0607 CAMBRIDGE INTERNATIONAL MATHEMATICS

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1 CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME the May/June 0 series 007 CAMBRIDGE INTERNATIONAL MATHEMATICS 007/4 4 (Extended), maximum raw mark 0 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 bee 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 Rept Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes the May/June 0 series most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

2 Pagee IGCSEE May/Junee (i) 7. (7. ) 4 : 4 final answer SC answer 4: (.0( 0888 to. 08) B B 80 seen ( may be implied by ratir io answer) 7. (7...) : (iii) 000 M M M 70 = 44 4% seen (iv) 748.8[ [0] cao final answer M implied by 74. does not spoil method o 8.8 ( 8.8 to 8.80) SC answer 8.88 M log (000/0) log(..0) Allow.4 r 000/0 in methods. M M 0.0 n = multipliedd by..0 at least twice crectly M graphs that intersect as shown x M M graph of o y =..0 x( ( x + ) = x( ( x + ) M Iff M0, M, B x( x + +) r x(xx x + ) Condone missing brackets if crect expansions followw 7 B B x = 7x (x + ) = (xx + ) ) o. e. final answerr 0,, 7 y y + + = M y = y + o..e. betterr B B i..e crc rect equation without fractions leadingg to y = Cambridgee International Examinationss 0

3 Pagee IGCSEE May/Junee (c) (i) 0 soi w 00 soi w + 0( (w + ) 0 0w = w(w + )) better 00 w(ww + ) = o..e. B B M Iff not seen onlyy implied by further wking. e.g. wx = 0 is not sufficient. i..e. crect multiplication of an equation inn the crect mat allow 0( (w + ) 0w =.w(ww + ) alsoo allow overr common denominat i..e. crect collection of two terms w + ww = 0 E Established with at least onee mem intermediate linee with no errs omissionss h 0 min ww www 4 B w = r w = wwww M (ww + + )( w ) good sketch of quadratic showingg zeros quadratic mulaa completing square reaching g ± M M (ww + a) )(ww + b ) with ab = a + b = sketch of quadraticc crect substitutions inn quadratic mula bee simplifying (ww + ) 8 = 4 Trial and improvement alloww M at least trials comparison of distances and times (unlesss crectt answer foundd withw trials) B F T 0 r positive root crectly intoi hours and minutes y = x o..e. finf al answer B y = x + c o. e. y = kx. seen (i) Ruled line through (, 0) andd (0, 4) B ruled line thrt ough (0,, 4) gradientt off T B tiny part nott shaded only if positive gradient andd cuts x-axis SC crect area unshaded Cambridgee International Examinationss 0

4 Page 4 Mark Scheme Syllabus IGCSE May/June (c) y = x 7 B y = x + c y = kx 7 4 M rise/run = and M crect method finding c Answer x 7 implies M M 4.7 M if at least mid-values seen (0, and ) from 80,, sum of 70 Columns from 00 to 0 and 0 to 40 Heights 0. and 0., Accept freehand 4. www M cos 0 A 8800 to [cos = ] 8 8. (. to.) M A Allow use of 4. M crect implicit statement Strictly dependent on at least M SC if crect without wking (c) (. to.4) 80 only if answer between 70 and M 0. 0 (i) 700 (700. to 700.4) 4 Allow as final answer full marks M [BC ]= + M BC area triangle ABC M if one of the five areas missing is increct.[0] (.0 to.0) (i) 0.00 (c) 4.4 (4.4 to 4.4) M 0 + (44) (80) (Square roots., 4.08 ) M tan = sin = cos = Cambridge International Examinations 0

5 Pagee IGCSEE May/Junee [ 0] 00,, [Feb] th B r [Feb]] th. B r [0] 0 M M r 77 + soi r B f seenn (.0 to.) (c) (i) 74 caoo finall answer 0.4 (d)(i) B f 0.40 r i.e not dpp 8 B B r po quality sketchh Sketchh couldd be withw h different winw ndow.. a different function e.g. y = x x..4 (.4 too.44) 0.78 (0.77 ) B B x Y.4.4 too.44 x > 0 x Y=0. Y Condone < r Y etcc if one negative root if one positive roott [4].88 (.77 )) M r 8 sin. e.g coss 700 ( ) ABB M M r 8 = sinn o. e. r above expression without squaree root.777 r.788 (.77 to.77..) 70 M r 00 π π 8π Allow as a final answer but must be exact (c).0 too..0 wwww M r 00 π π sin M M r 00 π π 8 andd M r sin70 (.0 to. 0 )) (0( ) Cambridgee International Examinationss 0

6 Pagee IGCSEE May/Junee (i) B inai ccurate sketch of cosxx B inai ccurate sketch of sin x n( ) x = 80 Condone π 800 (c) ( 80, ), Condone π 800 (d) 700 Condone 4 π 70 (e) (i) 0 Y g( (x) Y Condone strict inequalities, alloww x y g(x) and alloww separate inequalities in parts ( i) and Y g(x) Y (f) 4. (4. 4 ), 7 (7.0 to 7 7.), (g) Crect areaa shaded. (i) 4 o..e. F all parts accept decimals percentages with thee usual rules sf. Do not penalise increct cancelling converting. Do not accept ratioss wds.. o..e. SC r 0.. if no fraction seen (iii) o.eo. (i), and, and B anya one of the positionn e in a crect cao M r ( to ) Cambridge International Examinations 0

7 Page 7 Mark Scheme Syllabus IGCSE May/June (iii) cao M ( to 0.0) (c) SC answer of 4 = 777 seen 4 = seen M attempted products of k, k > 8.7 ( ) 8.. (i) r = 4.t , 0.0. B r = 4.t + c r = kt + 0 Allow x t Negative (iii) (. to.4) equation only if linear p + q M crect route from O to X PQ = q p crect unsimplified answer p + q B kp + q p + kq, k 0 crect unsimplified expression M crect route from X to Y p + mq + nq, m 0, n 0 (c) ± 4, If 0 sced, M + k = Cambridge International Examinations 0

MARK SCHEME for the October/November 2013 series 0580 MATHEMATICS

MARK SCHEME for the October/November 2013 series 0580 MATHEMATICS CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME f the October/November 013 series 0580 MATHEMATICS 0580/ Paper (Extended), maximum raw mark 70