Cambridge International Examinations Cambridge International General Certificate of Secondary Education. Published
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1 Cambridge International Eaminations Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper October/November 06 MARK SCHEME Maimum Mark: 80 Published This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the eamination. It shows the basis on which Eaminers were instructed to award marks. It does not indicate the details of the discussions that took place at an Eaminers 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 Eaminer Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 06 series for most Cambridge IGCSE, Cambridge International A and AS Level components and some Cambridge O Level components. IGCSE is the registered trademark of Cambridge International Eaminations. This document consists of 6 printed pages. UCLES 06 [Turn over
2 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November Abbreviations awrt answers which round to cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent rot rounded or truncated SC Special Case soi seen or implied www without wrong working 0.6 OR ( ) ( )( ) and 0.6 a( ) + b( + ) ( )( )( + ) ( ) oe a+ b a+ b 6 b and a D D www use of or ( ) but not both. solve correct term quadratic www Common denominator or ( )( + ) equate constant terms and terms. both correct solve two linear equations to obtain a or b both correct lg lg lg0 soi anywhere soi anywhere + 0 lg lg lg oe + 0 ( )( ) only soi division; logs may be removed obtain correct term quadratic equation and attempt to solve must not remain. UCLES 06
3 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November (i) t 0 N e 8 or Do not accept non integer responses. 0.0t N e 0.0t 00 e 000 ln t ln0. t (days) insert and make -0.0t e subject take logs and make t the subject awrt 7.7 (iii) dn 0.0t 00e dt dn t 8 ± 67 (.0) dt 0.0t ke where k is a constant k 00 or awrt ± 67 mark final answer (i) dy 7 d + dy 8 7 d Equation of tangent : y 6 y insert into their gradient and use (, 6) and their gradient of tangent in equation of line. Tangent cuts curve again ( )( )( ), y equate curve and their linear answer from (i). factorise: ( ± ) and a two or three term quadratic is sufficient. Allow long division withhold final if (, ) not clearly identified as their sole answer. 6 (i) cos sin cos sin + tan + cot sin cos + + cos sin cos sin cos +sin cos +sin ( cos sin )( cos +sin ) cos +sin ( ) sin cos tan and cot cos sin Attempt to multiply by cos and sin AG sin + cos sin cos cos sin tan., 8.7 equate and collect sin and cos oe FT from tan k UCLES 06
4 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November (i) h 9 9 A ( ) 9 ( 7 ) B//0 Must be clear that 9 is the height of the trapezium. + oe must be seen AG da d ( ) ( ) 0. da d (i) f' ( ) A 6 or 8 8 or or.6 ( + ) ( ) ( + ) 9 ( + ) A//0 product rule on correct function minus each error, allow unsimplified. equate to 0 and simplify to a linear or quadratic equation. correct three term quadratic obtained Etra positive answer loses penultimate. ignore negative solution. quotient rule or product rule all correct 6 6 www beware 9 9 gets A0 ( + ) d + c + FT c their 9 7 D top limit bottom limit in their integral. or 0.0 or 0.96 or 0. (iii) y y + y + make y or the subject f ( ) Domain : FT take cube root (as long as y or equals a fraction with terms in or y only) oe FT change and y can be done at any time Allow upper limit of.86. Do not isw UCLES 06
5 Page Mark Scheme Syllabus Paper Cambridge IGCSE October/November (i) tangent touches circle + k k 8 ( ) ( ) k + 8k k+ 6 0 or better Equal roots as tangent touches circle : b ac ( k) ( k ) k 6 k + only D eliminate y or allow unsimplified use of discriminant on term quadratic soi oe any inequality loses last b 0 a 9 y OR tangent y cuts radius y + at y OR Obtain 0+ 0 oe ( )( ) 0 y use b a find equation of radius and attempt to solve with tangent obtain any term quadratic using their non zero k and reach (iii) TP ( 0.) + ( + 0.8) for using their T and ( 0, ) Signs must be correct.. UCLES 06
6 Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE October/November (i) rj 000 cos0 + t 000 p cos0 coordinate oe y coordinate oe.tcos tcos0 000 t.cos70 + cos0 09 awrt or 090 or 00.cos0 cos p ( ) p. awrt (i) Free choice : no. of ways 6 C C 0 0 D equate their values (must be terms) make t the subject allow one sign error equate their y values(must be terms) and insert their t or t. 6 C another n Cr term only C and answer or vice versa Both Mr and Mrs Coldicott C C 0 0 C another n Cr term only C and answer or vice versa (iii) Mr C and not Mrs C C C( 60) Not Mr C and Mrs C C C ( ) Total 80 OR Total (i) neither Neither C C 0 Total An incorrect final answer does not affect the awarding of the first two marks. www UCLES 06
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