Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 07/6 Paper 6 (Extended) May/June 07 MARK SCHEME Maximum Mark: 40 Published 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 ds 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 07 series f most Cambridge IGCSE, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components. IGCSE is a registered trademark. This document consists of 7 printed pages. UCLES 07 [Turn over
07/6 Cambridge IGCSE Mark Scheme May/June 07 MARK SCHEME NOTES The following notes are intended to aid interpretation of mark schemes in general, but individual mark schemes may include marks awarded f specific reasons outside the scope of these notes. Types of mark M A B Method marks, awarded f a valid method applied to the problem. Accuracy mark, awarded f a crect answer intermediate step crectly obtained. F accuracy marks to be given, the associated Method mark must be earned implied. Mark f a crect result statement independent of Method marks. When a part of a question has two me method steps, the M marks are in principle independent unless the scheme specifically says otherwise; and similarly where there are several B marks allocated. The notation dep is used to indicate that a particular M B mark is dependent on an earlier mark in the scheme. Abbreviations awrt cao dep FT isw nfww rot SC soi answers which round to crect answer only dependent follow through after err igne subsequent wking not from wrong wking equivalent rounded truncated Special Case seen implied UCLES 07 Page of 7
07/6 Cambridge IGCSE Mark Scheme May/June 07 A INVESTIGATION VIRUS (a) 7, (b) n (c) 4 (a) V V D V V D D D V V D D D D D V V D D D V V D V V (b), 6 B f each (c) [p =] 4n 4 M f 4n seen (d), 4 (e) [ ] t = n n M f n soi (f) Substitution leading to 6 B f each and crect diagram continued sequence of, 4, 6 with differences of 6, 0 seen (g) M f and 0 f continuation of the sequence from 6 as 8, 3, 4, 8, UCLES 07 Page 3 of 7
07/6 Cambridge IGCSE Mark Scheme May/June 07 3(a) [8,],, with suppting diagram(s) seen and 4() 3 =, 4(3) 3 =, 4(4) 3 = soi solving 4n 3 =, 4n 3 =, 4n 3 = to obtain n =, 3, 4 differences of 4 implying 4n k and substituting at least one of n =, 3, 4, to find k B f each B f any two crect values found from diagrams and verified by calculation 3(b) n n M f, 34, 3 seen Communication: Seen in three of the following questions b c e At least 3 differences of seen; may be in table in (a) At least 3 differences of 4 seen ; may be in table in (b) F rows of differences with at least 3 differences in the nd row; may be in table in (d) c 7 = their(n ) seen algebraic change of subject 7 of their t = n seen and then n = continuation of sequence (need not be term by term) b g At least one me crect diagram drawn Attempt at crect method to solve their 3-term quadratic equation in n e.g. if crect, (n )( n 0) = 0 ( n )( n 0) = 0 ( ) ± ( ) 4 0 n = () ( ) ± ( ) 4 0 n = sketch of relevant graphs 3b F, 34, 3, 76, [03] seen and two rows of differences UCLES 07 Page 4 of 7
07/6 Cambridge IGCSE Mark Scheme May/June 07 A MODELLING SCOUT S PACE km = 000 m and h = min min = h (a) 000 seen (b) awrt 0.8 0 6 isw (c) awrt 33.3 33 3 isw 3(a) 30 30 0 0 4 0 33 6 3 83 66 3 3 Walking: 0 = 30 = Jogging: 0. = 30. = = 7 3(b) [.00] to.0 nfww their(0.8 33.3) FT 7 3(c) 7.[0] to 7.36 FT their (b) 3.6 4(a) 30 x 0 x 000 6 000 leading to 0 83 6 x 3 UCLES 07 Page of 7
07/6 Cambridge IGCSE Mark Scheme May/June 07 4(b) x 0y 6 3 7 M Allow this mark f total dist / time attempt i.e. f crect numerat over a constant; igne units f this mark x 0y 6 3 their 7 000 M Allow 3.6 Crect simplification to x 4 y A Note: Answer is given so evidence must be seen; must have at least one interim step x 0y after 6 3 seen 7 000 Alternative method using ratios and the approach speed time speed time time time x y 30 30 7 30 x y 40 300 3 400 M Or two times given as a ratio a : b equivalent to : 4 b : a equivalent to 4 : e.g. : : 0. : 0. x y 7 x 4y 00 00 00 DM ax by a b a and b with crect values of completion to given answer x 4 y A If 0 sced, SC f x y x 4y = only 7 4(c) 3x x 4 x isw M f x 8x 4(d) 7x x 4y.x isw M f =.x 8 4(e) 4.6 3 4 M f x 4 0 = 7 UCLES 07 Page 6 of 7
07/6 Cambridge IGCSE Mark Scheme May/June 07 [ ] 6 x S = y M f y seen and 0 seen and seen 6 300 and 3 seen Communication: Seen in three of the following questions b c 3b 3c 4c f 83.3 000 ; may be in steps 4 4 e.g. 0 : 83.3 and 30: x compared e.g. 0 000 f 83.3 e.g. 0 : 66.6 and 30 : x compared e.g. their (0.8 33.3) their(4.) f e.g. 7 7 seen f comparison of ratios e.g. 4. to 7 x to 0 30 = 83.3 x 0 30 = 66.6 x f multiplying by a crect conversion fact e.g. ( their.0) ( their.0) 30 000 000 ( their.0) 3.6 seen Note: Division by 000 may be implied by sight of m / h and km / h etc. f crect units seen e.g. 3 x km/h 4e f crect units e.g. 4.6 km / h f showing how to get e.g. 30 30 0 80 f showing how to get 0 e.g. 30 ; may be in steps 80 f a crect step in simplification of 0x y 3 their towards answer 000 UCLES 07 Page 7 of 7