Cambridge International Examinations Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper March 07 MARK SCHEME Maximum Mark: 80 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 does not indicate the details of the discussions that took place at an Examiners 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 Examiner 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 7 printed pages. UCLES 07 [Turn over
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 (a) (i) 0 (ii) 0 (b) X Y Z either X Y Y or X Z Z Y Z completely correct Venn diagram. UCLES 07 Page of 7
0606/ Cambridge IGCSE Mark Scheme March 07 (i) complete cycles having a maximum at y and a minimum at y completely correct curve o (ii) ( 90, ) 3 x 3 x a + a + 0a a 3, so a b ( theira), leading to b 0 c 0 ( theira) 3 6 leading to c correct attempt to obtain b (a) (i) 3 0 for determinant for matrix (ii) 3 M 0 pre-multiplication by the matrix from part (i) 7 M oe 3 6 A,,0 each element error (b) 3a+ ( 6a ) a 3 correct use of a determinant UCLES 07 Page 3 of 7
0606/ Cambridge IGCSE Mark Scheme March 07 (i) LHS sinθ sinθ sin θ sinθ cos θ sinθ cotθ cosθ dealing with cosecθ and attempt at dealing with fractions correct use of identity completely correct proof (ii) cotθ cosθ cosθ 3 3cotθ cosθ cosθ 0 cosθ 3cotθ 0 ( ) cosθ 0 cotθ, so tanθ 3 3 π 3π θ,, θ.,.39, use of part (i), manipulation and factorisation dealing with cotθ and attempt to solve for each pair of solutions (allow.7 and.7) 6 (a) (i) 0 30 (ii) 70 (iii) 00 (b) (i) 3 (ii) (iii) Twins in team of C 0 Twins in team of 3 Total www UCLES 07 Page of 7
0606/ Cambridge IGCSE Mark Scheme March 07 7 (a) 0 8 7 8 90 attempt to obtain magnitude of 8 and use it (b) p q+ p 0 p+ q+ 3 7 dealing with the scalar and with addition p q+ p 0 p+ q + 3 7 equating like vectors and simplifying both equations correct leading to p, q p 0, q 38 p p + 0 0 elimination of q and subsequent solution of quadratic 8 (i) dy cos d x x + ( c) integration to obtain the form acos x correct, condone omission of c cosπ + c dy 3 cos d x x attempt to find c May be implied by a correct c (ii) y 3x sin x ( + c ) π + c π y 3x sinx oe integration to obtain the form asin x correct, condone omission of c attempt to find c (iii) When π x, d y 3 3 d x Normal equation: π y+ x 3 3 y 0.789x 0.9 cao FT attempt to obtain perpendicular gradient and normal equation FT on their d y from (i). Allow dx unsimplified UCLES 07 Page of 7
0606/ Cambridge IGCSE Mark Scheme March 07 9 (i) 0 θ 0π θ π use of sector area to obtain θ (ii) Arc length AB π ( ) BC 0 + 0 0 0 cosθ BC 0 or π π sin sin 0 BC 9.0 Perimeter 0.6 FT FT their θ valid attempt to obtain BC (iii) Area Either π 9.0 sin π + 0π 0 sin area of triangle ACB area of relevant segment.6 allow awrt Or π 0π + 0 0sin.6 allow awrt, for area of triangle AOB or AOC for a complete method UCLES 07 Page 6 of 7
0606/ Cambridge IGCSE Mark Scheme March 07 x 3 3 0 ( ) 3 x At A x. Either Area 3 ( ) 3 3 3 x d x. 9 3 ( x ). 9 3 ( 3). 0 9 3 0 Or line AB: y 3x 3. D attempt to find x-coordinate of B x-coordinate of B x-coordinate of A plan and attempt to find the area of the triangle. Allow unsimplified attempt at integration, must be in the form ( x ). correct integration attempt to use limits correctly equation of AB and attempt to integrate Area ( ) 3 3 x 3 x d x. 3x 3x 9 3 9 3 9 3 0 (i) ln y ln A+ bx 0.7 ln A + b 3.7 ln A +.b ( x ). D attempt at integration, must contain the form ( x ). correct integration attempt to use correct limits correctly may be implied by later work use of either point correctly in above equation or equivalent one correct equation leading to b and ln A.3, so A 0.73 or e.3, for dealing with ln correctly to obtain A. (ii) ln y.3 + x ln y.7 y.9 valid attempt to find y. Must include correct substitution and dealing with ln correctly. UCLES 07 Page 7 of 7