0580 MATHEMATICS 0580/42 Paper 42 (Extended), maximum raw mark 130

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1 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS Iteratioal Geeral Certificate of Secodary Educatio MARK SCHEME for the May/Jue 00 questio paper for the guidace of teachers 0580 MATHEMATICS 0580/4 Paper 4 (Exteded), maximum raw mark 30 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 must be read i cojuctio with the questio papers ad the report o the examiatio. CIE will ot eter ito discussios or correspodece i coectio with these mark schemes. CIE is publishig the mark schemes for the May/Jue 00 questio papers for most IGCSE, GCE Advaced Level ad Advaced Subsidiary Level syllabuses ad some Ordiary Level syllabuses.

2 Page Mark Scheme: Teachers versio Syllabus Paper IGCSE May/Jue Abbreviatios cao correct aswer oly cso correct solutio oly dep depedet ft follow through after error isw igore subsequet workig oe or equivalet SC Special Case www without wrog workig Qu. Aswers Mark Part Marks (a) or or 8 3 of 40 or 8 5 of 40 oe Accept reverse e.g. 90 : 50 = 3 : 5 ad = (b) (i) 5 www M for 90 5 www M for oe (c).4 fial aswer cao M for oe implied by aswer. oe (d) (i) 58.7 fial aswer cao 3 SC for 58.7 or M for oe (0) 00 the M (depedet o the first M) their 0 oe Aswers of 08.7 or 08.7 imply first M (..) www M for 00 oe 50 5 (a) (i) 8 B each compoet 7 www ft ft their 5 ad their 8. M for (their 5) + (their 8) (b) (i) v c or (v c) cao M for CV soi (iii) c + v agai allowig brackets cao M for OM e.g. OC + CM or better see or v their (i) or c + their (i) v c agai allowig brackets cao M for ay correct route e.g. MV + VL or their (i) v 3 or 3 v their (b) UCLES 00

3 Page 3 Mark Scheme: Teachers versio Syllabus Paper IGCSE May/Jue Throughout this questio isw ay cacellig or chagig to other forms, after correct aswer see. Pealty of for sf decimals or percetages. Do ot accept ratio or worded forms. (a) (i) (iii) (iv) 4 oe (0.7) Allow oe oe (0.333) Allow oe (0.833) Allow (b) (i) oe (0.078) Allow , M for 3 3 oe (0.7) www Allow , M for oe 3 (c) (i) oe 4 oe 4 (d) 5 (but ot from roudig) M for repeatig oe e.g. 3 4 (a) (i) Triagle with vertices ( 4, 4), (, 4), (, ) Triagle with vertices (, 3), (, ), (3, ) SC for traslatio 7 or k k 3 SC two correct vertices or 90 aticlockwise about (0, 0) (b) (i) Reflectio oly y = x oe Marks idepedet but must be sigle trasformatio to score ay marks Stretch oly x-axis oe ivariat (factor) 3 Marks idepedet but must be sigle trasformatio to score ay marks UCLES 00

4 Page 4 Mark Scheme: Teachers versio Syllabus Paper IGCSE May/Jue (c) (i) (iii) B each colum ft ft ft factor i (b) oly if stretch ad ca recover to correct matrix SCft for right-had colum ft ft ft to 0, ± or for 3, allow 0.33 or better 0 to (a) (cos) 80 5 M M for correct implicit expressio 90 = A A for (cos) = (b) (i) 5(.0.) ft ft ft 50 their (a) 305(.0.) ft ft ft 80 + their (b)(i) (c) 80si (54.98 to 55) or 80cos (35 to 35.0) oe or 80si (30 their (b)) or 80cos(their (b)(i) 90) oe 47(.4.) cao www 3 M A B for to 55 or 35 to 35.0 soi i correct positio. Provided either agle is acute (d) 90si 30 si 70 M TR M for = si 30 implicit equatio 90 si 70 or other correct 47.9 ( ) cao www 3 A (e) oe Allow : as aswer. SC figs i aswer which could be a ratio. (a) 4 3 π.4 3 M Must see method to at least 4 figures A (b) (i) 4.4, 9., 4.8,, Ay order 4 (3.5 3.) ft ft (iii) 35 or 3 or 37 ( ) ft ft ft their (b) 57.9 (oly if positive) (iv) 507 ( ) ft ft M for ( ) or their 3 legths. UCLES 00

5 Page 5 Mark Scheme: Teachers versio Syllabus Paper IGCSE May/Jue (c) (i) Height see or implied as 4.8 or better π.4 their height 5 ( ) www 3 M M A Idep 74 or 73 ( ) ft ft ft their (c)(i) 57.9 oly if positive (iii) cao www 3 3 M for π.4 (3.7 to 3.), ad M idep for π 4.8 their height from (c)(i) 7 (a) www 4 M M (b) 55, 80 M A mid-values ay three soi Use of Σfx dep o x aywhere i each iterval (icludig lower boud) allow slips or omissios Deped o secod M (c) 8 poits plotted ft, igorig (0, 0) Reasoable icreasig curve or polygo through their 8 poits P3ft Cft Pft for or 7 plotted, Pft for 4 or 5 plotted Codoe startig at (5, ) ad ft oly if shape correct. (d) Either horizotal or vertical lie at least cm log at y = 50 o the curve (e) (i) (iii) (iv) 3 40 must be iteger SC for 0 4 see ad must be iteger 8 (a) (p + q) 5 oe fial aswer SC for (p + q) oe see (b) x + 9(x 3) = 5 or better 5.(0) fial aswer B3 B B for x + 9(x 3) or B for x or 9(x 3) 5.(0) ww is B oly (c) a + c = 5 oe 3a + c = 39 oe Correctly elimiatig a or c B B M A A Codoe cosistet use of other variables or M3 for 3a + (5 a) = 39 or 3(5 c) + c = 39 o.e. Allow oe umerical slip. If A0, SC for 7, 35 UCLES 00

6 Page Mark Scheme: Teachers versio Syllabus Paper IGCSE May/Jue (a) (i) Similar Allow elargemet 4.5 M for AX 9 3 = 3 (iii) 3.5 cao M for or oe e.g. usig base ad 3 height but other methods must be complete (iv) 80 x y oe 80 x oe (b) (i) 9 B B 48 ft ft ft 0.5 their (b)(i) (iii) 97 ft ft ft 45 their (b) (iv) 35 oe (c) 80( ) 0 = 30 oe or = 0 oe M or 80( ) = 8 30 oe or 8 = 80 8 www 3 A 0 (a) Petago Octago 0, M for 9e = 80 oe allow diagram to show this if reasoably clear 8 30 or M for 8 30 or (b)(i) (c)(i) p =, q = 3 3 M for substitutig a value of e.g. 4(4 q) = 3 p or M for umber of diagoals from oe vertex is 3 (allow i words) ad B for oe correct value. If 0, SC for ( 3) see ft ft ft their (c)(i) allow oly if ft calculates to a positive iteger. (iii) 0 cao SC for aswer of 7 or M for their formula = 70 (d) 3 cao UCLES 00

UNIT 4C Itera,on: Correctness and Efficiency. General Idea: Any one Itera,on. i L SORTED SORTED

UNIT 4C Itera,on: Correctness and Efficiency. General Idea: Any one Itera,on. i L SORTED SORTED UNIT 4C Itera,o: Correctess ad Efficiecy 1 L Geeral Idea: Ay oe Itera,o SORTED i i L SORTED 2 1 Look Closer at Iser,o Sort Give a list L of legth, > 0. 1. Set i = 1. 2. While i is ot equal to, do the followig: