0606 ADDITIONAL MATHEMATICS

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1 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the March 06 series 0606 ADDITIONAL MATHEMATICS 0606/ Paper, maimum raw mark 80 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 06 series for most Cambridge IGCSE and Cambridge International A and AS Level components. IGCSE is the registered trademark of Cambridge International Eaminations.

2 Page Mark Scheme Syllabus Paper Abbreviations awrt cao dep FT isw oe rot SC soi www answers which round to correct answer only dependent follow through after error ignore subsequent working or equivalent rounded or truncated Special Case seen or implied without wrong working a + 9= + + ( ) + a + 8= 0 For distinct roots, ( a ) Critical values and a>, a < > 6 M M A A for attempt to equate the line and the curve and obtain a term quadratic equation for use of the discriminant for critical values for correct range a=, b= 0, c = B B for each 6 log + log = log log + = log log = = cao Alternative scheme: log log log + = log log log + = log = = cao B,B B B B B B for log log B for log for final answer for change of base for log work) for final answer (must be from correct Cambridge International Eaminations 06

3 8 6 y Page Mark Scheme Syllabus Paper (i) B B B B for a line in correct position for ( 0, ), (, 0 ) for correct shape for y = +, touching the -ais for (., 0 ), ( 0, ) = + leading to = = leading to = Alternative: ( ) = ( + ) leading to = 0 =, = B M A M A,A for = for correct attempt to deal with negative branch. for = for equating and squaring to obtain a term quadratic equation A for each. (a) (i) 9 P 6 = 6080 B Must be evaluated P P = M,A M for attempt a product of perms (iii) B,B B for either 80, or realising that there are possible positions for the symbols (b) (i) 0 C6 C 00 M A for unsimplified form 8 C C 0 M A for unsimplified form 6 (i) ( ) f > 6 B Allow B for y > 6 f ( ) = ln( 6) Domain: > 6 Range: f ( ) R M A B B for a complete method f = or y = must be ( ) must be using the correct variable in both (iii) f ( ) e = B (iv) 6+ e = e M for a complete, correct method leading to = ln A Cambridge International Eaminations 06

4 Page Mark Scheme Syllabus Paper a 7 9 = + + = 8 a+ 8b = 7 (i) f b ( 0) M for attempt at f ( ) 8a b= a b a b = 70 leading to a= 6, b = ( )( + ) M DM B,,0 each error A for attempt at f( ) = f( ) Allow if the wrong way round for attempt to solve simultaneous equations A for both (iii) ( )( )( + ) M AFT for attempt to factorise their quadratic factor must be linear factors 8 (i) lg y = lg A+ blg Gradient =. so b =. Intercept =. A = 7. when = 00, lg = lg y =.8 ( allow.8 to.9) (iii) when y = 8000, lg8000 =.9, lg =.0 leading to =,.0 0 or B M A M A M A M A may be implied by later work for attempt at gradient for b =. for attempt to find y-intercept for, allow awrt 8 for correct use of graph or equation for correct use of graph or equation Cambridge International Eaminations 06

5 Page Mark Scheme Syllabus Paper 7 π θ = oe 9 (i) r θ = r ( π θ) M A for a valid method allow in degrees π r+ r+ r = 0, leading to r = 7.80(..) M A for valid method Must show enough accuracy to get A (iii) Perimeter π π = r+ r tan 8 = =.6 B,B B B for arc length, B for twice AC for.6 (iv) Area π = ( r AC) r = or equivalent method using triangles B,B B for area of quadrilateral, allow unsimplified, B for sector area.08 Area. B for area in given range B M 0 (i) ( ) + ( ) A for ( ) for attempt at differentiation of a product for all else correct ( ) = ( ) ( ) d d = ( ) ( ) ( ) d = ( ) ( ) ( ) ( ) = + M B,B M DM A for attempt to use part (i) B for ( ), allow if divided by divided by B for ( ), allow if for taking out a common factor of ( ) for attempt to obtain a linear factor (iii) 0 M AFT for attempt to use limits correctly p + q FT on their Cambridge International Eaminations 06

6 Page 6 Mark Scheme Syllabus Paper cosecθ + cosecθ + (i) = cosecθ cosecθ + cosec θ = cot θ = tan θ Alternative scheme: sin θ sinθ = cosecθ cosecθ + sinθ + cosθ = ( sinθ + sin θ) ( sinθ sin θ) sin θ M A M A M A for attempt to obtain a single fraction all correct as shown for use of correct identity for finishing off for attempt to obtain a single fraction in terms of sinθ only all correct as shown sin θ = cos θ M for use of correct identity = tan θ A for finishing off tan θ = 6+ tanθ tanθ + tanθ = 0 ( )( ) tanθ =, tanθ = M DM for attempt to use (i), to obtain a quadratic equation and valid attempt to solve for attempt to solve trig equation o o o o θ = 6.,.7,., 0.7 A,A for each pair Cambridge International Eaminations 06

0606 ADDITIONAL MATHEMATICS

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the October/November 0 series 0606 ADDITIONAL MATHEMATICS 0606/ Paper, maimum raw