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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education

MARK SCHEME for the May/June 2007 question paper

0580 and 0581 MATHEMATICS
0580/04 and 0581/04 Paper 4 (Extended), maximum raw mark 130

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 before marking began. All Examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. Mark schemes must be read in conjunction with the question papers and the report on the examination.



CIE will not enter into discussions or correspondence in connection with these mark schemes.

CIE is publishing the mark schemes for the May/June 2007 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page 2

Mark Scheme IGCSE – May/June 2007 2 400 520 000 1 : 5 000 000 or n = 5 000 000 Time = 2hrs 8 mins or 128 (mins) = 2.13(33..) (hours) oe soi 1580 ÷ their time 738 – 742 cso B2 B2 B2 B1 B1 M1 A1

Syllabus 0580 and 0581 SC1 for figures 24 SC1 for figures 52

Paper 04

1 (a)

(i) (ii)

(b)

(i)

SC1 for 5 000 000 seen in final answer or n = figs 5 oe in final answer

(ii)

Implies previous B1 Accept 128 60 soi is by correct answer www 4 (12.3 seen earns B1M1) [10]

2 (a) (b) (c)

Axes to correct scale Correct triangle A(2,1)B(3,3)C(5,1) A1(1,2), C1(1,5), B1(3,3) ft their ABC

S1 B1 B2

Accept 2mm accuracy throughout Condone absence of labels B1 for 2 correct points Condone absence of labels and sides but not incorrect suffices B1 for 2 correct points Condone absence of labels and sides but not incorrect suffices SC1 for rotation of their A1B1C1 90° clockwise about the origin If triangle ABC is rotated correctly treat as mis-read Indep (Only possible answer)

(d)

A2(–2,1), C2(–5,1), B2(–3,3) ft their A1B1C1

B2

(e)

Reflection y-axis oe cso (i) A3(2, –1), C3(5, –4), B3(3,0)

B1 B1 B3

(f)

B2 for 2 correct points plotted Condone absence of labels and sides If B0, M1 for any set up of matrix multiplication seen for at least one point and A1 for correct result (If correct triangle A2B2C2 used treat as MR, and the co-ords are (–2, 3), (–5, 6), (–3, 6))

(ii)

Shear, y-axis invariant oe

B1,B1 Allow factor of either +1 or –1 if invariant line omitted, but dependent on shear or stretch B2 B1 for the left hand column [15]

(iii)

1  1 

0  1 

© UCLES 2007

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Mark Scheme IGCSE – May/June 2007 0.5×40.3×26.8sin92 oe 539.6 – 540 M1 A1 M1 M1

Syllabus 0580 and 0581

Paper 04

3 (a)

(i)

Any other method must be complete (s = 58.13 – 58.15) ww scores zero + 26.82 M1 − 2 × 40.3 × 26.8 cos 92 (AB = ) square root of above and a correct combination M1 (dep) Accept if found in (i) ww scores zero

(ii)

AB 40.3 = oe sin 92 sin 55 ( AB = ) 40.3 × sin 92 sin 55
49.2 or 49.16 – 49.18

(AB ) = 40.3
2

2

A1

(iii)

55 Angles in the same segment oe 33 correct or ft Similar or enlarged

B1 B1dep B1 B1 M1 A1 ft 88 – their 55, if answer is positive

(iv) (v) (vi)

XD 20.1 = oe 40.3 26.8 30.2(25)

XD 20.1 = sin their (iii ) sin their (iv) 30.2(309…) cao Any other method must be complete ww scores zero May be implied by next line Accept correct ratio statement May be implied by next line Implies previous M2 Dep (no errors in any line) If M0, SC1 for y(2y – 1) – (y + 1)(y + 2) = 2y2 – y – y2 – y – 2y – 2 = y2 – 4y – 2 p + (or −) q r B1for 4 and 2, B1 for 42-4(1)(-2) q If of form p + (or −) r B1 for 42-4(1)(-2) but may recover the other B1 from answers SC1 for rounding or truncating to 1 dp or more – 0.44948…,...
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