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 May/June 07 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 May/June 07 series for 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

2 0606/ 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 for specific reasons outside the scope of these notes. Types of mark M A B Method marks, awarded for a valid method applied to the problem. Accuracy mark, awarded for a correct answer or intermediate step correctly obtained. For accuracy marks to be given, the associated Method mark must be earned or implied. Mark for a correct result or statement independent of Method marks. When a part of a question has two or more 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 or B mark is dependent on an earlier mark in the scheme. Abbreviations awrt cao dep FT isw nfww oe rot SC soi answers which round to correct answer only dependent follow through after error ignore subsequent working not from wrong working or equivalent rounded or truncated Special Case seen or implied UCLES 07 Page of 7

3 0606/ Cambridge IGCSE Mark Scheme May/June 07 (a). log7. = or log7 = 7 or ( )log 7 = log. correct first anti-logging step log7. [ = ]. or log7 = 7 log. or = log7 isolates.6(...) (b) p q oe B B for each term If B0 then allow for numerator of q or denominator of p q (i) B and C with valid reason B B for one graph and valid reason or both graphs and no reason (ii) B only with valid reason B B for graph B or valid reason [ ] m = or 0 soi 0. or = m c and = 0.m cand subtracting/substituting to solve for m or c, condone one error Y = their 0( X ) or Y = their 0( X 0.) or = their 0 c or = their 0 0. y = ( their m) ( their c) or y = ( their m ) or y = ( their m) 0. c or using their m or their c to find their c or their m, without further error their m and c must be validly obtained 0 y = or y = 0 or y = 0 0. cao, isw UCLES 07 Page of 7

4 0606/ Cambridge IGCSE Mark Scheme May/June 07 (a)(i) (a)(ii) ( ) or better 6 (b) uuur uuur uuur OR = OP PQ soi B uuur uuur uuur or OR = OQ PQ soi uuur uuur OR = ( ) or OR = ( ) p q p q q p uuur OR = p qoe (a) ( ) ( ) soi M for one correct product of the sum 7 (b) 9 9 C C C C oe M for one correct product of the sum [60 8 = ] = n n = 6 their(6 ) their6 ( a) = 6b oe 6 (6 ) their(6 ) = 00 their a b oe attempts to solve D dep on both marks being awarded; must have correctly or correct FT eliminated one unknown a = b = 60 UCLES 07 Page of 7

5 0606/ Cambridge IGCSE Mark Scheme May/June 07 7(i) 9 k 0( ) 9 or better 0 ( ) ( their sin ) 9 ( ( ( ) )) cos their ( ) ( ) ( sin ) cos 0 clearly applies product rule all correct 7(ii) d e = e d soi B d tan sec d ( ) = soi clearly applies correct form of quotient rule ( ) tan their e e their sec ( tan ) B or correct form of product rule to e (tan ) e (tan ) e (tan ) sec ( ) ( ) tan e e sec ( tan ) isw all correct 8(i) π B 6 [cm] B 8(ii) π [major arc = ] π their their r 0π 6 cao 8(iii) π ( their6) π their π ( their6) sin their π ( their6) their π ( their6) sin their Sector triangle π their 6 (Sector triangle) 0π 9 UCLES 07 Page of 7

6 0606/ Cambridge IGCSE Mark Scheme May/June 07 9(i) y 9 = with attempt to swop and y at some point or 9 = y attempt to swop; may be in later work that contains an error f = oe 9 condone y =... etc; must be a function of > 0 B 9(ii) f() or fg( ) = oe 9(iii) [ ]( ) gf = 9 [ ] gf ( ) = 8( ) or better their 8 79 = 8 9 ( 6[ = 0] ) their provided their(8 79) of the form a b for non-zero a and b.6 oe only must disregard other solution 0(a) sin = 0., sin = 0. π π π π,,, oe (b) y = tan soi A for any correct pair of angles if M0 then SC for a correct pair of angles 8.(9...) and 98.(9...).7, 9.7 A for each UCLES 07 Page 6 of 7

7 0606/ Cambridge IGCSE Mark Scheme May/June 07 0(c) Uses cot z= cosec z oe for using correct identity or identities to obtain an equation in terms of a single trigonometric ratio cosec z 7 cosec z = 0 ( cosec z )( cosec z ) [ sin z = ] sin z = D for dealing with quadratic 9.,. A for each (i) 0 0 = 0 0 = 0 or better; equates and solves as far as clearing the fraction = = 0 oe Simplifies as far as = L = 6. cao squares and simplifies to 6. [ y = ] B (ii) (area of trapezium = ) their 7.6 B FT = their 6., y = their using any valid method 0 6. ( ) 0 d ( 0 ) d = ( 0 ) k or or 0 d = 0 k 0 0 ( ) 0 ( 6.) their (6.) their 7.6 oe 0 0 or ( ) limits used correctly or correct FT and subtraction of trapezium; 99 their 7.6 their 8 or 8. oe allow 8... rot to or more sf UCLES 07 Page 7 of 7

Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education. Published

Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper 07 MARK SCHEME Maximum Mark: 80 Published This mark scheme