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 March 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 March 07 series for most Cambridge IGCSE, Cambridge International A and AS Level components and some Cambridge O Level components. IGCSE is a registered trademark. This document consists of 8 printed pages. UCLES 07 [Turn over

2 0606/ Cambridge IGCSE Mark Scheme March 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 www 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 without wrong working isw B or eact equivalent Solve = 0 or ( ) = 00 = A (i) $ 000 B t = e oe 000 [t = ] (.07...) years A UCLES 07 Page of 8

3 0606/ Cambridge IGCSE Mark Scheme March 07 (i) multiply out correctly B or divide out correctly Finding another factor B ( ) or ( + ) or ( ); method must be seen Either ( ) ( 4) Or ( )( + )( + ) Or ( )( )( + ) B For stating a relevant quadratic factor for their linear factors Attempts to factorise quadratic ( ) ( + )( ) oe A mark final answer Alternative method: B for finding a second linear factor using any valid method and B for finding a third linear factor using any valid method and B for finding the final linear factor using any valid method and B for fully correct product stated; mark final answer If fully correct product stated but no method shown then B only. 4 Eliminates y + k = + 4 Collects terms 6+ 4 k = 0 soi A Applies b 4ac ( 6) 4()(4 k ) or better k < oe A Alternative calculus method: Equates gradients 4 = Finds point of tangency (., 4) Substitutes into y = + k 4 = (.) + k UCLES 07 Page of 8

4 0606/ Cambridge IGCSE Mark Scheme March 07 0 = 4 = seen B may be later in working; must be convinced that calculator has not been used ( ) ( ) leading to ( ) + + their = + oe + their = + equates their area to given area and factorises to collect terms; may still have 0 + their = + their their [ ] divides and attempts to rationalise; may still have 0 or forms a pair of simultaneous equations e.g. p+ 0q= p+ q = numerator must have at least terms; 9 0 denominator may be [ = ] + www A or p =, q = or solves their simultaneous equations to find one unknown 6 (a) (i) oe or a = and b = oe B mark final answer B for and B for 60 [ = ] their( ) their oe may be in steps A (b) (i) Valid eplanation B e.g. If > 0.7 then all the arguments are positive as required. oe = loga a may be seen in e.g. log a ( a ) = + log log (4 ) = log (4 ) soi a a completion to given result A UCLES 07 Page 4 of 8

5 0606/ Cambridge IGCSE Mark Scheme March = 0 oe or (6 4) = 0 oe e.g. equates, anti-logs, rearranges and factorises or divides OR rearranges, combines using correct log law, anti-logs and factorises or divides (iii) ( ) [ = ] 4 6 or oe A inclusion of = 0 is A0 7 (a) [ r = ] cos0 oe or for [ r = ] cos60 or for [ r = ] cos40 [r = ]. or rot to 4 or more sf A not from wrong working sin sin0 = their. or better or sin y sin0 = 0 their. or better [ =] awrt 9. A or [y =] awrt their AFT or 80 + their y (b) 94 [km/h] west B B for 94 [km/h] y B or 6 8 (i) ( 4) = ( 6) y= + c and c = [ m AB = ] or oe 8 y 7= ( ) or 4= ( 8) y A or y= + c and c = 44 their 44 = + 6 their valid method of solution for their equations; must be of equivalent difficulty = 8 y = isw A A UCLES 07 Page of 8

6 0606/ Cambridge IGCSE Mark Scheme March 07 [ m = ] y their( ) = ( their 8) isw AFT FT their D; y= + c and c = their 9 (a) ke + (+ c) for some non-zero integer k where k k = A (b) (i) d(ln ) = d soi B ( theirln ) d their y = d ( ln ) correct form of quotient rule or equivalent product rule applied; brackets may be omitted or misplaced for correct, isw A may be unsimplified; allow recovery of brackets ln d + d = + d (ln ) ln d = + c ( ) B rearranges and uses their answer to (i) + their ln (+ c) AFT correct or correct FT completion; must not be their UCLES 07 Page 6 of 8

7 0606/ Cambridge IGCSE Mark Scheme March 07 0 (i) 4 tan( 0) = B 0= tan soi 4.6 and.6 isw A or for.6 and.6 isw.6 and 0.6 isw A or for.6 and 0.6 isw Penalty of mark if all 4 angles given correctly but prematurely approimated OR if any etra angles are given besides the correct 4 If A0 A0 then allow SC for.(0...),.(0...), 4.(0...), 9.(0...) seen OR for 6.(0 ), 4.(0 ), 4.(0 ), 60.(0 ) seen cos cos = cos uses sin = cos cos + cos = 0 oe A ( )( ) cos cos + [ = 0] factorises or solves their -term quadratic in cos [ = ] 60, 00,80 A A for any two correct (i) g B g() = 0 valid comment e.g. domain of f is B B B for either (iii) or = soi B or 4 = A or correct term equivalent or a = 0., b =., c = UCLES 07 Page 7 of 8

8 0606/ Cambridge IGCSE Mark Scheme March 07 (iv) B (v) y = 0 B or y y = 0 ( y) ± ( y) 4()( ) [ = ] or [ y = ] ( ) ± ( ) 4()( ) Eplains why negative square root should be discarded B at some point f ( ) = A allow y = If zero scored, allow SC for showing correctly that the inverse of the given is f. f (i) [length of rectangle = ] 0 B [A =] 0 their sin 60 oe Correct completion to given answer 6+ A = 0 4 A oe B 6+ their 0 = 0 4 oe =.6 A allow rot to or more sf A = A allow.9... rot to or more sf UCLES 07 Page 8 of 8

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

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