Cambridge International Examinations Cambridge International General Certificate of Secondary Education. Published

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1 Cambridge Iteratioal Examiatios Cambridge Iteratioal Geeral Certificate of Secodary Educatio CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/4 Paper 4 (Exteded) May/Jue 06 MARK SCHEME Maximum Mark: 0 Published This mark scheme is published as a aid to teachers ad cadidates, to idicate the requiremets of the examiatio. It shows the basis o which Examiers were istructed to award marks. It does ot idicate the details of the discussios that took place at a Examiers meetig before markig bega, which would have cosidered the acceptability of alterative aswers. Mark schemes should be read i cojuctio with the questio paper ad the Pricipal Examier Report for Teachers. Cambridge will ot eter ito discussios about these mark schemes. Cambridge is publishig the mark schemes for the May/Jue 06 series for most Cambridge IGCSE, Cambridge Iteratioal A ad AS Level compoets ad some Cambridge O Level compoets. IGCSE is the registered trademark of Cambridge Iteratioal Examiatios. This documet cosists of 6 prited pages. UCLES 06 [Tur over

2 Page Mark Scheme Syllabus Paper Cambridge IGCSE May/Jue Abbreviatios awrt aswers which roud to cao correct aswer oly dep depedet FT follow through after error isw igore subsequet workig oe or equivalet SC Special Case fww ot from wrog workig soi see or implied (a) Image at (5, 5), (7, 5), (6, 6), (5, 6) If 0 scored SC for traslatio k or k 4 (b) Image at (, ), (, 4), (, ), (, ) If 0 scored SC for reflectio i lie y = x (c) Image at (, 5), (, 7), (, 5), (, 6) If 0 scored SC for 90 clockwise about (, ) or SC for 90 aticlockwise about other cetre (d) (i) Elargemet [scale factor] [cetre] (, 4) If combied trasformatios, all three marks lost (ii) Stretch [factor] y-axis oe ivariat If combied trasformatios, all three marks lost (a) ad 60 4 oe M M for 60 9 [=70] 9 or 5 60 or50 or or 50 9 (b) (i) 0 M for 98.4[0] [0].8 oe or M for recogisig 98.4[0] is 8% (ii) 69.5 or 69.5 M for 98.4[0] 0 00 oe 98.4[0] 98.4[0] 0 or M for oe or 98.4[0] [0] (iii).6[0] cao fial aswer If 0 scored, SC for aswer 75% Cambridge Iteratioal Examiatios 06

3 Page Mark Scheme Syllabus Paper Cambridge IGCSE May/Jue (iv) 8 4 B for aswers 8.8 or 8.84 to or M for 50(.0) see oe or M for 50(.0) see oe where > (c) September or October 05 fww 5 B4 for 05 or 9 years ad 9 or 0 or 9.96 or 9.96 to 9.96 moths fww (a) (i) 60 or B for 9.8 or 9.8 see 500 log 50 or M for oe log(.005) or = 500 ad at least two valid trials or sketch of appropriate graph or M for [ = 500] or [ = 500] 00 If 0 scored SC for 4[.0] or.95 to.98 or.55 or.55 to.554 see (ii) 8 for [lq = ] 56 or [uq = ] 64 (iii) M for 88 see (b) 68.6 or M for 50 oe.75 or M for their distace.75 or for distace = 0 or for.4 ad.75 or 44 ad 05 or 8640 ad 600 see If 0 scored, SC for 77. or (a) 4 M for 6w+ 5( w+ 0) = 44 oe or better or for 6w ad 5(w + 0) oe (b) x + 4x 7 [ = 0] oe B i.e. a correct simplified quadratic equatio M for x + ( x+ )( x+ ) [ = 0] oe Sketch of appropriate graph or correct use of formula or completig square M dep Dep o a quadratic from additio of two areas. Must see some valid method 4.48 or 4.49 B for to or 6 4 or. or. or.5 Cambridge Iteratioal Examiatios 06

4 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE May/Jue (a) Ay of the followig Agle ADX = Agle BCX ad same segmet oe Agle DAX = Agle CBX ad same segmet oe Agle AXD = Agle BXC ad vertically opp oe for oe of the three pairs or for at least two pairs of agles without reasos or with icorrect reasos (b) 7.5 oe M for = 5 oe BX (c) 67. or 67.0 to 67. fww M for [cos = ] or M for 4.6 = + 5 5cos( AXD) 6 (a) Correct sketch M for shape i.e. startig at origi the oe maximum the oe miimum A for two zeros to right of x = 0 ad to the left of x = 0 (b).4 or.4 to.4 9[.0] or 8.97 (c) (9.49, ) or (9.486 to 9.487, ) (d) (6.4, ) or (6.4, ) (e) f(x) (f) Correct sketch of parabola shape from approximately y = 5.48 or (a) (i) 576 or to M for π 5 (6 or 6.7 to 6.8 ) M for π 5 (4 or 4. to 4. ) (ii) or to FT FT their (a)(i) M for their (a)(i) (iii) 87 or 88 FT FT with cosistet uits usual accuracy ad trucated M for 000 their (a)(ii) Cambridge Iteratioal Examiatios 06

5 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE May/Jue (iv) 6 or 6. to 6. 4 M for M for 04. ) or M for π 5 (57 or 57.0 to 57.) π (04 or 5 + () (b) 5.7 or M4 for 77 π ( + 0) or M for 77 π (+ 0) or M for πr ( ) πr ( r) r + + = 77 or M for r + ( r) oe 8 (a) [a, b, c = ],, [d = ] 0,, I ay order (b) (c) (d) Parabola vertex dowwards ad vertex below x-axis Cuts give graph i 5 places M A 9 (a) (b) 7 oe their (a) their (a) (c) 0 8 oe M for their(a) + their(a) + or M for a sigle product of two their (a) fractios with first fractio their (a) + (d) Cambridge Iteratioal Examiatios 06

6 Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE May/Jue (a) for [f(7) = ] or M for (x x 0) + 7 (b) x 7 oe M for y 7 = x or x = y + 7 or y 7 = x + (c) (x+ )(x+ ) fial aswer B for (x )(x+ 7 6) or for 4x + 8x+ or M for (x + 7) 6 (d) x + 5 x + 6 fial aswer fww 4 B for (x 6)(x + 5) or SC for ( x + a)( x+ b) where ab = 0 or a + b = ad for (x + 6)(x 6) AB (a) 5.4[0] or 5.96 M for ta4 = oe or better 8 (b) 0.4 or 0.8 fww 5 for agle D = 46 M for [sic = ] 8si( theird ) or M for = oe sic si( theird) A for [agle C =].6 or.6 to.6 OR for agle A = 56 their AB si( theira) M for [sic = ] 9 their AB 9 or M for = oe sic si( theira) A for [agle C =].6 or.6 to.6 (c) 48[.0] or 48. or to 48. cao M for 0.5 their(a) 9 si(90 + their(b)) oe (a) cao (b) (i) 9 for secod differeces 4, 0, 6 ad (ii) + oe M for cubic expressio but ot or k oly Cambridge Iteratioal Examiatios 06