0606 ADDITIONAL MATHEMATICS

Size: px

Start display at page:

Download "0606 ADDITIONAL MATHEMATICS"

Barbara Walton
6 years ago
Views:

1 PAPA CAMBRIDGE CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Internatinal General Certificate f Secndary Educatin MARK SCHEME fr the Octber/Nvember 0 series 0606 ADDITIONAL MATHEMATICS 0606/ Paper, maimum raw mark 80 This mark scheme is published as an aid t teachers and candidates, t indicate the requirements f the eaminatin. It shws the basis n which Eaminers were instructed t award marks. It des nt indicate the details f the discussins that tk place at an Eaminers meeting befre marking began, which wuld have cnsidered the acceptability f alternative answers. Mark schemes shuld be read in cnjunctin with the questin paper and the Principal Eaminer Reprt fr Teachers. Cambridge will nt enter int discussins abut these mark schemes. Cambridge is publishing the mark schemes fr the Octber/Nvember 0 series fr mst Cambridge IGCSE, Cambridge Internatinal A and AS Level cmpnents and sme Cambridge O Level cmpnents. IGCSE is the registered trademark f Cambridge Internatinal Eaminatins.

2 Page Mark Scheme Syllabus Paper Cambridge IGCSE Octber/Nvember dy 6 d When d y 0, d D fr attempt t differentiate all crrect dy fr equating t zer and an d attempt t slve fr., y fr bth, but n etra slutins (a) y fr crrect shape fr ma value f, starting at (0, ) and finishing at ( 80, ) - fr min value f (b) (i) must be psitive π 60 r r.05 rad (i) ( + ) ( c) y c + c, fr ( + ), fr ( + ) fr a crrect attempt t find c, but must be frm an attempt t integrate y + ( ) Allw fr c ( + ) 6 ft ft fr substitutin int their equatin t btain ; must have the first Cambridge Internatinal Eaminatins 0

3 Page Mark Scheme Syllabus Paper Cambridge IGCSE Octber/Nvember (i) 5y 7y + 0, fr 5, fr 7 ( 5 y )( y ) 0 y, ln 0. ln 5 fr slutin f quadratic equatin frm (i) fr use f lgarithms t slve equatin f the type 5 k must be evaluated t sf r better y, 0 5 (i) d y d d y When, y and d y Tangent: ( ) ( y ) D fr attempt t differentiate fr y fr attempt t find equatin f tangent allw equatin unsimplified Mid-pint (5, 9) () 5 9 fr midpint frm given crdinates fr checking the mid-pint lies n tangent Alternative Methd: Tangent equatin y Equatin f line jining (, 6) and (, ) y + Slve simultaneusly 5, y 9 Mid-pint (5, 9) fr a cmplete methd t find the crdinates f the pint f intersectin fr midpint frm given crdinates 6 (i) 6 ( p ) p + 0 p + fr 0p r 0p r 6 ( ) 6 C p r C p 6 r C p 0 p 60 p fr equating their term in t 60 and attempt t slve ( )( p + 0 p...) ft ft fr 9p, 96 r 9 their p Cefficient f is 80 9 p 8 fr 80 9p Cambridge Internatinal Eaminatins 0

4 Page Mark Scheme Syllabus Paper Cambridge IGCSE Octber/Nvember (i) A b b 5ab a a, b b fr, fr 5ab a a X BA a b 5a 5a a b 5b 5b D fr pst-multiplicatin by inverse matri fr crrect attempt at matri multiplicatin, needs at least ne term crrect fr their BA (allw unsimplified) fr each crrect pair f elements, must be simplified 8 (i) uuur AB, at P, + () 6 s at P, y + ( 6), y 7 fr cnvincing argument fr fr y 7 Gradient f AB 6, s perp gradient fr finding gradient f perpendicular + y Perp line: y 7 ( ) ( ) fr equatin f perpendicular thrugh their P Allw unsimplified (iii) Q 0, Area AQB.5 ft ft n their perpendicular line, may be implied fr any valid methd f finding the area f the crrect triangle, allw use f their Q; must be in the frm ( 0, q ). Cambridge Internatinal Eaminatins 0

5 y Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE Octber/Nvember (i) lg y lg a + lgb.5.5 fr the statement, may be seen r implied in later wrk, lg y lny lgy fr attempt t draw graph f against lg y Gradient lg b lg b 0. r ln b 0. 9 b.5 (allw. t.6) A,,0 D each errr in pints pltted fr attempt t find gradient and equate it t lg b, dependent n in (i) Intercept lg a lg a 0.7 r ln a. 0 a (allw.8 t.) D fr attempt t equate y-intercept t lg a r use their equatin with their gradient and a pint n the line, dependent n in (i) Alternative methd: Simultaneus equatins may be used prvided pints that are n the pltted straight line are used. a (allw.8 t.) b.5 (allw. t.6) D D fr a pair f equatins using pints n the line, dependent n in (i) fr slutin f these equatins, dependent n in (i) fr each Cambridge Internatinal Eaminatins 0

6 Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE Octber/Nvember (a) (i) (iii) (b) (i) 8 C 5 C , fr each, allw unevaluated with n etra terms Final answer must be evaluated and frm multiplicatin places are accunted fr Gender n lnger imprtant fr realising that places are accunted r that gender is n lnger imprtant 6 Need C fr 8008 Alternative Methd ( C6 0) ( 5 )...( 0 6) C + C C C C fr at least 5 f the 7 cases, allw unsimplified (a) cs cs 0 sin cs 0 sin fr use f implied cs ct sin, may be (b) Leading t cs 0, 90, 70 and cs y + π π π π y +, s 0, 90 sin, 0, 50 π 5π y, (0.5,.6) 6 6 0, 50 D D D, fr attempt t slve cs 0 crrectly frm crrect factrisatin t btain fr bth, n ecess slutins in the range fr attempt t slve sin crrectly t btain fr bth, cndne ecess slutins π fr dealing with sec y + crrectly fr crrect rder f peratins, must nt mi degrees and radians Cambridge Internatinal Eaminatins 0

7 Page 7 Mark Scheme Syllabus Paper Cambridge IGCSE Octber/Nvember (i) uuur AQ λb a uuur BP µ a b (iii) uuur λ a+ λb OR a + ( b a ) r λb ( λb a ) fr a + their (i) Allw unsimplified (iv) uuur 7 8 µ 7 8 b+ 8 µ a 8 OR b + ( a b ) r µ a ( µ a b ) 7 fr b + their 8 Allw unsimplified (v) 7 a+ λ b b+ µ a µ, µ Allw λ, λ Allw fr equating (iii) and (iv) and then equating like vectrs Cambridge Internatinal Eaminatins 0

Cambridge Assessment International Education Cambridge Ordinary Level. Published

Cambridge Assessment Internatinal Educatin Cambridge Ordinary Level ADDITIONAL MATHEMATICS 4037/1 Paper 1 Octber/Nvember 017 MARK SCHEME Maximum Mark: 80 Published This mark scheme is published as an aid