Cambridge International Examinations Cambridge International General Certificate of Secondary Education MATHEMATICS 080/ Paper (Extended) October/November 06 MARK SCHEME Maximum Mark: 70 Published This mark scheme is published as an aid to teachers cidates, 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 befe marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper the Principal Examiner Rept f Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes f the October/November 06 series f most Cambridge IGCSE, Cambridge International A AS Level components some Cambridge O Level components. IGCSE is the registered trademark of Cambridge International Examinations. This syllabus is approved f use in Engl, Wales Nthern Irel as a Cambridge International Level /Level Certificate. This document consists of printed pages. [Turn over

Page Mark Scheme Syllabus Paper Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied 6 n 7 final answer B 4 (a).47 0 6 7.9 0 8 0 0 oe must be shown M 8k k 0k 0k 0 cao A 6 Thursday M f.4 found at least two of:.8,.6 4 found 7 0.4 0.6 0. 0.09 M f decimal conversion 0.6 0. 0.6 8 4. 4. B f each both answers reversed 9 (a) A A ruled line joining (6, ) to (80, 8) 0 (a).9[0].900 to.90.7.7 to.7 8 60 M f 4 000 40 0 00 00 oe 4.7.7 to.7 M f π

Page Mark Scheme Syllabus Paper 9 oe, must be a fraction M f. 0. oe B f 9 k 4 (a) 0 47. M f 4. oe (a) 68 9 M f 60 40 oe 80( n ) n = 40 oe 6. M f d = ( ) k w + better their k M f [d=] ( ) 7+ M f.(4 + ) = d(7 + ) oe 7 y = x oe M f oe 8 M f perpendicular gradient their = 8 oe If zero sced, SC f answer y = kx k 0 8 (a) x oe final answer (c) x + final answer M f crect first step, e.g. x = y = x y

Page 4 Mark Scheme Syllabus Paper 9 (a) Crect tangent. grad.9 B No daylight between tangent curve at point of contact. Consider point of contact as midpoint between two vertices of daylight, the midpoint must be between x = 0.8 x =. dep on B M f rise also dep on any tangent drawn run close attempt at tangent at any point Must see crect implied calculation from a drawn tangent (, 8) 0 (a) E A B B f elements in the crect place 9. π 7 8 E C D E E F G (a) 4.4 4.4 to 4.4 M f 6. 4.7 sin 8 oe 0.7 0.7 M f sin = 00 07 7. 4 B f crect B f crect M f, 7, [ ] seen [FDs] 7n t+ m final answer 4 M f 7n(6p ) seen M f (t + m)(6p ) seen M f t(6p ) + m(6p ) 6p(t + m) (t + m)

Page Mark Scheme Syllabus Paper 4 y x + 6 oe x oe y > x oe final answers SC4 f y < x + 6, x >, y x oe B f y x + 6 oe B f y = x + 6 oe B f gradient = oe soi B f x y > x oe B f either x y > x oe f x = y = x with increct inequalities (a) CB 6 8 B f two crect entries (c) 47 4 7 oe isw B f k 4 7 seen det = 47 soi (d) The determinant is 0 oe