisation, e.g. x(5x 9) + (5x 9) SC f (5x + a)(x + b) where ab = 8 a + 5b = Cambridge International Examinations 04

51 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) 5 < t Y 40.5, 7.5,.5, 7.5, 4.5, 47.5 ( ) 50 their f 7. M M Mdep A At least 4 crect mid-values soi fx where x is in the crect interval allow one further slip [ = 865] Dependent on second method SC f crect answer with no wking (c) (i) 5, 9, 6 rectangular bars of height,.8 and.6 crect widths of 5, 5,0 and no gaps BFT B FT their (c)(i), on crect boundary lines BFT f crect heights If 0 sced f heights then SC f crect frequency densities soi 4 (a) Enlargement [SF] ½ oe [centre] (, 5) B f each (i) Image at (, 6), ( 8, ), ( 4, ) SC f reflection in any vertical line f crect points not joined Image at (, ), (, ), (6, 4) SC f rotation 90 [anti clockwise] around igin at (, ) (, ) ( 6, 4) f crect points not joined (iii) Image at ( 5, ), (, ), (, ) SC f translation by k k 5 f crect points not joined (c) (i) 0 0 B f a crect row column Rotation, 90 [anticlockwise] oe igin oe B f two elements crect Cambridge International Examinations 04

52 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a) (i) M f [g(7) =] x x 4 4 M f x = 6 x 6 = 0 M f 7 = (x )(x + ) better (c) x² + 7x [= 0] soi B 7 ± (7) 4()( ) () BFT BFT FT x² + 7x ± their k [k 0] oe BFT f 7 4()( ) better oe p + q p q If in fm, r r BFT f 7 and () better 7 x oe ,.8 final answers BB If B0, SC f answers 4.7 and and.76.. seen f 4.68 and.8 seen f answer 4.68 and.8 (d) x + 5 x M f crect first step better, e.g. 5 y = x + + x = y x = 5y y + = 5x 5 y = x 5 5 (e) Cambridge International Examinations 04

53 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (a), 7.75, 8.875,, Accept f 7.75 and f Crect curve 4 BFT f 8 9 crect plots BFT f 6 7 crect plots BFT f 4 5 crect plots Point must touch line if exact be in crect square if not exact (including boundaries) (c) (i) Any integer less than 7 greater than 0 7, 8 9 (d) y = 5x + ruled and fit f purpose B B f sht line but crect freehand full length crect line f ruled line through (0, ) (but not y = ) f ruled line with gradient 5 (acc ± mm vertically f hizontal unit).45 to.5 and 0.4 to 0.5 B B f each (e) Tangent ruled at x =.5 7 to 7 (a) (i) [= ] 000 [= 495] 495[l] 000 = [ml] B M M No daylight at point of contact. Consider point of contact as midpoint between two vertices of daylight, the midpoint must be between x =.4 and.6 Dep on B close attempt at tangent at x =.5 M f y step/x step f their tangent (i) M f [ 60] oe [660] After 0 sced, SC f answer figs figs to 7.5 M f oe π M f [r figs495 = ] π figs495 [ π r = ] better Cambridge International Examinations 04

54 Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (c) 5 4 B f answer 60 M f ( ) oe M f 45 ( ) oe M f (d) 4.4[4..] to 4.45 M f cos ( /45) oe, e.g. sin (75 their (c))/45 tan ((75 their (c))/ ) M f cos = /45 oe sin = (75 their (c))/45 tan = (75 their (c))/ (a) Angle LPQ = soi cos their P 9.50[...] B M A M f crect implicit cos rule A f 560. to sin PQL = 58sin their P oe 9.5 M M f sin PQL sin( their P) = oe to 5.09 B (c) (i) M f oe [0][.].08 to.09 FT FT their 8 (d) to 7.78 M f 74.5 oe soi by.888 to sf better M f dist speed.85 (e) to 0.74 M f 58 sin their P oe 9.5 sin their M f 58 x = sin their P oe x 9.5 = sin their 9 (a) , (i) 4n oe M f 4n + k 7 (iii) 50 FT FT their (i) = 00 solved and then answer truncated dep on linear expression of fm an + k M f their 4n = 00 their 4n Y 00 Cambridge International Examinations 04

55 Page 7 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (c) p = and q = 5 with some crect suppting wking leading to the solutions 5 M f any of p + q + = 0 oe, p + q + = oe, p + q + = 6 oe, 4 p + 4q + = 5 oe, 5 p + 5q + = their 8 oe, etc. M f any one of these M indep f crectly eliminating p q from pair of linear equations A f one crect value If 0 sced SC f values that satisfy one of their iginal equations After M0, crect answers SC (d) n n n(n ) B f answer n + k[n] M f their quadratic from (c) + their linear from (i) 0 (a) (i) final answer M f final answer M f oe 6 6 M f identifying crect pairs (4, 6), (6, 4) and (5, 5) 7 Refers to most combinations oe Dependent on previous mark (c) 4 47 oe M4 f oe M f crect probabilities shown added from those above M f seen oe 6 6 And M f seen oe 6 6 oe alone added to a n probability not of the fm 6 Cambridge International Examinations 04

56 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 04 series 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 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 October/November 04 series f 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.

57 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied Qu. Answers Mark Part Marks (a) (i) 5.7[...] M f [AD = ] oe better to 54. M f tan [BCD =] (.6) B f.4 seen oe + 7 (iii) 65.8 M f 4. 7 oe 6. 6 FT FT their (a)(iii) 4 crectly evaluated M f their (a)(iii) M f [scale fact =] oe soi (a) (i) 7 [=805] oe 7 [= 805] to 0.77 M f ( ) 8 [ 00] final answer 5 B4 f 96.5[0] [area A total sales] B f 040 [area B] and [area C] [area B + area C] B f 040 [area B] [area C] M f 76 [B tickets] and M f 48 [C tickets] After 0 sced SC f answer of 96 SC f 754 (A total sales) Cambridge International Examinations 04

58 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November (c) M f oe 0.95 M f 584 associated with 95[%] (a) (i) 5 Angles in same segment dep Accept same arc, same side of same chd 04 Angle at centre is twice angle at circumference (iii) 4 Angle between tangent and radius = 90 Accept double, but not middle, edge Accept right angle, perpendicular (i) 7.65 to M f cos56 M f crect implicit fmula and A f 58.5 to to 49.4 M f [sinbec =] M f 7 sin56 oe their (i) sin56 = sin BEC their (i) 7 oe 4 (a) (i) Ariven with comparable fm f both shown difference between the two fractions shown Accept probabilities changed to decimals percentages (to sf better) (iii) 6 oe M f oe M f + oe their (a) M f seen 5 5 (i) Completes tree diagram crectly B f 5 values crect B f value crect 6 9 oe 50 5 M f Cambridge International Examinations 04

59 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (iii) 5 (a) (i) (iii) (iv) 44 oe M f their their their oe M f their their their oe identifies the 7 routes attempt to add 7 probabilities with at least 5 crect oe B f three crect elements 0 B f either crect in this fm 5 M f understanding to find the inverse of Q 0 and M f det = f k k 0 0 Alternative a b 0 = 0 c d 0 Leading to a c = and c = 0 then a = and b d = and d = then b = M all four equations, M f a pair of crect equations 6 (a) (i) 8 x final answer 5x 7 y final answer M f elements crect (iii) 6x 8 final answer M f 6x k kx 8 Cambridge International Examinations 04